Free Printable SPM Revision 3 F4: C1-C4

1.

A factory produce 3 types of hand glove, nitrile, vinyl, surgery. All hand glove must undergo two process. Process I and process II, the following table show time required for process I and II for each type of product and the cost required for each type of product. In certain period, the factory produce x nitrile glove, y vinyl glove and z surgery glove, time required for process I and process II is 6 hours and 2 hours respectively. The cost involved is RM 450, Form three linear equation and solve x, y and z.

a)

x=40

y=20

z=20

b)

x=30

y=30

z=30

c)

x=90

y=2

z=30

d)

x=30

y=30

z=20

2.

Two group of worker order drink in coffeeshop, first group have 10 workers and they order 5 glasses coffee, two glasses milo and 3 glasses orange juice costing RM 23.60 second group worker have 6 workers and they order 3 glasses coffee, one milo, two glasses orange juice costing RM 14.20. The cost of one coffee and three glasses orange juice is same as 4 glasses milo, if cost of one coffee, one milo and orange juice is RMx, RMy and RMz, form three linear equation, and solve x,y,z.

a)

x=2

y=5

z=4.5

b)

x=2

y=2.8

z=2.6

c)

x=2

y=2.6

z=2.8

d)

x=2.8

y=2

z=2.6

3.

log₂5 + log₂(x - 1) = 1

a)

$\frac{7}{5}$

b)

$\frac{5}{7}$

c)

5

d)

45

4.

Given the solution for $x\sqrt[]{7}=x\sqrt[]{2}+\sqrt[]{32}$ is $\frac{a+b\sqrt[]{14}}{5}$ . Without using a calculator, find the values of a and b.

a)

a=9

b=3

b)

a=8

b=4

c)

a=7

b=3

d)

a=9

b=4

5.

Given p(x) = ax + b and p²(x) = 16x + 21 where a < 0. Find the value of a and b.

a)

a=4

b=9

b)

a=-4

b=7

c)

a=4

b=-7

d)

a=-4

b=-7

6.

Rationalise the following denominator.

$\frac{15}{\left(\sqrt[]{3}+5\right)^2}$

a)

23- $\sqrt[]{5}$

b)

$\frac{150\sqrt[]{3}-420}{-484}$

c)

$150\sqrt[]{3}-210$

d)

$\frac{210-75\sqrt[]{3}}{242}$

7.

Given that f(x) = x + 5 and g(x) = 3x – 4, find the value of fg^-1(4).

a)

22

b)

4

c)

$\frac{3}{23}$

d)

$\frac{23}{3}$

8.

Given the function f : x → 3x – 4, find the values of x when f(x) maps onto itself.

a)

1

b)

4

c)

2

d)

6

9.

Given the function k(x) = x – 3 and h(x) = 2x + 5, find k^-1h ^-1(x).

a)

x+7

b)

$\frac{x+1}{4}$

c)

$\frac{2x+1}{4}$

d)

$\frac{x+1}{2}$

10.

Given the function f(x) = 2x – 9 and the composite function fg^-1(x) = 11x + 13, find g(x).

a)

5x-9

b)

$\frac{11}{2x-22}$

c)

$\frac{x-11}{22}$

d)

$\frac{11x+22}{2}$

11.

Given that -5 is one of the roots of the quadratic equation x² - x + p = 0.Find the value of p.

a)

-30

b)

30

c)

5

d)

67

12.

Given that f(x) = - (x + 3)² + 4m – 2, where m is a constant. Find the value of m if the maximum value of the function is 6.

a)

8

b)

4

c)

2

d)

-2

13.

simplify

$\sqrt[]{512}$

a)

$\sqrt[]{5}$

b)

3

c)

$\sqrt[]{2}$

d)

16 $\sqrt[]{2}$

14.

The functions f and g are defined by f:x → 4x - 3 and g:x → x + 3. Calculate the value of fg(4).

[type in the number only]

(a)

15.

Given that log_x3 = p and log_x7 = q, express log₇3x³ in terms of p and q.

a)

q-3p

b)

2p-q

c)

$\frac{q+3}{p}$

d)

$\frac{p+3}{q}$

16.

2x + y - z = 5

x + 2y + 2z = 5

-x + y + 2z = 1

a)

x=1

y=-2

z=-3

b)

$x=\frac{1}{3}$

$y=\frac{10}{3}$

z=-1

c)

x=1

$y=\frac{1}{5}$

z=3

d)

$x=\frac{1}{3}$

y=2

z=5

17.

Given the function g : x → px + q and the composite function g² : x → 64x – 45, find the value of p and q where p > 0.

a)

p=1

q=3

b)

p=4

q=3

c)

p=8

q=5

d)

p=5

q=8

18.

2x + y + 6z = 6

3x + 3y + 6z = 11

3x + 2y = 7

a)

x=3

y=5

z=1

b)

x=1

y=3

$z=\frac{1}{3}$

c)

x=2

y=4

z=1

d)

x=1

y=2

$z=\frac{1}{3}$

19.

$\frac{8}{2\sqrt[]{6}+3}-\frac{4}{2\sqrt[]{6}-3}$

a)

$\frac{8\sqrt[]{6}-36}{15}$

b)

$4\sqrt[]{6}-25$

c)

14- $\sqrt[]{34}$

d)

$\sqrt[]{3}-4$

20.

$\sqrt[]{2x-3}-5\sqrt[]{x-2}=0$

a)

x=22

b)

$x=\frac{23}{47}$

c)

x=23

d)

$x=\frac{47}{23}$

SPM Revision 3 F4: C1-C4

Total questions: 20

Worksheet time: 2hrs 5mins

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