Mathematics Paper 1
Grade 12
Senior Certificate Examinations
Past Papers 2016

INSTRUCTIONS AND INFORMATION 
Read the following instructions carefully before answering the questions.

1. This question paper consists of 11 questions.
2. Answer ALL the questions.
3. Number the answers correctly according to the numbering system used in this question paper.
4. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers.
5. Answers only will not necessarily be awarded full marks.
6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise.
7. If necessary, round off answers to TWO decimal places, unless stated otherwise.
8. Diagrams are NOT necessarily drawn to scale.
9. An information sheet with formulae is included at the end of the question paper.
10. Write neatly and legibly. 

QUESTIONS

QUESTION 1 
1.1  Solve for x: 

1.1.1  4x² – 25 = 0 (3)
1.1.2  x² – 5x - 2 = 0 (correct to TWO decimal places)  (3)
1.1.3  (2 - x)(x+4) ≥ 0 (3)
1.1.4   x - 3x^½ =  (5)

1.2  Solve for x and y: 

2x – y +1=0 and  x² – 3x -4- y = y²   (6)

1.3  Given: f(x) = √12x+1 

1.3.1  Write down the domain of f. (1)
1.3.2 Solve for x if f(x)=2x-1. (5)
[26]

QUESTION 2 
2.1  Given the arithmetic series: a + 13 + b + 27 + ... 

2.1.1 Show that a=6 and b = 20 (2)
2.1.2 Calculate the sum of the first 20 terms of the series. (3)
2.1.3 Write the series in QUESTION 2.1.2 in sigma notation. (2)

2.2 Given the geometric series: (x - 2)+(x² – 4)+(x³ + 2x² - 4x - 8) + ... 

2.2.1 Determine the values of x for which the series converges. (4)
2.2.2 If x= -³/₂, calculate the sum to infinity of the given series. (3)
[14]

QUESTION 3 
The first four terms of a quadratic number pattern are -1 ; 2 ; 9 ; 20.
3.1 Determine the general term of the quadratic number pattern. (4)
3.2 Calculate the value of the 48th term of the quadratic number pattern. (2)
3.3 Show that the sum of the first differences of this quadratic number pattern can be given by S_n = 2n² +n (3)
3.4  If the sum of the first 69 first differences in QUESTION 3.3 equals 9 591 (that is, S69 = 9 591), which term of the quadratic number pattern has a value of 9 590? (2)
[11]

QUESTION 4 
The sketch below shows the graphs of f(x) = -x² – 2x+3 and g(x)= mx +q.
Graph f has x-intercepts at A and B(1 ;0) and a turning point at C.
The straight line g, passing through A and C, cuts the y-axis at E.

4.1 Write down the coordinates of the y-intercept of f. (1)
4.2 Show that the coordinates of Care (-1; 4). (3)
4.3 Write down the coordinates of A. (1)
4.4 Calculate the length of CE. (6)
4.5 Determine the value of k if h(x) = 2x +k is a tangent to the graph of f. (5)
4.6 Determine the equation of g^-1, the inverse of g, in the form y= ... (2)
4.7 For which value(s) of x is g(x)≥ g^-1(x)? (3)
[21]

QUESTION 5 

The sketch below shows the graphs of f(x) =      3   + q and g(x) = 2^x +r 
                                                                          x - p

• g intersects the vertical asymptote of f at A. 
• B is the common y-intercept of f and g. 
• y= 2 is the common horizontal asymptote of f and g.
  
  

5.1 Write down the value of r. (1)
5.2 Determine the value of p. (4)
5.3 Determine the coordinates of A. (3)
5.4 For which value(s) of x is f(x) - g(x) ≥ 0? (2)
5.5 If h(x) = f(x-2), write down the equation of h. (2)
[12]

QUESTION 6 

6.1 How long would the price of an asset take to reduce by a third of its original value if it depreciates on a reducing balance at a rate of 4,7% p.a.? (4) 
6.2 Lebogo bought a tractor for Rx on 1 April 2016.

• She will trade in this tractor when she replaces it with a similar one in 5 years time on 1 April 2021.
• The tractor depreciates by 20% p.a. according to the reducing-balance method.
• The price of a similar tractor increases by 18% annually.
• Lebogo calculated that if she deposited R8 000 per month into a sinking fund, which paid interest at 10% p.a. compounded monthly, she would have enough money to cover the replacement cost of the tractor. She made the first deposit in this fund on 30 April 2016 and will continue to do so at the end of every month until 31 March 2021. 

6.2.1 Determine, in terms of x, what the book value of the current tractor will be on 1 April 2021 (that is, 5 years after it was bought). Give your answer correct to FIVE decimal places. (2)
6.2.2 Determine, in terms of x, what the price of a similar new tractor will be on 1 April 2021. Give your answer correct to FIVE decimal places. (2)
6.2.3 Calculate the amount accumulated in the sinking fund on 1 April 2021. (4)
6.2.4 Calculate the value of x, the price of the current tractor. Round off your answer to the nearest thousand. (4)
[16] 

QUESTION 7 
7.1 Determine f′(x) from first principles if f(x) = 3x² - 5 (5)
7.2 Determine ^dy/_dx if:

7.2.1 y=2x⁵ + ⁴/_x³ (3)
7.2.2 y=(√x-x²)² (4)
[12] 

QUESTION 8 

Sketched below are the graphs of f(x) = (x - 2)²(x - k) and g(x) = mx +12 

• A and D are the x-intercepts of f. 
• B is the common y-intercept of f and g. 
• C and D are turning points of f. 
• The straight line g passes through A. 
  

8.1 Write down the y-coordinate of B. (1)
8.2 Calculate the x-coordinate of A.(3)
8.3 If k=-3, calculate the coordinates of C. (6)
8.4 For which values of x will f be concave down? (3)
[13]

QUESTION 9 
A 340 ml can with height h cm and radius r сm is shown below. 

9.1 Determine the height of the can in terms of the radius r. (3)
9.2 Calculate the length of the radius of the can, in cm, if the surface area is to be a minimum. (6)
[9]
QUESTION 10 
10.1 A tournament organiser conducted a survey among 150 members at a local sports club to find out whether they play tennis or not. The results are shown in the table below. 

10.1.1 What is the probability that a member selected at random is: 

(a) Female (2)
(b) Female and plays tennis (1)

10.1.2 Is playing tennis independent of gender? Motivate your answer with the necessary calculations. (3) 

10.2 The probability of events A and B occurring are denoted by P(A) and P(B) respectively. 
For any two events A and B it is given that: 

• P(B') = 0,28 
• P(B) = 3P(A) 
• P(A or B) = 0,96 

Are events A and B mutually exclusive? Justify your answer. (4)
[10]

QUESTION 11 

Five boys and four girls go to the movies. They are all seated next to each other in the same row. 

11.1 One boy and girl are a couple and want to sit next to each other at any end of the row of friends. In how many different ways can the entire group be seated? (3)
11.2 If all the friends are seated randomly, calculate the probability that all the girls are seated next to each other. (3)
[6]

TOTAL: 150 

INFORMATION SHEET

ACCOUNTING
GRADE 12
SENIOR CERTIFICATE EXAM
MEMORANDUM
JUNE 2016

MARKING PRINCIPLES:

1. Penalties for foreign items are applied only if the candidate is not losing marks elsewhere in the question for that item (no foreign item penalty for misplaced item). No double penalty applied.
2. Penalties for placement or poor presentation (e.g. details) are applied only if the candidate is earning marks on the figures for that item.
3. Full marks for correct answer. If the answer is incorrect, mark the workings provided.
4. If a pre-adjustment figure is shown as a final figure, allocate the part-mark for the working for that figure (not the method mark for the answer).
5. Unless otherwise indicated, the positive or negative effect of any figure must be considered to award the mark. If no + or – sign or bracket is provided, assume that the figure is positive.
6. Where indicated, part-marks may be awarded to differentiate between differing qualities of answers from candidates.
7. This memorandum is not for public distribution, as certain items might imply incorrect treatment. The adjustments made are due to nuances in certain questions.
8. Where penalties are applied, the marks for that section of the question cannot be a final negative.
9. Where method marks are awarded for operation, the marker must inspect the reasonableness of the answer before awarding the mark.
10. In awarding method marks, ensure that candidates do not get full marks for any item that is incorrect at least in part.
11. Be aware that some candidates provide valid alternatives beyond the memorandum.
12. Codes: f = foreign item; p = placement/presentation.

MEMORANDUM

QUESTION 1
VALUE ADDED TAX
1.1                                             (3) 

1.2.1                                        (12)

1.2.2                                                                                                                                    [2]

1.3 CREDOTIR'S RECONCILIATION
1.3.1                                [14]

foreign items -1 per line if candidate earned a mark on that line

1.3.2                                                                 [4]

QUESTION 2
2.1 ABE ACCESSORIES
2.1.1                                               [15]

 Foreign items: -1 max -2
2.1.2                                     [8]

 
2.2 NEW FASHION MANUFACTURERS
2.2.1                  [5], [3]

2.2.2            [4]

2.2.3            [4], [4]

2.2.4            [3], [4]

QUESTION 3
3.1   CONCEPTS         [4]

3.2.1     [8]

3.2.2     [6]

3.2.3            [5]

3.2.4           [7]

3.3.1      [6]

3.3.2             [4]

QUESTION 4
4.1   CONCEPTS       [4]

4.2   PARADISE LIMITED
4.2.1 Ordinary Share  Capital            [6]    Presentation or incorrect / incomplete details -1 max -2

RETAINED INCOME                   [10]         Presentation or incorrect / incomplete details -1 max -2

4.2.2   BALANCE SHEET (STATEMENT OF FINANCIAL POSITION) ON 29 FEBRUARY 2016           [35] 

Foreign entries -1 max -2
Presentation/incorrect or incomplete details -1 max -2
All current liabilities may be shown as trade and other payables

4.3 AUDIT REPORT
4.3.1   [3]

4.3.2   [3]

4.3.3   [2] , [2]

QUESTION 5
5.1 CONCEPTS      [4]

5.2 MAFUSA LTD
5.2.1          [16]

5.2.2          [5]  , [4]

5.2.3          [7]

-1 per line for incorrect use of brackets
Presentation or incorrect / incomplete details -1 max -2
5.2.4          [5]  , [3]

5.2.5          [8]

5.2.6          [4]  , [4] 

5.2.7          [6]

5.2.8          [2]   , [2]

  
QUESTION 6
6.1                          [12]

6.2.1                          [4]

  
6.2.2                          [4]

  
6.2.3                          [4]

  
6.3                          [4]  

6.4                          [4]  

6.5                          [6]  , [2]      

                                                                                                                                                                                                                      TOTAL:300

Accounting Paper
Grade 12
Amended Senior Certificate Exam
Past Papers And Memos-2016

INSTRUCTIONS AND INFORMATION
Read the following instructions carefully and follow them precisely.

1. Answer ALL the questions.
2. Show ALL workings to achieve part-marks.
3. You may use a non-programmable calculator.
4. You may use a dark pencil or blue/black ink to answer the questions.
5. Where applicable, show ALL calculations to ONE decimal point.
6. Write neatly and legibly.
7. Use the information in the table below as a guide when answering the question paper. Try NOT to deviate from it.
   

   QUESTION 1: 35 marks; 20 minutes
   Topic of the question:	This question integrates:
   VAT and Reconciliations	Financial accounting VAT calculations Reconcile a Creditors' Ledger Account to a statement of account Managing resources Internal control and internal audit

   
   

   QUESTION 2: 50 marks; 30 minutes
   Topic of the question:	This question integrates:
   Manufacturing	Managerial accounting                                                     Production Cost Statement Analyse and interpret break-even point Managing resources Internal control and internal audit

   
   

   QUESTION 3: 40 marks; 25 minutes
   Topic of the question:	This question integrates:
   Inventory Valuation, Internal Control and Problem-solving	Managing resources Inventory valuation: FIFO and weighted-average method Internal control and internal audit

   
   

   QUESTION 4: 65 marks; 40 minutes
   Topic of the question:	This question integrates:
   Concepts, Balance Sheet and Audit Report	Financial accounting Concepts Prepare Balance Sheet                                                     Ordinary share capital and retained income notes

   
   

   QUESTION 5: 70 marks; 40 minutes
   Topic of the question:	This question integrates:
   Fixed Assets, Cash Flow Statement and Analysis and Interpretation of                        Financial Statements	Financial accounting Cash Flow Statement                                          Analyse and interpret financial information Managing resources                                                     Fixed asset management

   
   

   QUESTION 6: 40 marks; 25 minutes
   Topic of the question:	This question integrates:
   Budgeting	Managerial accounting Analyse and interpret a Projected Income Statement   Managing resources Internal control

   
   
   

QUESTIONS

QUESTION 1: VAT AND RECONCILIATIONS
VALUE-ADDED TAX                                                                                                                            (35 marks, 20 minutes)
1.1 Indicate whether the following statements are TRUE or FALSE. Write only 'true' or 'false' next to the question number (1.1.1–1.1.3) in the ANSWER BOOK.

1.1.1 VAT paid by a business on goods purchased is called VAT input.
1.1.2 It is compulsory for all businesses to register for VAT.
1.1.3 VAT returns to SARS are submitted after every six months of trading activities.
                                                                                                                                                        (3 x 1)                (3)

1.2 You are provided with information relating to Super Stores for the VAT period ended 29 February 2016 (two months). The standard VAT rate is 14%.
REQUIRED:

1.2.1 Taking into account the errors and omissions, calculate the VAT amount that is either payable to or receivable from SARS.(12)
1.2.2 The internal auditor discovered that the owner, Nelson, used the VAT collected from customers to pay salaries and bonuses; therefore, he could not meet the VAT deadline.
What comment would you offer Nelson concerning this practice? State ONE point.                           (2)

INFORMATION:

1. Amount due to SARS on 1 February 2016, R44 800.
2. Amounts from the journals on 29 February 2016:
   

   	INCLUDING VAT	VAT AMOUNT
   Sales	564 300	69 300
   Credit purchases of stock	191 520	23 520
   Stock returned by debtors	52 440	6 440
   Bad debts written off	39 900	4 900

3. The following errors and omissions were noted:•
   • Stock taken by the owner, cost price R6 000 (excluding VAT), has not been recorded.
   • VAT on sales was recorded incorrectly. Certain goods with a selling price of R50 000 (excluding VAT) should have been recorded as zero-rated items.
   • VAT on discounts granted to debtors was not recorded. The total discounts allowed amounted to R19 152.

 1.3 CREDITORS' RECONCILIATION
Thanda Stores buys goods on credit from Minty Suppliers.
REQUIRED:
1.3.1 Use the table provided to indicate the changes that must be made:

• In the Creditors' Ledger Account in the books of Thanda Stores
• In the Creditors' Reconciliation Statement on 29 February 2016                                                                       (14)

1.3.2 An investigation into the transaction on 2 February 2016 for Invoice 560 revealed that Pearl Fakude (purchasing manager) ordered goods for herself. These goods were not taken into stock.
State TWO internal control measures that the business can use to prevent similar incidents from happening in future.(4)

INFORMATION:

1. Creditors' Ledger of Thanda Stores
   Minty Suppliers
   

   DATE		DETAILS	FOL.	DEBIT	CREDIT	BALANCE
   Feb.	01	Balance	b/d			52 200
   	02	Invoice 560	CJ		44 200	96 400
   	04	Debit Note  52	CAJ	2 700		93 700
   	07	Cheque 443	CPJ	31 350		62 350
   		Discount received	CPJ	3 300		59 050
   	20	Invoice 996	CJ		11 100	70 150
   	23	Cheque 575	CPJ	13 200		56 950
   	24	Invoice 590	CJ		24 000	80 950
   	28	Cheque 580	CPJ	13 800		67 150
   		Discount received	CPJ	1 380		65 770
   	29	Invoice 592	CJ		44 400	110 170

2. Statement of account received from Minty Suppliers
   

   MINTY SUPPLIERS                     No. 2169 205 Kingsview Road Durban 3201
   Debtor: Thanda Stores                           25 February 2016
   DATE		DETAILS	DEBIT	CREDIT	BALANCE
   Jan.	25	Balance			67 200
   	28	Receipt 110		15 000	52 200
   Feb.	02	Invoice 560	49 200		101 400
   	04	Credit Note 09	2 700		104 100
   	07	Receipt 122		31 350	72 750
   		Discount allowed		1 650	71 100
   	18	Invoice 571	28 800		99 900
   	23	Receipt 138		13 200	86 700
   	24	Invoice 590	21 600		108 300
   	25	Delivery charges	3 300		111 600

3. An investigation revealed the following errors and omissions:
   1. Invoice 996 was for goods that Thanda Stores bought from another supplier, Mondi Suppliers.
   2. Invoice 560 was recorded correctly on the statement of account.
   3. Invoice 571 was an error on the statement. This was for goods supplied to another business.
   4. The discount allowed on 7 February 2016 is correct as per the statement of account.
   5. Thanda Stores omitted to deduct the trade discount allowed on Invoice 590.
   6. Goods for R2 700 were returned by Thanda Stores to Minty Suppliers on 4 February 2016.
   7. In terms of the contract Minty Suppliers charges a delivery fee to all its customers.
   8. The statement of account only includes transactions up to 25 February 2016.
                                                                                                                                                        (35)

QUESTION 2: MANUFACTURING                                                                                   (50 marks; 30 minutes)
2.1  ABE ACCESSORIES
Abe Accessories manufactures cellphone covers. The information below is in respect of the financial year ended 29 February 2016.

REQUIRED:

2.1.1 Prepare the Factory Overhead Cost Note. Show ALL calculations in brackets.                             (15)
2.1.2 Prepare the Production Cost Statement for the year ended 29 February 2016.                              (8)

INFORMATION:

1. Stock balances:
   

   	29 FEBRUARY 2016	1 MARCH 2015
   Work-in-process stock	R9 320	R30 640

2. Transactions for the year ended 29 February 2016:
   

   Consumable stores used in the factory	R129 300
   Salaries and wages:
   Production wages	?
   Other factory workers	R97 500
   Administration	R250 000
   Sales department	R130 000
   Sundry expenses:
   Factory	R31 500
   Offices	R28 000
   Water and electricity	R50 000
   Insurance	R24 000

3. Additional information and adjustments
   • The factory cleaner was omitted from the salaries and wages list for February 2016. Her details are as follows:
     
     

     Gross salary	Deductions	Net salary	Employer's Contribution
     R3 800	R420	R3 380	R380

     The employer's contribution is added to the salaries and wages.
   • An amount of R4 000 is still outstanding for water and electricity for February 2016. The factory uses 60% of the water and electricity.
   • Insurance has been paid from 1 March 2015 to 30 June 2016. This expense must be allocated to the factory, administration and sales departments in the ratio 3 : 2 : 1 respectively.
4. The business manufactured 10 500 cellphone covers at a cost of R82,40 per unit.

2.2NEW FASHION MANUFACTURERS
This business is owned by Gloria Smit. She makes and sells dresses. The financial year ends on 29 February 2016.

REQUIRED:

2.2.1           

• Gloria is concerned about the wastage of direct materials. Calculate the number of metres of fabric that was wasted.(5)
• Gloria feels that the wastage is significant. Give a calculation to support her opinion.(3)

2.2.2 Give TWO possible reasons for this wastage and, in EACH case, give advice to prevent this from happening in future.(4)
2.2.3 Break-even point and production:

• Calculate the break-even point for the year ended 29 February 2016.(4)
• Explain why the business should be satisfied with the number of units made during the current financial year. State TWO points.(4)

2.2.4 The direct material used to make the dresses is purchased locally at a cost of R150 per metre. Gloria is considering importing the fabric, as it will cost R120 per metre (all costs included). If she decides to import the fabric:

• What effect will it have on the production cost of a dress? Provide a calculation to support your answer.(3)
• State TWO other consequences of importing the direct material.(4)

INFORMATION:

1. Direct materials:
   2,5 metres of fabric is used for each dress.
   

   	Number of metres of fabric
   Opening stock	525
   Purchases	12 450
   Raw materials issued to factory	?
   Closing stock	1 475

2. Production levels:
   

   	2016	2015
   Total number of units produced and sold	4 500	3 800
   Break-even point	?	3 200

3. Additional information:
   

   	Total	Per unit
   Sales	R2 925 000	R650
   Fixed cost	R900 000	R200
   Variable cost	R1 575 000	R350

                                                                                                                   [50]

QUESTION 3: INVENTORY VALUATION, INTERNAL CONTROL ANDPROBLEM-SOLVING     (40 marks; 25 minutes)

3.1 CONCEPTS
Give ONE word/term for each of the following descriptions by choosing a word/term from the list below. Write only the word/term next to the question number (3.1.1–3.1.4) in the ANSWER BOOK.

3.1.1This method assumes that stock is sold in order of date purchased.
3.1.2This system ensures that cost of sales is calculated at the point of sale.
3.1.3This method of stock valuation assigns a unique or individual value to each stock item.
3.1.4This stock system is more suited for low-value goods that are purchased in bulk. 
                                                                                                                                                         (4 x 1)             (4)

3.2LYNN STORES
You are provided with information relating to Lynn Stores. The business sells one type of leather shoes. The financial year ends on 29 February 2016. The business uses the weighted-average method for stock valuation and the periodic stock system.
REQUIRED:

3.2.1Calculate the value of the closing stock on 29 February 2016 using the weighted-average method.(8)
3.2.2Calculate the following for the year ended 29 February 2016:

• • Cost of sales
  • Gross profit                                                                              (6)

3.2.3Calculate the average stock-holding period (in days) on 29 February 2016.(5)
3.2.4Calculate the value of the closing stock by using the FIFO method.(7)

INFORMATION:

1. Stock:
   

   Date	Pairs of shoes	Total value(including carriage)
   1 March 2015	520	R320 770
   29 February 2016	325	?

2. Purchases:
   

   Date	Pairs of shoes	Cost price per pair	Total purchases	Carriage per pair	Total cost (including carriage)
   31/05/2015	460	R650	R299 000	R18	R307 280
   01/08/2015	700	R680	R476 000	R18	R488 600
   15/10/2015	500	R710	R355 000	R30	R370 000
   01/02/2016	300	R725	R217 500	R30	R226 500
   TOTAL	1 960		R1 347 500		R1 392 380

3. Returns:
   Thirty pairs of shoes from the purchases on 1 February 2016 were not of a high quality. These were returned to the supplier. The business account was credited with R22 650 (including carriage on purchases).
4. Sales:
   2 115 pairs of leather shoes were sold during the financial year. The selling price was kept constant at R1 400 per pair.

3.3 PROBLEM-SOLVING
You are provided with information of three jeans shops with different owners in Johannesburg. Each shop has a floor space of 100 m2.
REQUIRED:

3.3.1Identify ONE problem in Shop 1 and ONE problem in Shop 2. Quote figures. In EACH case, give ONE point of advice.(6)
3.3.2Explain TWO good decisions that Chad has made in respect of Shop 3.
Quote figures.(4)
Information per shop for December 2015:

                                                                                                                                               [40]

QUESTION 4: CONCEPTS, BALANCE SHEET AND AUDIT REPORT
                                                                                                               (65 marks; 40 minutes)
4.1CONCEPTS
Choose an explanation from COLUMN B that matches a concept in COLUMN A. Write only the letter (A–D) next to the question number (4.1.1–4.1.4) in the ANSWER BOOK.

                                                                                                                                          (4 x 1)         (4)
4.2 PARADISE LIMITED
The information below relates to Paradise Ltd. The financial year ended on 29 February 2016.

REQUIRED:
4.2.1 Prepare the following notes for the year ended 29 February 2016:

• Ordinary share capital(6)
• Retained income(10)

4.2.2 Prepare the Balance Sheet (Statement of Financial Position) on 29 February 2016. Show ALL workings.(35)

INFORMATION:

1. List of balances extracted from the accounting records of Paradise Ltd on 29 February 2016, the end of the financial year, unless otherwise stated.
   

   	R
   Ordinary share capital (See Information B.)	?
   Retained income (1 March 2015)	1 634 000
   Loan from director: J Jonas (See Information E.)	1 155 000
   Fixed assets at carrying value (1 March 2015)	12 278 400
   Fixed deposit: Sandton Bank	?
   Trading stock (balancing figure)	?
   Creditors' control	478 000
   Debtors' control	356 000
   Provision for bad debts (1 March 2015)	16 000
   Bank (favourable)	?
   Accrued expenses (expenses payable)	12 000
   Prepaid expenses	6 800
   SARS: Income tax (provisional tax payments)	1 012 000

2. Share capital:
   • Paradise Ltd is authorised to sell 5 000 000 ordinary shares.
   • 3 000 000 shares were in issue on 1 March 2015, the beginning of the financial year, R6 000 000.
   • 1 000 000 new shares were issued on 1 December 2015 at a market-related value of R5,00 per share.
   • 200 000 shares were repurchased on 20 February 2016 from a shareholder who was relocating to another country. A payment of R770 000 was made on 20 February 2016.
3. Dividends:
   • The directors paid an interim dividend of R840 000 on 28 August 2015.
   • A final dividend of 44 cents per share was declared on 29 February 2016. All shares (including the shares repurchased on 20 February 2016) qualify for final dividends. These dividends will be paid on 31 March 2016.
4. Net profit before tax:
   • After taking into account all relevant information, the net profit before tax was accurately calculated to be R3 800 000.
   • Income tax at the rate of 28% must still be brought into account.
5. Loan from Director J Jonas:
   • The loan was originally received on 1 December 2013.
   • This loan is to be repaid over 5 years in equal monthly instalments with effect from 31 December 2013. All payments have been made.
   • Interest is not capitalised and has been paid in full.
6. Provision for bad debts:
   The provision for bad debts must be maintained at 5% of the outstanding debtors.
7. Fixed assets and depreciation:
   • No fixed assets were purchased or sold during the financial year.
   • Depreciation for the financial year ended 29 February 2016 was R890 000.
8. The following financial indicators were calculated after all adjustments had been taken into account:
   

   Current ratio	1,3 : 1
   Acid-test ratio	0,8 : 1

4.3 AUDIT REPORT
You are provided with an extract of the independent auditor's report of Topstar Ltd for the financial year ended 31 October 2015.

REQUIRED:

4.3.1 What type of audit report did Topstar Ltd receive? Choose from the following: unqualified, qualified, disclaimer. Give a reason for your choice.(3)
4.3.2 To whom is an audit report addressed? Give a reason for your answer.(3)
4.3.3 Explain why the auditor mentioned the following in the audit report:

• • IFRS(2)
  • Companies Act (Act 61 of 1973)(2)

INFORMATION:
Extract from the audit report:

                                                                                                                                                                                                                               [65]
QUESTION 5: FIXED ASSETS, CASH FLOW STATEMENT, ANALYSIS ANDINTERPRETATION OF FINANCIAL STATEMENTS
                                                                                                                                                                      (70 marks; 40 minutes)
5.1CONCEPTS
Choose the correct word(s) from those given in brackets. Write only the word(s) next to the question number (5.1.1–5.1.4) in the ANSWER BOOK.

5.1.1 The mortgage bond to finance the purchase of a fixed asset is a (financial asset/non-current liability).
5.1.2 Distributable reserves, such as retained income, are part of (shareholders' equity/non-current assets).
5.1.3 The amount due by SARS in respect of income tax is a (current asset/current liability).
5.1.4 An investment, such as a fixed deposit at 9% p.a. interest over five years, will be shown as a (current asset/financial asset).
                                                                                                                                                                                       (4 x 1)       (4)

5.2 MAFUSA LTD
The information presented relates to the financial year ended 30 April 2016.
NOTE:  When financial indicators are required to support answers, you have to give the name of the financial indicator and the actual figure, ratio or percentage.
REQUIRED:

5.2.1 Refer to Information C.Calculate the missing amounts denoted by (a) to (d) for equipment in the Fixed Asset Note. Show all workings.(16)
5.2.2 Calculate the following amounts for the Cash Flow Statement. Show ALL workings

• • Income tax paid(5)
  • Net changes in cash and cash equivalents(4)

5.2.3 Complete the section on FINANCING ACTIVITIES in the Cash Flow Statement.(7)
5.2.4 Calculate the following financial indicators on 30 April 2016:

• • Return on average shareholders' equity(5)
  • Net asset value(3)

5.2.5 Comment on the overall liquidity position of the company. Quote THREE relevant financial indicators (with figures).(8)
5.2.6 The directors decided to change the dividend pay-out policy in 2016.

• • Provide calculations that indicate the policy change.(4)
  • Explain the effect of this change of policy on the company. State TWO points.(4)

5.2.7 One of the directors feels that the company should pay back the loan as soon as possible. What are your views about this? Quote and explain TWO relevant financial indicators with figures.(6)
5.2.8 Explain why the shareholders are satisfied with:

• • The market price of the shares on the JSE(2)
  • The price at which the 75 000 shares were repurchased on 25 April 2016(2)
    In EACH case, quote figures/financial indicators.

INFORMATION:

1. Information extracted from the Income Statement on 30 April 2016:
   

   	R
   Operating profit	1 590 000
   Interest expense	300 000
   Net profit before income tax	1 279 000
   Net profit after income tax	895 300

2. Information extracted from the Balance Sheet on 30 April 2016:
   

   	2016(R)	2015(R)
   Fixed deposit	200 000	520 000
   Current assets(including cash and cash equivalents)	946 550	887 250
   Cash and cash equivalents	125 750	54 750
   Shareholders' equity	7 166 850	6 142 800
   Ordinary share capital	6 660 000	5 600 000
   Retained income	506 850	542 800
   Non-current liabilities	1 800 000	2 750 000
   Current liabilities	526 750	509 500
   Trade and other payables	285 600	232 800
   Bank overdraft	0	92 000
   Shareholders for dividends	231 250	176 000
   SARS: Income tax	9 900	8 700

3. Fixed assets:
   Fixed assets comprise land and buildings and equipment.
   Extract from the Fixed Asset Note:
   

   	EQUIPMENT
   Cost (1 May 2015)	3 640 000
   Accumulated depreciation (1 May 2015)	(a)
   Carrying value (1 May 2015)	2 002 000
   Movements:
   Additions	900 000
   Disposals	(b)
   Depreciation	(c)
   Carrying value (30 April 2016)
   Cost (30 April 2016)	(d)
   Accumulated depreciation (30 April 2016)

   
   
   • Equipment is depreciated at 15% p.a. on cost.
   • On 31 August 2015 old equipment costing R750 000 was sold for cash at its carrying value. The accumulated depreciation on this equipment was R491 750 on 1 May 2015.
   • On 1 December 2015 new equipment valued at R900 000 was purchased.
   • There were no other movements.
     
     
4. Share capital and dividends:
   The business is registered with an authorised share capital of 1 200 000 ordinary shares.
   

   1 May 2015	The issued share capital consisted of 800 000 ordinary shares.
   1 February 2016	200 000 ordinary shares were issued at R8,00 per share.
   25 April 2016	75 000 ordinary shares were repurchased from a retired shareholder at a total cost of R600 000.
   30 April 2016	There were 925 000 shares in issue.Total dividends for the financial year amounted to R871 250.

5. The following financial indicators were calculated on 30 April:
   

   	2016	2015
   Current ratio	1,8 : 1	1,7 : 1
   Acid-test ratio	0,9 : 1	1,3 : 1
   Stock-holding period	52 days	68 days
   Debtors' collection period	47 days	30 days
   Creditors' payment period	30 days	30 days
   Debt-equity ratio	0,3 : 1	0,4 : 1
   Return on capital employed	11%	13%
   Return on shareholder's equity	?	14,5%
   Earnings per share	107 cents	112 cents
   Dividends per share	105 cents	40 cents
   Net asset value per share	?	768 cents
   Market price per share (JSE)	960 cents	777 cents
   Repurchase price per share	800 cents	-
   Interest rate of loan	14%	13%

                                                                                                      [70]

QUESTION 6: BUDGETING
                                                                                                                                                                (40 marks; 25 minutes)
You are provided with a partially completed Projected Income Statement of Senoge Stores prepared by the bookkeeper for the period 1 May 2016 to 30 June 2016. The business is owned by Susan Senoge.
REQUIRED:
6.1 Calculate the missing amounts denoted by (a) to (d) in the Projected Income Statement.(12)
6.2 Taking into account the additional information, calculate the following:

6.2.1 The monthly salary due to the sales manager in June 2016(4)
6.2.2 The total credit sales expected in July 2016(4)
6.2.3 The cost price of the new vehicle purchased on 1 May 2016(4)

6.3 Comment on the control of the telephone and water and electricity. What advice would you offer Susan? State ONE point.(4)
6.4 Susan wants to reduce the maintenance budget to R500 per month and then use this saving for staff training. What should she consider before making this change? State TWO points.(4)
6.5 A new competitor started operating from nearby premises in May 2016. Refer to the actual figures for May 2016 and:

• Explain how Susan responded to this threat. State THREE points. Provide figures/calculations to support your answer.(6)
• Explain whether Susan's response was successful or not. Provide figures.(2)

INFORMATION:

1. Salaries and wages:
   • The cleaner will receive an 8% increase in June 2016.
   • The business employs a sales manager and an administration manager. The sales manager earns R400 more than the administration manager (per month). The managers are entitled to an increase of 7% p.a. from 1 June 2016.
2. The business uses a mark-up percentage of 60% on cost.
3. Credit sales comprise 80% of total sales. Sales are expected to increase by 10% per month and by 12% during July 2016.
4. A delivery vehicle was purchased on 1 May 2016. Vehicles are depreciated at 15% per annum on cost. The accountant did not take this into account when preparing the Projected Income Statement for May 2016.
5. Rent income increased by 9% on 1 June 2016.
6. Information (amongst others) from the Projected Income Statement for May 2016 to June 2016:
   

   	MAY BUDGETED	MAY ACTUAL	JUNE BUDGETED
   Sales	180 000	195 000	198 000
   Cost of sales	(112 500)	(150 000)	(b)
   Gross profit	67 500
   Other income		19 200
   Rent income	(d)		10 028
   Commission income	12 500	8 000	13 000
   Discount received	1 800		1 980
   Gross operating income
   Operating expenses	(45 650)
   Salaries (two managers)	18 000	18 000
   Wages (cleaner)	1 800	1 800	(c)
   Maintenance	5 000	2 000	5 000
   Motor vehicle expenses	0	4 000	0
   Administration expenses	8 450	8 420	8 500
   Telephone, water and electricity	2 000	4 880	2 000
   Insurance	1 800	1 800	1 800
   Advertising	2 400	9 600	2 400
   Depreciation	6 200	9 000
   Trading stock deficit	0	1 680
   Operating profit	(a)
   Interest income	350	350	350
   Profit before interest expense	46 500
   Interest expense	(500)	(500)	(500)
   Net profit	46 000

                                                                                                                                                 [40]
                                                                                                                                   TOTAL:300

Physical Sciences P1
Grade 12
June 2016
NSC Past Papers And Memos

INSTRUCTIONS AND INFORMATION

1. This paper consists of EIGHT questions. Answer ALL the questions
2. Number the answers correctly according to the numbering system used in this question paper.
3. Leave one line between two sub-questions, for example between QUESTION2.1 and QUESTION 2.2.
4. You may use a non-programmable calculator.
5. You may use appropriate mathematical instruments
6. Show ALL formulae and substitutions in ALL calculations.
7. Round off your final numerical answers to a minimum of TWO decimal placeswhere necessary.
8. Give brief motivations, discussions, et cetera where required
9. Write neatly and legibly.

QUESTIONS

QUESTION 1: MULTIPLE-CHOICE QUESTIONS
Four options are provided as possible answers to the following questions. Each question has only ONE correct answer. Choose the answer and write only the letter(A - D) next to the question number (1.1 - 1.10)..
1.1 Which one of the following represents a scalar quantity?

1. Work of -10 J
2. An acceleration of 10 m·s^-2
3. A force with a magnitude of 10 N
4. Velocity with a magnitude of 10 m·s^-1                                                                                                            (2)

1.2 An object X, mass m, is moving at constant velocity v along a smooth,horizontal surface. An identical object Y is dropped onto object X and stays there. Which one of the following represents the velocity of the combination X + Y?

1. Zero
2. ½v
3. v
4. 2v                                                                                                                                                                    (2)

1.3 A rock is dropped from a tall building. Which one of the following combinations correctly describes the acceleration and velocity of the rock while it is falling? Ignore the effect of air resistance.

                                                                                                                                                                                   (2)
1.4 Three separate, identical blocks are in contact with each other in a straight line. They are at rest on a smooth, horizontal surface. Each of these blocks has a mass m. Another block with the same dimensions, but with mass 2m,moving at a velocity v, collides ELASTICALLY and in the same straight line with the three stationary blocks.

Which one of the following diagrams represents the situation immediately after the collision?



                                                                                  (2) 
1.5 A girl is standing on the surface of the earth and drops a ball. After the first second of its motion it has a displacement y. A similar experiment is done on the surface of the moon. What would the displacement during the first second be if the gravitational acceleration on the moon is ¹/₆ of that of the earth?
Ignore the effects of friction.

1. ¹/₆y
2. ¹/₃y
3. ³/₅y
4. ⁵/₆y                                                                                                                                                               (2)

1.6 A car, moving at a constant velocity with kinetic energy K, undergoes a displacement x in time t. If the car's kinetic energy changes to 2K, it will undergo a displacement of .......in the same time at the new constant velocity.

1. 4x
2. 2x
3. √2 x
4. ¹/_√2 x                                                                                                                                                              (2)

1.7 In the circuit represented below, the internal resistance of the battery is negligible.

Which one of the following combinations correctly represents the changes in the reading on the voltmeter and the ammeter when a copper wire is used to connect the two black dots? (2)

1.8 Two blocks, P and Q, manufactured from the SAME MATERIAL (coefficient of  kinetic friction is μ in both cases) and with masses of 2m and m respectively,are placed on the hypotenuse of a triangular wooden block as shown below.The distance between the blocks is x. The heavier block (P) is above Q. When they are released SIMULTANEOUSLY, they move down the inclined plane at increasing velocity.

How is the distance x affected while the two blocks move?

1. Increases.
2. Decreases.
3. Remains the same.
4. It is not possible to tell from the available information.                                                                                    (2)

1.9 A ball is dropped from rest. Ignore air friction. Which one of the following graphs best represents the relationship between:
each of kinetic energy (K),gravitational potential energy (U) and mechanical energy (M) as functions of the displacement of the ball?   (2)

1.10 Three electric charges, each with magnitude Q, are kept stationary in thesame plane at three corners (X, Y and Z) of a rectangle. The long and short sides of the rectangle have lengths of 2r and r respectively.

The NET ELECTROSTATIC force on the charge at Z, due to the other TWO charges, is equal to F.
The charge at Y is then MOVED and placed at P, and the charge at X is REPLACED by another negative charge with a different magnitude. What should the magnitude of the NEW charge at X be to keep the MAGNITUDE ofthe NET ELECTROSTATIC force on the charge at Z the same as before?

1. 4Q
2. 2Q
3. Q
4. Q                                                                                                                                                                  (2)
                                                                                                                                                                       [20]

QUESTION 2
A block of mass 4 kg is connected to another block of mass 2 kg by a light,inextensible string. The system is pulled up a rough plane, inclined at 30° to the horizontal, by means of a constant force of 73,8 N parallel to the plane, as shown inthe diagram below.

The magnitude of the kinetic frictional force on the 4 kg block is 20 N. The coefficientof kinetic friction applicable to the 2 kg block is 0,589.
2.1 Define the concept frictional force.                                                                                                                (2)
2.2 State Newton's second law of motion in words.                                                                                            (3)
2.3 Draw a free-body diagram, with labels, showing ALL the forces acting on the 4 kg block as it moves up the incline. Please be mindful of the following:

• You may not include components of forces in your diagram.
• You may not use numbers as labels.                                                                                                      (5)

2.4 Calculate the magnitude of the kinetic frictional force on the 2 kg block.                                                    (4)
2.5 Calculate the tension in the string that connects the two blocks.                                                                (6)
2.6 The system is pulled up the rough incline once more, but this time the twoblocks are swapped as indicated below. How will this influence each of thefollowing? Choose your answer from DECREASES, REMAINS THE SAMEor INCREASES.

2.6.1 The acceleration of the 2 kg block                                                                                                   (2)
2.6.2 The force of friction on the 4 kg block                                                                                              (2)
2.6.3 The tension in the string                                                                                                                  (2)
                                                                                                                                                                 [26]

QUESTION 3
A stationary rocket on the ground is launched vertically upwards. After 4 s, the rocket's fuel is used up when it is 225,6 m above the ground (Point R). At this instant the velocity of the rocket is 112,8 m·s^-1. The rocket reaches its MAXIMUM heightABOVE ground at point S. Ignore the effects of air friction. Assume that g does not change during the entire motion of the rocket.

3.1 Draw a free-body diagram, with labels, of the forces acting on the rocket at point P. The lengths of your arrows should represent the comparative magnitudes of the forces.                                                                                                                                    (3)
3.2 What is the direction of the acceleration of the rocket at:

3.2.1 point P; and                                                                                                                                        (1)
3.2.2 point Q?                                                                                                                                              (1)

3.3 At which point (P or Q) is the rocket in free fall? Give a reason for theanswer.                                             (2)
3.4 Take UPWARD MOTION as POSITIVE and use ONLY EQUATIONS OF MOTION to calculate the following:

3.4.1 The magnitude of the acceleration of the rocket between theground and point R                             (3)
3.4.2 The time it takes from the moment the rocket is launched until itstrikes the ground again                (6)

3.5 Take UPWARD AS POSITIVE and sketch a velocity-time graph for the motionof the rocket from the moment it is launched (at t = 0 s) until it strikes theground.
Indicate the following values on the graph:

• Velocity of the rocket on the ground
• Velocity of the rocket at each of points R and S
• Time at point R; and
• Time at which the rocket strikes the ground.                                                                                           (6)
                                                                                                                                                                 [22]

QUESTION 4
Percy, mass 75 kg, rides at 20 m.s^-1 on a quad bike (motorcycle with four wheels) with a mass of 100 kg. He suddenly applies the brakes when he approaches a red traffic light on a wet and slippery road. The wheels of the quad bike lock and the bike slides forward in a straight line. The force of friction causes the bike to stop in 8 s.
4.1 Define the concept momentum in words.                                                                                      (2)
4.2 Calculate the change in momentum of Percy and the bike, from themoment the brakes lock until the bike comes to a stop. (4)
4.3 Calculate the average frictional force exerted by the road on the wheels tostop the bike.           (4)
4.4 Write down the work-energy theorem in words.                                                                            (2)
4.5 Calculate the work done by the frictional force to stop the bike.                                                   (3)
                                                                                                                                                            [15]

QUESTION 5
A block of wood, mass 1,595 kg, is placed on the edge of a table 1,5 m above thefloor.The block is struck by a bullet, mass 0,005 kg, moving at an UNKNOWN horizontal velocity. After the impact, the bullet is embedded in the block, which falls tothe floor. The block strikes the floor with a speed of 5,6 m.s^-1. Ignore all types of friction.

5.1 State the principle of conservation of mechanical energy in words.                                         (2)
5.2 Use the principle of conservation of mechanical energy to calculate themagnitude of the velocity with which the block leaves the table. (5)
5.3 State the principle of conservation of momentum in words.                                                     (2)
5.4 Calculate the magnitude of the velocity with which the bullet strikes theblock.                        (4)
                                                                                                                                                        [13]

QUESTION 6
The speed of sound in air depends among others on the air temperature. The following graph shows this relationship.

6.1 Which one of temperature or speed is the dependent variable?                                                (1)
6.2 The gradient of this graph is equal to 0,6 m·s-1·K-1. With how much does the speed, in m·s^-1, increase for every 5 K increase in temperature? (1)
6.3 Two experiments are done to verify the Doppler Effect. In the first experiment, an object approaches a stationary observer X at a constant speedof 57,5 m·s-¹. The object is equipped with a siren that emits sound waves at afixed frequency of 1 000 Hz. The motion takes place in still air at a temperature of 295 K.

6.3.1 Describe what the Doppler Effect is.                                                                               (2)
6.3.2 What is the speed of sound, in m·s^-1, in air at 295 K?HINT: Use the graph                   (1)
6.3.3 Calculate the frequency measured by observer X.                                                         (4)
6.3.4 In the second experiment, the object moves away from observer X at the same constant speed as before. What should the air temperature, in kelvin, be to make it a fair test between the two experiments?  (1)

6.4 Consider the three diagrams below. Each one represents the source (with the siren) and observer X. Two of the diagrams are applicable on the above mentioned experiments.

6.4.1 Which diagram is applicable to experiment 2?                                                            (1)
6.4.2 Which diagram is NOT applicable to any of the experiments?Give a reason for your answer. (2)
                                                                                                                                             [13]

QUESTION 7
7.1 A small metal sphere X, on an insulated stand, carries a charge +2 nC.nC.

7.1.1 What is an electric field?                                                                                               (2)
7.1.2 Draw the electric field pattern associated with X.                                                         (2)
7.1.3 Calculate the magnitude of the electric field at any point 1 m from the centre of X.     (3)

7.2 An identical sphere Y, which carries a charge of -7nC, is used to touch X.The two spheres are afterwards placed 2 m apart as shown below.

7.2.1 In which direction did the electrons flow while X and Y were incontact? Write down X TO Y or Y TO X. (1)
7.2.2 Calculate the charge on X after the separation.                                                         (3)
7.2.3 State Coulomb's law in words.                                                                                   (3)
7.2.4 Calculate the electrostatic force that is exerted on X due to the presence of Y.        (5)
                                                                                                                                            [19]

QUESTION 8
A satellite orbiting at a height h above the earth's surface. the height h is 5% of the earth's radius.

8.1 State Newton's Law of Universal Gravitation in words                                                          (2)
8.2 Calculate the value of g at the height above the earth's surface                                           (5)
8.3 How would the value of g in QUESTION 8.2 above change if the value of h is decreased? Write down INCREASE, DECREASE or REMAIN THE SAME  (1)
8.4 With what factor would the gravitational force of attraction between the satellite and the earth change if the distance between theri centres is halved? Justify your answer. (3)
                                                                                                                                                     [11]

QUESTION 9
A design engineer in charge of the crash worthiness of new automobiles models conducts experiments by smashing them into fixed massive barriers at 50 km.h^-1.A new model of a car of mass 1 500 kg takes 0,15 s from the time of impact until it is brought to rest.
9.1 Define the term impulse.                                                                                                        (2)
9.2 Calculate the impulse of the car.                                                                                            (5)
9.3 Calculate the average force exerted by the barrier on the car.                                              (4)
                                                                                                                                                     [11]
                                                                                                                                                     TOTAL: 150

Physical Sciences P1
Grade 12
June 2016
NSC Past Papers And Memos

INSTRUCTIONS AND INFORMATION

• This question paper consists of TEN questions.
• Answer ALL the questions
• Number the answers correctly according to the numbering system used in this question paper
• Leave ONE line between two sub questions, for example betweenQUESTION 2.1 and QUESTION 2.2.
• Write neatly and legibly
• You may use a non-programmable calculator
• You may use appropriate mathematical instruments
• Show ALL formulae and substitutions in ALL calculations
• Round off your FINAL numerical answers to a minimum of TWO decimal places
• Give brief motivations, discussions, et cetera where required

QUESTIONS

QUESTION 1: MULTIPLE-CHOICE QUESTIONS

Four options are provided as possible answers to the following questions. Each question has only ONE correct answer. Write only the letter (A–D), corresponding to the correct answer of your choice, next to the question number (1.1–1.10) in theANSWER BOOK, for example 1.11 D.

1.1 The diagram below shows a compressed spring between two trolleys initially at rest on a horizontal, frictionless surface. Trolley A has a mass of 2 kg and trolley B has a mass of 1 kg. A string holds the trollies together.

The string is cut and the trollies move apart. Compared to the magnitude ofthe force the spring exerts on trolley A, the magnitude of the force the spring exerts on trolley B is …

1. half as great.
2. the same
3. twice as great.
4. four times as great.                                                                                                                                                                                   (2)

1.2 A net force acts on each of the isolated objects, R and S, as shown below.

The mass of S is three times that of R. When effects of friction are ignored,the rate of change of momentum of S is X. What is the rate of change of momentum of R under the same conditions?

1. ¹/₉X
2. ¹/₃X
3. X
4. 3 X                                                                                                                                                                                                         (2)

1.3 An object moving with a constant velocity v has a kinetic energy E. Which one of the following will be true for the kinetic energy if the object has aconstant velocity of 2v?

1.  ½ E
2. E
3. 2E
4. 4E                                                                                                                                                                                                         (2)

1.4 A sphere is attached to a string, which is suspended from a fixed horizontal bar as shown in the sketch.

The reaction force to the gravitational force exerted by the earth on thesphere is the force of the …

1. bar on the sphere.
2. string on the sphere.
3. sphere on the earth.
4. bar on the string.                                                                                                                                                                                     (2)

1.5 A ball is dropped from height h above the ground and reaches the ground with kinetic energy E. From which height must the ball be dropped to reach the ground with kinetic energy 2E? (Ignore all effects of friction.)

1. 2h
2. 3h
3. 4h
4. 8h                                                                                                                                                                                                         (2)

1.6 The velocity versus time graph below represents the movement of an object under the influence of gravitational force ONLY.

The displacement of the object in time 3t is …

1. ^?/_?vt.
2. 7vt
3. ^?/_?vt.
4. -^?/_?vt.                                                                                                                                                                                           (2)

1.7 A net force F accelerates two isolated objects, P and Q, from rest on a straight line for time t as shown below. Object P experiences an acceleration of a and object Q an acceleration of 2a.

If the amount of work done by net force F on object P equals W, the amount of work done on Q will be …

1. W.
2. ½ W.
3. 2 W.
4. 4 W.                                                                                                                                                                                                (2)

1.8 Which ONE of the following can be explained by the Doppler Effect?

1. A source of sound moves closer to a listener, the sound observed by the listener becomes louder.
2. If light shining on a metal has a frequency that is high enough,electrons will be emitted from the metal.
3. A spectrum will be shifted towards shorter wavelengths than expected if the light comes from distant celestial objects moving towards the observer.
4. A spectrum of frequencies of electromagnetic radiation is emitted when an atom makes a transition from high energy to a lower energy state.                                                                                                                                                                                                         (2)

1.9 The red shift can be used to estimate the speed of a galaxy relative toearth. Which ONE of the following statements is CORRECT? Distant galaxies are moving …

1. faster than closer galaxies and the universe is expanding.
2. faster than closer galaxies and the universe is contracting.
3. slower than closer galaxies and the universe is contracting.
4. moving at the same speed as closer galaxies and the universe remains unchanged.                                                                 (2)

1.10 A ball is dropped onto a concrete floor and bounces off the floor to thesame height from which it was dropped. Which ONE of the following laws best explains why the ball experiences an upward force? Newton’s …

1. first law of motion.
2. second law of motion.
3. third law of motion.
4. law of universal gravitation.                                                                                                                                                          (2)
                                                                                                                                                                                                        [20]

QUESTION 2
A girl stands on a platform in a classroom. She throws a ball vertically downwardsto the floor hoping that the ball, after it bounced on the floor, will hit the ceiling of the classroom. She throws the ball with a velocity of 8 m·s^-1 from the height of 1,8 m above the floor. Ignore the effects of friction. 

2.1 Write down the magnitude and direction of the acceleration of the ball immediately after the ball left her hand.                                (2)
2.2 Is the motion of the ball while moving downwards towards the floor a freefall? Answer YES or NO. Explain your answer.                (2)
2.3 Calculate the magnitude of the velocity with which the ball hits the floor.                                                                                            (4)
2.4 How long does it take the ball to hit the floor?                                                                                                                                      (3)

2.5 Determine by means of calculations, whether the ball will reach the ceiling after its first bounce on the floor.                                   (5)
2.6 Sketch a velocity-time graph for the motion of the ball, from the time the ball is thrown until it reaches the maximum height after the bounce.
Clearly show the following on the graph:

• The initial velocity of the ball
• The velocity and time when the ball hits the floor
• The velocity and time when the ball leaves the floor                                                                                                                      (4)
                                                                                                                                                                                                         [20]

QUESTION 3
A crate of mass 86 kg is accelerating down a surface inclined at an angle of 25° to the horizontal.

A man applies a force F upwards parallel to the plane in an attempt to prevent the crate from sliding down the inclined plane. In spite of the man’s efforts the crate is accelerating down the incline.
3.1 The applied force is a non-conservative force. What is meant by a non-conservative force?                                                           (2)
3.2 The coefficient of kinetic friction (μ?) between the crate and the surface ofthe plane is 0,22. Prove that the magnitude of the kinetic frictional force is168,04 N. (2)
3.3 State work-energy theorem in words.                                                                                                                                                   (2)
3.4 Draw a labelled free-body diagram of all the forces acting on the crate.                                                                                              (4)
3.5 The crate accelerates parallel down the inclined plane for a distance of0,9 m at 1,54 m·s-2. Use the work-energy theorem and calculate the workdone by the man on the crate.                                                                                                                                                            (5)
                                                                                                                                                                                                                  [15]

QUESTION 4
A 5 kg rigid crate moves from rest down path ABC as shown in the diagram below
(diagram not drawn to scale).
Section AB of the path is frictionless whilst section BC is a rough surface. Assume that the crate moves in a straight line down the path.

4.1 State, in words, the principle of the conservation of mechanical energy.                                                                                  (2)
4.2 Use the principle of the conservation of mechanical energy to calculate the velocity of the crate when it reaches point B.    (4)

4.3 Apart from friction, write down the names of TWO other forces that act onthe crate as it moves down section BC.                (2)
4.4 In which direction does the net force act on the crate as it moves downsection BC? Write down only B to C or C to B.         (1)

4.5 How will the velocity of this 10 kg crate at point B compare to that of the5 kg crate at B?
      Write down only GREATER, SMALLER or EQUAL TO.                                                                                                            (1)
                                                                                                                                                                                                        [10]

QUESTION 5
5.1 A submarine can use the Doppler effect to detect the speed of the ship. A submarine at rest and just below the surface of the water, detects the frequency of a moving ship as 437 Hz, which is 0,985 times the actual frequency of the sound emitted by the ship. The speed of sound in water is1 470 m·s^-1.

5.1.1 State Doppler effect in words.                                                                                                                                    (2)
5.1.2 Is the ship moving away from or towards the submarine? Give areason for your answer.                                        (2)
5.1.3 Calculate the speed of the ship.                                                                                                                                 (5)

5.2 Light emitted from distant stars demonstrates the phenomenon known as red shift.
Explain how the phenomenon known as red shift can be used to explain an expanding universe.                                            (2)
5.3 Absorption spectra from the Sun and another galaxy is shown below:
Study the atomic absorption spectra and answer the question that follows:

Does the spectrum of the other galaxy constitute a RED SHIFT or BLUESHIFT?                                                                   (1)
                                                                                                                                                                                                 [12]

QUESTION 6
A 4 kg block on a horizontal, rough surface is connected to an 8 kg block by a light, inelastic string that passes over a frictionless pulley as shown below. Thecoefficient of kinetic friction between the block of 4 kg and the surface is 0,6.

6.1 Draw a free-body diagram showing the forces acting horizontally on the4 kg block.                                                          (2)
6.2 Calculate the acceleration of the system.                                                                                                                            (7)
6.3 Calculate the magnitude of the tension in the string.                                                                                                          (3)
6.4 Calculate the magnitude of the frictional force that acts on the 4 kg block.                                                                        (4)
                                                                                                                                                                                                  [16]

QUESTION 7
Collisions between vehicles take place on the roads in our country daily. In one ofthese collisions, a car of mass 1 650 kg, travelling at a velocity of 25 m·s^-1 to the left, collides head-on with a minibus of mass 3 050 kg, travelling at 15 m·s^-1 to the right. The two vehicles move together as unit in a straight line after collision.

7.1 Calculate the velocity of the two vehicles after the collision.                                                                                                    (5)
7.2 Prove by means of calculations that the collision was inelastic.                                                                                              (9)
7.3 New cars have crumple zones to help minimise injuries during accidents.
Airbags and padded interiors can also help to reduce the chances of fatalinjury or serious injury.
Use a principle in Physics to explain howcrumple zones can reduce the chances of fatal or serious injury.                                 (3)
                                                                                                                                                                                                       [17]

QUESTION 8
The diagram below shows a spaceship, with a mass of 3 500 kg, travelling in the vacuum of space in an orbit around the earth, with a mass of
5,98 × 10²⁴ kg at a constant speed. There is a distance of 8,53 × 10⁶ m between the earth and the spaceship centres.

8.1 Define the Newton’s law of Universal Gravitation.                                                                                                                  (2)
8.2 Calculate the gravitational force that the earth exerts on the spaceship.                                                                                (4)
8.3 How does the force exerted by the spaceship on the earth compare to theforce calculated in QUESTION 8.2 above?
Write ONLY greater than, smaller than or equal to.                                                                                                                    (1)
8.4 Name and state the Newton’s Law of motion used to make a choice in QUESTION 8.3 above.                                             (3)
8.5 Due to the change in the distance between the earth and the spaceship centres, the force increased by a factor of 4. Calculate the new distance between the earth and the spaceship centres.                                                                                                                             (4)
                                                                                                                                                                                                      [14]

QUESTION 9
Two identical objects P and Q with a mass of 10 kg each, are moving side by side with an initial velocity of 5,5 m·s^-1 east on a horizontal surface. The following graphs show the net force experienced by each object respectively during thesame time interval.

9.1 Calculate the total impulse experienced by object Q in 10 s.                                                                                                     (5)
9.2 Compare without using any calculations the total impulse for object P withthat of object Q.
Write down only GREATER THAN, LESS THAN or EQUAL TO.                                                                                                    (2)
9.3 Calculate the final velocity of object Q.                                                                                                                                       (4)
                                                                                                                                                                                                         [11]

QUESTION 10
Two point charges of magnitudes +4 nC and -6 nC are placed at points A and C respectively. These charges are respectively 20 mm and 25 mm away from point R as shown in the diagram below:

10.1 Draw the electric field pattern formed between the two point charges(A and C).                                                                        (3)
10.2 Calculate the net electric field at R due to the two point charges.                                                                                               (7)
10.3 If the distance between the two charges (A and C) is reduced by 15 mm.
Calculate the electrostatic force that charge A exerts on charge C.                                                                                                    (5)
                                                                                                                                                                                                            [15]
                                                                                                                                                                                               TOTAL: 150

DATA FOR PHYSICAL SCIENCES GRADE 12 PAPER 1 (PHYSICS)
TABLE 1: PHYSICAL CONSTANTS

TABLE 2: FORMULAE

MOTION

FORCE

WORK, ENERGY AND POWER

WAVES, SOUND AND LIGHT

ELECTROSTATICS

Physical Sciences
P1
Grade 12
June 2016 Memorandum
Nsc Past Papers And Memos

MEMORANDUM

QUESTION 1

                                                                                                                           [20]

QUESTION 2

2.1	9,8 m·s-2 ✓ , downwards✓	(2)
2.2	Yes✓ Only gravitational force is acting on the ball ✓ OR The ball is moving under the influence of its weight✓	(2)
2.3	Upwards +OPTION 1 Vf2 = Vi2 + 2gΔy ✓ = (-8)2 ✓ + 2(-9,8)(-1,8) ✓   Vf = 9,96 m·s-1 ✓ Downwards + OPTION 2 Vf2 = Vi2 + 2gΔy ✓ = (8)2 ✓ + 2(9,8)(1,8) ✓ Vf = 9,96 m·s-1 ✓ OPTION 3 OPTION4 EM (Top) = EM (Floor) (mgh+½mv2)Top = (mgh+½mv2)Floor ✓ m(9,8)(1,8) + ½ m(8)2 ✓= 0 + ½ mv2 ✓               17,64 + ½ (64) = ½ v2 ∴ v = 9,96 m·s-1✓	(4)
2.4	POSITIVE MARKING FROM 2.3 OPTION 1 Downwards + Vf = Vi + gΔt ✓ 9,96 = 8 + 9,8Δt ✓ Δt = 0,2 s ✓ Upwards + Vf = Vi + gΔt ✓ -9,96 = -8 + (-9,8)Δt ✓ Δt = 0,2 s ✓  OPTION 2 Downwards + Δy = viΔt + ½ gΔt2 ✓ 1,8 = 8Δt + ½ (9,8) Δt2  ∴ Δt = 0,2 s ✓ Upwards + Δy = viΔt + ½ gΔt2 ✓ -1,8 = -8Δt + ½ (-9,8) Δt2 ∴ Δt = 0,2 s ✓  OPTION 3 Downwards + Δy = ??+ ?? Δt ✓             2  1,8 = 9,96+82 Δt                 2 ∴ Δt = 0,2 s ✓  OPTION 4 Upwards + Δy = ??+ ?? Δt ✓             2 -1,8 = −9,96+(−8) Δt                     2 ∴ Δt = 0,2 s ✓	(3)

2.6
	Upwards as positive Marking Guidelines  Marks  Initial v at -8 m.s-1  ✓ Positive marking from 2.3 & 2.4 Time and velocity shown with which ball hits the floor/ Velocity (-9,96 m.s-1 ) and time (0,2 s) with which ball hits the floor.  ✓ Positive marking from 2.3 & 2.4 Time and velocity shown with which ball leaves the floor/ Velocity (7,97 m.s-1) and time (0,21 s) with which ball leaves the floor./  ✓ Two parallel lines ending at v = 0 m.s-1 on t-axis.  ✓ Upwards as positive Marking Guidelines  Marks  Initial v at 8 m.s-1/   Positive marking from 2.3 & 2.4 Time and velocity shown with which ball hits the floor/ Velocity (9,96 m.s-1) and time (0,2 s) with which ball hits the floor.  ✓ Positive marking from 2.3 & 2.4 Time and velocity shown with which ball leaves the floor/ Velocity (-7,97 m.s-1) and time (0,21 s) with which ball leaves the floor.  ✓ Two parallel lines ending at v = 0 m.s-1 on t-axis.  ✓	(4)

                                                                                                                                           [20]

QUESTION 3

                                                                                                                                                                                   [15]

QUESTION 4

QUESTION 5

                                                                                                                                                                                                                                                                    [12]

QUESTION 6

6.1		(2)
6.2	OPTION 1  OPTION 2 Fnet = maFnet = ma At/by  A:4 kg block In x-direction. T – ff = mAa T – μN = mAa✓ T – μmAg =mAa ( equation 1) At/by A:4 kg block In y direction (up) N – Fg = 0 N = Fg = mg At/by B:8 kg block In the x direction –T + Fg = mBa✓ –T + mBg = mBa (equation 2) Solving the system of equations T – μmAg – T + mBg = mAa + mBa✓ Removing T and isolating a: –μmAg + mBg = (mA + mB)a✓ –(0,6)(4)(9,8) +(8)(9,8)✓ = (4+8)a✓ 54,88 = 12a a = 4,57 m·s-2 ✓   Adding Eq 1 & Eq 2 4a +23,52 + 8a – 78,4 = 0✓ 12a = 54,88 ∴ a = 4,57 m·s-2✓	(7)
6.3	OPTION 1 T – ff = mAa T -μmAg = mAa T -23,52 ✓= 4(4,57) ✓ T = 41,8 N ✓  OPTION 2 –T + mBg = mBa –T+ (8)(9,8) ✓ = (8)(4,57) ✓ T = 41,84 N✓	(3)
6.4	OPTION 1 FF = μN✓ N = mg FF =μmg=(0,6)(4)✓ (9,8) ✓=23,52N✓ OPTION 2 T – FF = mAa ✓ 41,8 - FF✓ = 4(4,57) ✓ FF = 23,52 N✓	(4)

                                                                                                                                        [16]

QUESTION 7

                                                                                                                                                                                                                                       [17]
QUESTION 8  

                                                                                                                                                                                                                                                                                                                                                 [14]

QUESTION 9

                                                                                                                [11]

QUESTION 10

                                                                                                               [15]

 Total : 150