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2

Question 1 A department store has advertised a discount of 35% on all items in the store. The price of a lady’s blouse including the discount is R60,00. What was the original price of the blouse? [1] R81,00

[2] R92,31

[3] R99,00

[4] R104,00

[5] None of the above

Question 2 Solve the following equation for x:

5 32 16.x

Question 3 Simplify the following expression

2 1 1 1 12 2 .3 2 2 2 6

16

1112

1724

23

[1]

[2]

[3]

[4]


15

[1] 1

[2] 5

[3]

[4] 0, 2



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4

Question 4 Simplify the following expression:

24 34

4

4.

xx y

y

11

4

3

4

3

2

11

4

[1] 2

2[2]

[3] 2

[4] 2


xy

y

x

xy

y

Question 5 Evaluate

3

1073log

7

and give your answer correct to three decimal places. [1] 3,022

[2] 4,581

[3] 7,516

[4] 8,123



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6

Question 6 The graphs 1, 2, 3 and 4 below, represent the graphs of

13

13

13

13

[1] 0; 4 2 0; 3 6 0; 5 0, respectively.

[2] 0; 3 6 0; 4 2 0; 5 0, respectively.

[3] 0; 3 6 0; 4 2 0; 5 0, respectively.

[4] 0; 4 2 0; 3 6 0; 5 0, respectively.

y x y x y x y

y x y x y x y

y x y x y x y

y x y x y x y

[5] none of the above.

[1] [2]

[3] [4]

1

3

½


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8

Question 7 Find the slope of the straight line passing through the points (5 ; 10) and (6 ; 8). [1] 2

[2] 0, 2

[3] 0, 2

[4] 2


Question 8 The values of p and q that satisfy the set of equations

3 2 9 0

4 6 25 0,

p q

p q

are:

12

12

3 272 4

32

[1] ; 4.

[2] 4; 1 .

[3] ; .

[4] ; 4.


p q

p q

p q

p q

Question 9 A linear line cuts the y-axis at 10 and passes through the point (2 ; 4). The equation of the line is.

13

13

[1] 10.

[2] 10.

[3] 3 10.

[4] 3 10.


y x

y x

y x

y x


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10

Question 10 The regular price of a bicycle is R1 300,40 and the current sale price is R980,20. By what percentage was the price reduced? Choose the option closest to the correct answer. [1] 24,62%

[2] 30,38%

[3] 69,62%

[4] 75,38%


Question 11 If the demand function is P = 90 – 2Q, where P and Q are the price and quantity respectively, give an expression for the price elasticity of demand in terms of P only.

1

2

90[1]

2

[2] 90

[3] 90

[4] 90


P

PP

P

P

PP

P

Question 12 If the demand function is

215 5P Q

where P and Q are the price and quantity respectively, determine the point price elasticity of demand if the price P equals 15.

515

403

2015

340

[1]

[2]

[3]

[4]



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12

Question 13 Solve the following system of linear equations:

2 8 (1)

2 0 (2)

2 – 2 2 (3)

p q r

p q r

q r

The sum of the values of p, q and r of the solution is

1 7.

2 1.

3 1.

4 7.

5 none of the above.

Question 14 The information in the following market is:

Demand function : 35 0,1

Supply function : 10 0,2

Q P

Q P

where P and Q are the price and quantity respectively. Calculate the equilibrium price and quantity.

[1] 20; 150

[2] 200; 15

[3] 150; 20

[4] 66,66; 28


P Q

P Q

P Q

P Q


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Question 15 The cost y (in rands) of manufacturing x bicycles is 240 720.y x How many bicycles have been manufactured if the cost is R30 000? [1] 120

[2] 122

[3] 123

[4] 125


Question 16 The consumer surplus for the demand function 50 4P Q when the market price in equilibrium is P = 10, is [1] 12,50.

[2] 112,50.

[3] 200.

[4] 312,50.


Question 17 The weekly growth of a mouse in a research laboratory takes place according to the formula:

46,04

1 13,720(0,596)xy

where y is the average mass (in grams) and x the number of weeks since birth. What is the average mass of a mouse after 10 weeks? [1] 42,72

[2] 46,04

[3] 46,12

[4] 50,17


g

g

g

g


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Question 18 A company makes two products, A and B. Product A requires 12,5 hours of machining time and 30 minutes of finishing time per unit. Product B requires 10 hours of machining time and one hour of finishing time per unit. There are 10 000 hours and 600 hours available for machining and finishing respectively. Severe material shortages for the two products will limit their production to a maximum of 700 units for product A and 400 units for product B per day. If x and y are the number of units of product A and B produced per day respectively, choose the system of inequalities that describes the process.

[1] 12,5 10 10 000; 0,5 600; 700; 400; , 0

[2] 12,5 10 10 000; 0,5 600; 700; 400; , 0

[3] 12,5 10 10 000; 0,5 600; 700; 400; , 0

[4] 12,5 10 10 000; 0,5 600; 700; 400; , 0

[5] None of t

x y x y x y x y

x y x y x y x y

x y x y x y x y

x y x y x y x y

he above

Question 19 The roots of a quadratic function are 2 and 3. The coordinates of the turning point are

[1] (0,5; 6,25).

[2] ( 0,5; 6,25).

[3] (0,5; 5,25).

[4] ( 0,5; 5,25).


Question 20 The demand function of a firm is 150 0,5 ,Q P where P and Q represent the price and quantity respectively. At what value of P is marginal revenue equal to zero? [1] 0

[2] 75

[3] 113

[4] 150



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Question 21 Questions 21, 22 and 23 are based on the following: Lighting Warehouse produces q solar lamps at a fixed cost of R10 000 per week. Each lamp costs R150 to produce and is sold for R350. What are the equations for total revenue, total cost and profit function?

350 ;150 10 000;200 –10 000

150 10 000;200 –10 000;350

350 ;200 –10 000;150 10 000

200 –10 000;350 ;150

[1]

[2]

[3]

[4]

[5] None of the

10 000

above

q q q

q q q

q q q

q q q

Question 22 Calculate the break-even quantity per week.

1 20

2 50

3 100

[4] 2 00


Question 23 How many lamps were produced and sold if they made a loss of R2 000?

1 10

2 40

3 50

[4] 60



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Question 24 Find the values of x for which the function 3 2( ) 2 9 12 36f x x x x has a maximum or a minimum value.

1 1; 2

2 1; 2

3 1; 6

[4] 3; 6


x x

x x

x x

x x

Question 25 If the total revenue is given by

5 22 10 15,TR x x x what is the marginal revenue when x = 5? [1] 150

[2] 6 250

[3] 6350

[4] 6 450


Question 26 Find the derivative of the function:

2

.d x x

dx x

1 3

2 2

1 1

2 2

5 1

2 2

25

32

3 1[1]

2 2

3 1[2]

2 2

2[3] 2

5

2 2[4]

5 3[5] None of the above

x x

x x

x x

x x


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22

Question 27 Evaluate the following integral:

13 32 ( ) .x x x dx

3

2

522

522

3

2

2[1]

3

2[2]

2 5

5[3]

2 2

[4]


x x c

xx c

xx c

x x c

Question 28 Evaluate the following definite integral:

2

1( 2 3) .x dx

[1] 5

[2] 3

[3] 3

[4] 6



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Question 29 In the graph below the following set of inequalities

10

5 4 40

4

, 0

x y

x y

x

x y

was drawn and the feasible region of the set of inequalities shaded in grey.

R

Q

x = 4

x + y = 10

5x + 4y = 40

S

O

Determine the maximum value of the profit function

18 12 ,Z x y subject to the set of inequalities above. The maximum profit is equal to [1] 120

[2] 132.

[3] 144.

[4] 192.



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Question 30

Which set of graphs represents the functions

2 2 2 2A: 2 0; B : 0; C : 3 0; D : 0?y x y x y x y x

[1] [2]

[3] [4]


TOTAL: [100]


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UNISA 2015

his paper c onsists of 27 pages and paper for rough work, plus … · t re a c his paper c ading...

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