Free Printable RANDOM REVISION

1.

Solve the system of equations.
y = 4x+1
3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

2.

Solve:
-2x + 5y = -1
4x - 2y = -6

a)

(-2, -1)

b)

(2, 7)

c)

(3, 1)

d)

(-1, -2)

3.

Solve the system.

a)

(5, -6, 3)

b)

(2, 3, -1)

c)

(-4, 2, 5)

d)

No Solution

4.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

5.

Write the following quadratic expression in completed square form...

x² + 4x + 10

a)

(x + 4)² + 6

b)

(x + 2)² + 6

c)

(x + 4)² - 6

d)

(x + 2)² - 6

6.

Solve

a)

(2,3) and (3,-15)

b)

(-3,-15) and (4,-8)

c)

(-3,15) and (8,4)

d)

(-8,4) and (-4,10)

7.

Factorise:

3x^2-3x-36

a)

$3\left(x-3\right)\left(x+4\right)$

b)

$\left(x-4\right)\left(x-3\right)$

c)

$\left(x-4\right)\left(x+3\right)$

d)

$3\left(x-4\right)\left(x+3\right)$

8.

The positive real root of the equation : 64x² - 1 = 0 is ______

a)

8

b)

⅛

c)

1⁄16

d)

1⁄4

9.

Find the discriminant for

3x^2-3x+3

a)

$\sqrt{-27}$

b)

-27

c)

27

d)

-9

10.

Factorise $x^3+1$ can be factorised in the form of $\left(x+1\right)\left(f\left(x\right)\right)$ .

What is $f\left(x\right)$

a)

$x^2+x-1$

b)

$x^2-x+1$

c)

$\left(2x-1\right)^2$

d)

$\left(x+1\right)^2$

11.

Determine the roots of the polynomial.
f(x) = (x+1)(x-4)(x+2)

a)

1, 4, 2

b)

-1, -4, -2

c)

1, -4, 2

d)

-1, 4, -2

12.

Determine the roots of the polynomial.
f(x) = (x-2)(x+3)²

a)

2, 3

b)

2, -3

c)

-2, 3

d)

-2, 3, 3

13.

Determine the roots of the polynomial.
f(x) = -x(x+1)(x-3)

a)

-1, 3

b)

0, -1, 3

c)

1, -3

d)

0, -3, 1

14.

Solve the system.

a)

$x=3,\ y=-2,\ z=4$

b)

$x=2,\ y=-3,\ z=1$

c)

$x=-3,\ y=2,\ z=-1$

d)

$x=3,\ y=-2,\ z=1$

15.

Check whether the long division is correct and hence, state whether

x+2

is one of the factor for

2x^3-3x^2+4x+5

a)

long division incorrect,undefined is not a factor

b)

long division incorrect,undefined is a factor

c)

long division correct,undefined is not a factor

d)

long division correct,undefined is a factor

16.

Factorise $2x^3+18x^2-24x-40$ if $x+1$ is one of its factors

a)

$\left(x+1\right)\left(x+10\right)\left(x-2\right)$

b)

$2\left(x+1\right)\left(x+10\right)\left(x-2\right)$

c)

$\left(2x-1\right)\left(x+10\right)\left(x-2\right)$

d)

$\left(x+1\right)\left(x-10\right)\left(x+2\right)$

17.

Find the point of intersection between $y=4x+1$ and $y=\sqrt{2x+2}$

a)

$\left(-\frac{1}{2},\ -1\right)$

b)

$\left(\frac{1}{8},\ \frac{3}{2}\right)$

c)

$\left(-\frac{1}{8},\frac{1}{2}\ \right)$

d)

$\left(\frac{1}{2},\ 3\right)$

18.

Which of these quadratic expressions has a non zero discriminant?

a)

$x^2+x+1$

b)

$x^2+2x+1$

c)

$x^2+4x+4$

d)

$x^2-6x+9$

19.

Given a quadratic equation $\left(a-3\right)x^2+2ax+3=0$ .

Choose which of these statements is TRUE.

a)

II and III

b)

I, III and IV

c)

II, III and IV

d)

I and III

20.

Determine the roots of the polynomial $f(x)=-(x+1)(x+4)(2x+2)$

a)

1, 4, 2

b)

1, 4, 1

c)

-1, -4, -2

d)

-1, -4, -1

21.

Which of the following is the equation of a circle with a center at (-1,3) and a radius of 4?

a)

(x-1)²+(y+3)²=4

b)

(x-1)²+(y+3)²=16

c)

(x+1)²+(y-3)²=4

d)

(x+1)²+(y-3)²=16

22.

Which circle has a center at (-3,-6) and passes through the point (-4,8)?

a)

(x-3)²+(y-6)²=197

b)

(x+3)²+(y+6)²=197

c)

(x-3)²+(y-6)²=32

d)

(x+3)²+(y+6)²=32

23.

a)

$(x+7)^2+(y-4)^2=81$

b)

$(x+7)^2+(y-4)^2=324$

c)

$(x-7)^2+(y+4)^2=324$

d)

$(x-7)^2+(y+4)^2=81$

24.

a)

(x+4)²+(y+13)²=16

b)

(x-4)²+(y-13)²=16

c)

(x-4)²+(y-13)²=64

d)

(x-4)²+(y-13)²=256

25.

Which of the following graphs represents this circle equation $\left(x-4\right)^2+\left(y+2\right)^2=36$

a)

b)

c)

d)

26.

Which of the following graphs represents this circle equation -- $x^{2\ }+\ \left(y-6\right)^{2\ }=\ 25$

a)

b)

c)

d)

27.

Determine the equation of the circle in standard form:

x² + y² + 4x + 6y - 36 = 0

a)

(x + 2)² + (y + 3)² = 49

b)

(x + 2)² + (y + 3)² = 13

c)

(x - 2)² + (y - 3)² = 49

d)

(x - 2)² + (y - 3)² = 13

28.

What is the equation of the circle?

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

29.

Is the point (3 , 5) inside, outside or on the circle with equation x² + y² = 9?

a)

Inside the Circle

b)

Outside the Circle

c)

On the Circle

30.

If $x^2-4x+y^2+6y+4=0$ is a general equation of a circle , choose the WRONG statement about this circle.

a)

Its centre lies in the 4th quadrant of the Cartesian plane

b)

The area of the circle is $9\pi\ unit^2$

c)

The circle intercept x axis once

d)

The circle intercept y axis once

31.

The general equation of a circle is given by $x^2+12x+y^2+8y-48=0$ .

What is the coordinate of its centre?

a)

$\left(6,\ 4\right)$

b)

$\left(-6,\ -4\right)$

c)

$\left(12,\ 8\right)$

d)

$\left(-12,\ -8\right)$

32.

The general equation of a circle is given by $x^2+12x+y^2+8y-48=0$ .

What is the length of its diameter?

a)

10

b)

20

c)

48

d)

5

33.

If the radius of the circle is 7, which statement is WRONG about the circle?

a)

centre at (-7, 7)

b)

it has y intercept at 7

c)

in general equation, the value of c is -49

d)

in standard equation, the value of h is equal the value of k

34.

The distance across the circle, through its center

a)

Radius

b)

Tangent

c)

Circumferene

d)

Diameter

35.

A circle passes through 3 points (−3 , 4) , (4 , 5) and (1 , −4).

Find its standard equation of the circle.

a)

$\left(x-1\right)^2+\left(y-1\right)^2=25$

b)

$\left(x+1\right)^2+\left(y+1\right)^2=25$

c)

$x^2+y^2-2x-2y-23=0$

d)

$x^2+y^2+2x+2y-23=0$

36.

A circle $\left(x+b\right)^2+\left(y+2b\right)^2=b^2$ is tangent with y axis with distance 1 unit.

Given that b is a positive integer, what is the standard equation of the circle?

a)

$\left(x+1\right)^2+\left(y+2\right)^2=1$

b)

$\left(x+2\right)^2+\left(y+4\right)^2=4$

c)

$\left(x-1\right)^2+\left(y-2\right)^2=1$

d)

$\left(x-2\right)^2+\left(y-4\right)^2=4$

37.

A circle passes through 3 points $(3,2),(6,3)\ and\ (0,3)$

Find the radius of the circle.

a)

5

b)

25

c)

9

d)

3

38.

If a circle is tangent to both axes, which of these statement is TRUE?

a)

the centre is $\left(r,\ r\right)$ , if the circle is on the first quadrant

b)

the centre is $\left(-r,-\ r\right)$ , if the circle is on the 2nd quadrant

c)

the centre is $\left(-r,\ r\right)$ , if the circle is on the 4th quadrant

d)

the centre is $\left(r,\ -r\right)$ , if the circle is on the 3rd quadrant

39.

What is the area of the circle?

a)

$9\pi$ unit

b)

$81\pi$ unit

c)

$6\pi$ unit

d)

$3\pi$ unit

40.

Given a circle with a center at (2,-3) and a radius of 3.

Which is the correct statement about the circle?

a)

the centre is on the first quadrant of the Cartesian plane

b)

the circle is tangent to the x axis

c)

the circle is tangent to the y axis

d)

the standard equation is (x-2)²+(y-3)²=9

41.

-2(x+2) < 14

a)

x < - 5

b)

x > -5

c)

x < -9

d)

x > -9

42.

What are the solutions?
-|−2r − 1| = 11

a)

{-6,5}

b)

{5,-6}

c)

-6

d)

No Solution

43.

Solve.
3| −8x| + 8 = 80

a)

{-7/3, 7/3}

b)

{-3,3}

c)

{11/3,-11/3}

d)

No Solution

44.

|b-8|+10>22

a)

-4<b<20

b)

b<-4 or b>20

c)

20<b<-4

d)

b=-4 or b=20

45.

What inequality does the number line graph represent?

a)

x ≥ 3

b)

x > 3

c)

x < -3

d)

x ≤ -3

46.

Which graph matches the inequality
r ≥ -6?

a)

A

b)

B

c)

C

d)

D

47.

When graphing an inequality, what does a closed circle mean?

a)

The number is not included in the list of answers.

b)

The number is included in the list of answers.

48.

What inequality is graphed?

a)

x > 2 and x ≤ -3

b)

x > 2 and x < -3

c)

x > 2 or x ≤ -3

d)

x > 2 or x < -3

49.

Solve:

3x + 2 < -7 or -4x + 5 < 1

a)

All real numbers

b)

x < -3 and x > 1

c)

x < -3 or x < 1

d)

x < -3 or x > 1

50.

Which of the following would result in NO SOLUTION?

a)

x < 1 or x > 5

b)

x > 1 or x < 5

c)

x < 1 and x > 5

d)

x > 1 and x < 5

51.

Solve and give the final solution set:

5x + 1 < 21 OR 3x + 2 > -1

a)

All real numbers

b)

-1 < x < 4

c)

No solution

d)

x > 4 or x < -1

52.

When graphing b< 6 would you use an open or closed circle?

a)

Open

b)

closed

53.

Solve:
5 < x + 3

a)

x < 2

b)

x > 2

c)

x > 8

d)

x < 8

54.

Solve:
6x+10>5x-12

a)

x>2

b)

x<2

c)

x<-22

d)

x>-22

55.

Solve:
-3≤2x-1≤7

a)

-1≤x≤3

b)

-2≤x≤3

c)

-1≤x≤4

56.

Solve:
4x-2<-10 or 5x+2>12

a)

x<-3 or x>3

b)

x<-3 or x>2

c)

x<-2 or x>2

57.

Solve:
|3x+9|<6

a)

x<-1

b)

-1<x<5

c)

x<5

d)

-5<x<-1

58.

Solve:
|4x-8|≥12

a)

x≥5

b)

x≥5 or x≤-1

c)

x≤-1

d)

x≥1 or x≤-5

59.

Solve.

a)

x ≤ 14

b)

x < 14

c)

x ≥ 14

d)

x = 14

60.

$\frac{3}{x}\ge2$

a)

$0<x\le\frac{3}{2}$

b)

$0\le x\le\frac{3}{2}$

c)

$x\ge\frac{3}{2}$

d)

$x\le\frac{3}{2}$

61.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

62.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

63.

a)

A

b)

B

c)

C

d)

D

64.

Which is the equivalent of $xy^{-7}$ ?

a)

$\frac{x}{y^{-7}}$

b)

$\frac{x}{y^7}$

c)

$\left(xy\right)^{-7}$

d)

$\frac{1}{xy^7}$

65.

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

a)

-1

b)

5

c)

4

d)

1

66.

Write in index form.

log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

67.

Which is equivalent to $\log_7\ \frac{2}{3}$ ?

a)

$2\log_7\ \frac{1}{3}$

b)

$\log_73-\log_72$

c)

$\log_72-\log_73$

d)

$\frac{\log_72}{\log_73}$

68.

$\log8-\log2+2\log w$

a)

$\log\frac{4}{w^2}$

b)

$\log6w^2$

c)

$\log4w^2$

d)

$\log\frac{6}{w^2}$

69.

Solve for x

a)

x = 8

b)

x = 4

c)

x = 256

d)

x = 32

70.

Simplify fully:
√32

a)

4√8

b)

16√2

c)

4√2

d)

4√4

71.

Simplify fully:
2√45 - 5√45 + 9√16

a)

-9√5 + 36

b)

-3√45 + 144

c)

6√16

d)

6√106

72.

1. If a and b are positive integers, which of the following is/are correct?

$I.\sqrt{a^2+b^2}=a+b$

$II.\sqrt{a^2b^2}=ab$
$III.\sqrt{2a^2b}\times\sqrt{6a^3b}=2a^2b\sqrt{3a}$

a)

II only

b)

III only

c)

II and III only

d)

I, II and III

73.

The conjugate surd of $\left(3-\sqrt{2}\right)$ is

a)

$\sqrt{2}-3$

b)

$\sqrt{3}-\sqrt{2}$

c)

$3+\sqrt{2}$

d)

$\sqrt{3}-2$

74.

$\left(\sqrt{5}-\sqrt{4}\right)\left(\sqrt{5}+\sqrt{4}\right)=$

a)

$5-4$

b)

$5+4$

c)

$5^2-4^2$

d)

$5^2+4^2$

75.

$\frac{-2}{1+\sqrt{6}}$ Rationalize the following:

a)

$\frac{1+\sqrt{6}}{-2}$

b)

$\frac{-2+2\sqrt{6}}{-5}$

c)

$-\frac{2\sqrt{6}}{6}$

d)

$-2\sqrt{6}$

76.

What does the b in log_bA=x represent?

a)

Argument

b)

Base

c)

Exponent

d)

Bottom

77.

Simplify,

(z³yx) × (x²yz)

a)

z⁴y²x³

b)

6 zyx

c)

3z 2y 3x

d)

z²÷ x

78.

Simplify

a)

10x³

b)

x⁴ / 2

c)

x³

d)

x³ / 2

79.

Simplify

a)

A

b)

B

c)

C

d)

D

80.

Which of the following is considered as rationalising the denominator of $\frac{3-\sqrt{2}}{\sqrt{5}+4}$ ?

a)

$\frac{3-\sqrt{2}}{\sqrt{5}+4}\times\frac{3-\sqrt{2}}{\sqrt{5}-4}$

b)

$\frac{3-\sqrt{2}}{\sqrt{5}+4}\times\frac{\sqrt{5}+4}{\sqrt{5}+4}$

c)

$\frac{3-\sqrt{2}}{\sqrt{5}+4}\times\frac{4-\sqrt{5}}{4-\sqrt{5}}$

d)

$\frac{3-\sqrt{2}}{\sqrt{5}+4}\times\frac{\sqrt{5}-4}{\sqrt{5}-4}$

81.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

82.

Can the operation be performed?

a)

Yes

b)

No

83.

What are the dimensions of this matrix?

a)

3x1

b)

1x3

c)

3x3

d)

1x1

84.

a)

A

b)

B

c)

C

d)

D

85.

a)

A

b)

B

c)

C

d)

D

86.

Determine the dimension of the new matrix if both of these matrices are being multiplied.

a)

Can't multiply them

b)

4 x 2

c)

3 x 3

d)

4 x 3

87.

What is A₂₃

a)

14

b)

4

c)

1

d)

3

88.

What must be true in order to ADD two matrices?

a)

They must be square.

b)

The dimensions must be the same.

c)

The determinant can't equal 0.

d)

The column of the 1st matrix must equal the row of the 2nd matrix

89.

What do w, x, y and z equal in this matrix equation?

a)

w = 13, x = 4, y = 7, z = 23

b)

w = 13, x = -4, y = 11, z = 23

c)

w = 13, x = 4, y = 11, z = 23

d)

w = 13, x = 4, y = 11, z = 17

90.

Find the inverse of the matrix.

a)

b)

c)

d)

No Inverse Exists

91.

Find the values of x and y.

a)

$x=\frac{5}{2},\ y=1$

b)

$x=\frac{1}{2},\ y=3$

c)

$x=\frac{13}{2},\ y=1$

d)

$x=\frac{7}{2},\ y=-1$

92.

Find the value of n

a)

-10

b)

-8

c)

6

d)

10

93.

a)

b)

c)

d)

94.

What is the value of cofactor for matrix M on the third row, first column

a)

16

b)

-16

c)

2

d)

-2

95.

By using properties of determinant, what is the determinant of matrix B

a)

0

b)

1

c)

-1

d)

2

96.

What is the value of minor for matrix M on the second row, third column

a)

2

b)

-2

c)

3

d)

-3

97.

Is matrix M singular?

a)

No

b)

Yes

98.

Does matrix B has an inverse?

a)

No

b)

Yes

99.

A circle passes through 3 points; (2,1), (0,5) and (-1, 2).

Which of the followings is the system of linear equations to solve for the value of g, f, and c?

a)

b)

c)

d)

100.

Which of the following statements is FALSE for a singular matrix?

a)

Its determinant equal 0

b)

It does not have an inverse

c)

They are inverse of itself

d)

Matrices that have zero row or zero column

101.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

102.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

103.

a)

Function

b)

Not a Function

104.

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

a)

-42

b)

-26

c)

-18

d)

None of these.

105.

What type of function does this graph represent? State its gradient.

a)

LInear Function, increasing

b)

LInear Function, decreasing

c)

Constant Function, increasing

d)

Constant Function, increasing

106.

Which of the following is the incorrect statement about this function?

*the graph is sketched according to scale

a)

It has y intercept at -3

b)

The range for this function is $\left(-3,\ \infty\right)$

c)

This is a quadratic function with positive a

d)

The discriminant of this function is greater than 0

107.

The function represented by the blue line and the function represented by the orange line are inverse of each other.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

108.

a)

$D_{f^{-1}}=\left[0,\ \infty\right),\ R_{f^{-1}}=\left(-\infty,1\ \right]\$

b)

$D_{f^{-1}}=\left(-\infty,1\ \right]\ ,\ R_{f^{-1}}=\left[0,\ \infty\right)$

c)

$D_{f^{-1}}=\left(-\infty,1\ \right]\ ,\ R_{f^{-1}}=\left(-\infty,\infty\right)$

d)

$D_{f^{-1}}=\left(-\infty,\infty\right)\ ,\ R_{f^{-1}}=\left(-\infty,1\ \right]\$

109.

What is the range for a linear function $f\left(x\right)=5-3x,\ -2\le x<4$ ?

a)

$\left(-7,\ 11\right]$

b)

$\left[11,\ -7\right)$

c)

$\left(-7,\ 11\right)$

d)

$\left[11,\ -7\right]$

110.

How must the domain of $f\left(x\right)$ be restricted so that $g\left(x\right)$ can become its inverse?

a)

x ≤ 0

b)

x ≥ 0

c)

x ≤ 3

d)

x ≥ 3

111.

Does $f\left(x\right)=\left(x+1\right)^2+3$ has inverse?

a)

No

b)

Yes

112.

a)

b)

c)

d)

113.

This graph represent a quadratic function.
Which of these functions is the possible function?

*the graph is sketched not according to scale

a)

$y=-2x^2+1$

b)

$y=-\left(x-2\right)^2+1$

c)

$y=\left(x-2\right)^2+1$

d)

$y=-\left(x+2\right)^2+1$

114.

Which of the following is the possible function for this graph?

*graph is accurately sketched to scale

a)

y = -2x³+ x + 3

b)

y = (x - 2)(x + 1)(x + 3)

c)

y = (x + 2)(x - 1)(x - 3)

d)

y = -2x² + x + 3

115.

Which of the following is NOT the possible function for the graph?

*graph is not accurately sketched to scale

a)

$\left(x+2\right)^2\left(x-1\right)$

b)

$\left(x+2\right)^2\left(1-x\right)$

c)

$\left(x-3\right)\left(x+2\right)^2$

d)

$\left(x-2\right)\left(x+3\right)^2$

116.

Given $fg\left(x\right)=11-8x\$ and $g\left(x\right)=5-4x$ .

Find

f\left(x\right)

a)

$f\left(x\right)=2x+1$

b)

$f\left(x\right)=4x-9$

c)

$f\left(x\right)=1-2x$

d)

$f\left(x\right)=4x+9$

117.

Does the function $f\left(x\right)=8-x^3$ has an inverse?

a)

Yes

b)

No

118.

Which of the statement is CORRECT regarding $f\left(x\right)=\sqrt{x+1}$ ?

a)

III and IV only

b)

I, III and IV

c)

II and III only

d)

II, III and IV

119.

The illustrated graph is a surd function.

Which of the statement is INCORRECT?

a)

The starting point is at (2,-3)

b)

It has domain $\left(-\infty,\ 2\right]$

c)

It has range $\left[-3,7\right)$

d)

The graph has intercepts on both axis

120.

Choose the INCORRECT statement about a function.

a)

A function need to have one-to-one or many-to-one relation.

b)

A function need to have one-to-one or one-to-many relation.

c)

A function that has inverse has to be one-to-one relation

d)

There are 2 tests to determine one-to-one relation

121.

Given $gh\left(x\right)=-\ \frac{1+2x}{x+4}$ and $g\left(x\right)=x-1$ .

Find

h\left(x\right)

a)

$h\left(x\right)=\ \frac{3-x}{x+4}$

b)

$h\left(x\right)=\ \frac{3x-3}{x+4}$

c)

$h\left(x\right)=\ \frac{3+x}{x+4}$

d)

$h\left(x\right)=\ \frac{3x+3}{x+4}$

122.

Which of the following graphs represents y = −1 − x²?

a)

A

b)

B

c)

C

d)

D

123.

Which of the following graphs represents

y = x³ + 4?

a)

A

b)

B

c)

C

d)

D

124.

Which of the following is the function of the graph?

a)

y = 2x³ + 8

b)

y = 2x³ − 8

c)

y = −2x³ − 8

d)

y = −2x³ + 8

125.

This is one of the methods to prove a function is a one to one function.

Verify whether this is the correct way to show it.

a)

Yes

b)

No

126.

Which is the correct graph for the function $f\left(x\right)=4-\sqrt{x+1}$ ?

a)

b)

c)

d)

127.

Which graph shows the inverse of the graph above?

a)

b)

c)

d)

128.

a)

TRUE

b)

FALSE

129.

Was the inverse function found correctly?

a)

no,

b)

yes

130.

Which of the following functions has itself as inverse?

a)

$f\left(x\right)=\frac{1-x}{1+x}$

b)

$f\left(x\right)=1+x$

c)

$f\left(x\right)=x^3-1$

d)

$f\left(x\right)=1-x^2$

131.

An inverse for quadratic function generally doesn't exist.

What can we do to make the inverse exist?

a)

Limiting its range to only positive values

b)

Limiting its domain to half

c)

Reflect its negative axis

d)

Multiply the function with negative

132.

In completing the square for a quadratic $ax^2+bx+c$ , which of the following is NOT one of the steps?

a)

the value of a must be 1

b)

use $+\left(\frac{b}{2}\right)^2-\left(\frac{b}{2}\right)^2$

c)

factorise using $A^2+2AB+B^2=\left(A+B\right)^2$

d)

make the quadratic equal 0

133.

Which is the correct factorisation of a cubic function $f\left(x\right)=-2x^3-4x^2+10x+12$ ?

a)

$f\left(x\right)=-2\left(x+1\right)\left(x-2\right)\left(x+3\right)$

b)

$f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x+3\right)$

c)

$f\left(x\right)=-\left(x+1\right)\left(x-2\right)\left(x+3\right)$

d)

$f\left(x\right)=2\left(x+1\right)\left(x-2\right)\left(x+3\right)$

134.

Which is the correct factorisation of a cubic function $f\left(x\right)=\quad3x^3+27x^2+72x+48$ ?

a)

$f\left(x\right)=3\left(x+1\right)\left(x+4\right)^2$

b)

$f\left(x\right)=\left(x+1\right)\left(x+4\right)^2$

c)

$f\left(x\right)=3\left(x+1\right)^2\left(x+4\right)$

d)

$f\left(x\right)=\left(x+1\right)^2\left(x+4\right)$

135.

If a horizontal line touched a graph more than once, what can we say about the function?

a)

The inverse of the function doesn't exist

b)

The function is a one to one function

c)

The function is a linear function

d)

The inverse of the function is itself

136.

Given a function $f\left(x\right)=x^3+2x^2-5x-6$ .

Find its zeros.

a)

$-3,-1,2$

b)

$x=-3,\ x=-1,\ x=2$

c)

$\left(x+3\right),\ \left(x+1\right),\ \left(x-2\right)$

d)

$\left(x+3\right)\left(x+1\right)\left(x-2\right)$

137.

Which of the following statement is INCORRECT regarding the graph?

*pink = f(x)

*purple = g(x)

a)

f(x) and g(x) are inverse of each other

b)

Domain for f(x) is equal to the range of g(x)

c)

Both functions are one to one functions

d)

Range of f(x) is $\left(-\infty,\infty\right)$

138.

GIven $f\left(x\right)=x^2+4$ and $g\left(x\right)=x-9$ . Find the value of x if $fg\left(x\right)=gf\left(x\right)$

a)

x = 5

b)

$x=-\frac{1}{5}$

c)

x = -5

d)

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

139.

If there is a function $f\left(x\right)$ such that $f^2\left(x\right)=x$ , which of the following statement is FALSE?

a)

f(x) is inverse of itself

b)

$f^{13}\left(x\right)=f\left(x\right)$

c)

$f^{20}\left(x\right)=f\left(x\right)$

d)

$f^8\left(f\left(x\right)\right)=f\left(x\right)$

140.

Which of these is the test for one to one function?

*you can choose more than one

a)

Horizontal Line Test

b)

Algebraic method

c)

Vertical Line Test

d)

Arrow Test

141.

Solve:

2x² + 5x ≥ 12

a)

[-4, 1.5]

b)

(−∞, -4) U (1.5, ∞)

c)

(−∞, -4] U [1.5, ∞)

d)

no solution

142.

Solve: 5x - 10x² < 0

a)

(0, ½)

b)

[0, ½]

c)

(−∞, 0) U (½, ∞)

d)

(- ½ , 0)

143.

Determine the solution of the given quadratic inequality.

\left(x+2\right)\left(2x-3\right)>0

a)

$x<-2\ or\ x>\frac{3}{2}$

b)

$-2<x<\frac{3}{2}$

144.

Determine the solution of the given quadratic inequality.

\left(x+11\right)\left(3x+11\right)\ge0

a)

$x\le-11\ or\ x\ge-\frac{11}{3}$

b)

$-11\le x\le-\frac{11}{3}$

145.

-3x² + 6x - 3 > 0

a)

no solution

b)

all reals

c)

x = 1

d)

x ≠ 1

146.

-3x² + 45 ≥ 6x

a)

-5 < x < 3

b)

-5 ≤ x ≤ 3

c)

x < -5 or x > 3

d)

x ≤ -5 or x ≥ 3

147.

$8\left|x\right|+32>0$

a)

no solution

b)

all numbers

c)

$x>2,\ x<-2$

d)

$x=\pm2$

148.

Solve the quadratic inequality:

$x^2-4x-5\le0$

a)

$-1\le x\le5$

b)

$-5\le x\le1$

c)

$x\ge5\ OR\ \ x\le-1$

d)

$x\le-5\ OR\ \ \ x\ge1$

149.

Solve the quadratic inequality:

$x^2+3x-28\ge0$

a)

$x\ge4\ OR\ \ x\le-7$

b)

$x\ge7\ OR\ \ x\le-4$

c)

$-4\le x\le7$

d)

$-7\le x\le4$

150.

Solve the quadratic inequality:

$x^2-49\ge0$

a)

$x\le-7\ OR\ \ x\ge7$

b)

$x\ge-7\ OR\ \ x\ge7$

c)

$-7\le x\le7$

d)

$x\ge-7\ AND\ \ x\ge7$

151.

a)

(-2,2)

b)

$\left(-\infty,\ -2\right)\cup\left(2,\ \infty\right)$

c)

[-2,2]

d)

$\left(\infty,\ -2\right)\cup\left(2,\ -\infty\right)$

152.

Solve for x:
$\frac{3x-7}{x+2}>1$

a)

$\left(-2,\ \frac{9}{2}\right)$

b)

$\left(-\infty,-2\right)\cup\left(\frac{9}{2},\ \infty\right)$

c)

$\left(-\infty,-2\right)\cup\left(\frac{7}{3},\ \infty\right)$

d)

$\left(-2,\ \frac{7}{3}\right)$

153.

Solve the rational inequality and state your solution in interval notation.

$\frac{-x}{x-3}\ge0$

a)

$\left(0,\ +\infty\right)$

b)

$\left[0,\ 3\right)$

c)

$\left(-\infty,\ 0\right)\cup\left(3,\ +\infty\right)$

d)

$\left(-\infty,\ 0\right]\cup\left[3,\ +\infty\right)$

154.

a)

(-2,2)

b)

$\left(-\infty,\ -2\right)\cup\left(2,\ \infty\right)$

c)

[-2,2]

d)

$\left(\infty,\ -2\right)\cup\left(2,\ -\infty\right)$

155.

Do we need to check the answer for $\left|1-x\right|=2x-5$ ?

a)

Yes

b)

No

156.

Solve $\left|1-x\right|=2x-5$

a)

x=2, x=4

b)

x=-2, x=-4

c)

x=2

d)

x=4

157.

Do we need to check the answer for $\left|x^2+2x-4\right|=4$ ?

a)

Yes

b)

No

158.

Solve $\left|5-6x\right|>7$

a)

$\frac{-1}{3}\le x\le2$

b)

$x\le-2\ or\ x\ge\frac{1}{3}$

c)

$x<-3\ or\ x>\frac{1}{2}$

d)

$x<\frac{-1}{3}\ or\ x>2$

159.

State the solution set of $\left|7-3x\right|\le2x+5$

a)

$\left\{x:\ x\le-2\ or\ x\ge\frac{1}{5}\right\}$

b)

$\left\{x:\ x\in R\right\}$

c)

$\left\{x:\ \frac{2}{5}\le x\le12\right\}$

160.

Solve $\left|3x+1\right|\ge x-4$

a)

$\left\{x:\ x\le\frac{-5}{2}\ or\ x\ge\frac{3}{4}\right\}$

b)

$\left\{x:\ -\frac{5}{2}\le x\le\frac{3}{4}\right\}$

c)

$\left\{x:\ x\in\left(-\infty,\ \infty\right)\right\}$

161.

Find the inverse of the matrix

a)

b)

c)

d)

162.

Based on previous calculation, find the values of x, y and z.

a)

x=3, y=-1, z=-15

b)

x=1, y=-3, z=21

c)

x=3, y=-1, z=15

d)

x=3, y=1, z=-15

163.

Find the determinant for matrix A

a)

3

b)

-5

c)

9

d)

-1

164.

If $\left|A\right|=3$ and $\left|B\right|=-5$ , find the determinant for matrix AB

a)

-15

b)

-2

c)

-10

d)

-5

165.

a)

2a

b)

-a

c)

-2a

d)

a

166.

a)

2a

b)

-a

c)

-2a

d)

a

167.

a)

2a

b)

-a

c)

-2a

d)

a

168.

a)

27a

b)

3a

c)

$27a^3$

d)

$9a^3$

169.

If matrix AB were compatible to be multiplied, which of these statements is WRONG?

a)

The number of columns of matrix A is equal to the number of rows of matrix B

b)

The number of rows of matrix A is equal to the number of columns of matrix B

c)

The dimension of matrix AB is (number of rows matrix A) by (number of columns matrix B)

d)

170.

If $AB=4I$ , find $B^{-1}$

a)

$\frac{1}{4}A$

b)

$-\frac{1}{4}A$

c)

$4A$

d)

$-4A$

171.

Which of the following statements is TRUE for a singular matrix?

a)

Its determinant greater than 0

b)

It does not have an inverse

c)

They are inverse of itself

d)

Its determinant less than 0

172.

a)

b)

c)

d)

173.

Classify the matrix

a)

Square matrix, Diagonal matrix

b)

Triangular matrix, Diagonal matrix

c)

Square matrix, Identity matrix

d)

Square matrix, triangular matrix

174.

Given matrices A & B:
A is a (4x33) matrix
B is a (33x1) matrix
What are the dimensions of the product of A times B?

a)

4x1

b)

4x33

c)

33x1

d)

Matrix does not exist

175.

If two rows of a matrix A are identical, then det(A)

a)

Zero

b)

A positive number

c)

One

d)

Can not say

176.

Which of the following is a diagonal matrix?

a)

b)

c)

d)

177.

Which of the following is NOT a singular matrix?

a)

b)

c)

d)

178.

AB=C

What is the inverse for matrix A?

a)

b)

c)

d)

179.

What is the value of k?

a)

9

b)

5

c)

-9

d)

-5

180.

If matrix A+B were compatible to be added, which of these statements is CORRECT?

a)

$A+B=B+A$

b)

Matrix A and B will also be compatible to be multiplied

c)

$\left|A\right|=\left|B\right|$

d)

181.

a)

A

b)

B

c)

C

d)

D

182.

a)

A

b)

B

c)

C

d)

D

183.

Simplify $\frac{24x^3y^7}{2x^5y^2}$

a)

$\frac{12y^5}{x^2}$

b)

$\frac{24x^5}{y^2}$

c)

$12x^2y^5$

d)

$24$

184.

When

\sqrt{\frac{24x^3y^8}{xy^3}}

is simplified the result is (give your answer in rational exponent form).

a)

$2xy^2\left(6y\right)^{\frac{1}{2}}$

b)

$\left(24x^3y^5\right)^{\frac{1}{2}}$

c)

$2xy\sqrt{12x^3y^4}$

d)

$2x^2y\left(12x^2y^4\right)^{\frac{1}{2}}$

185.

$Rationalize\ \frac{5}{3+\sqrt{2}}+\sqrt{2}$

a)

$\frac{15+2\sqrt{2}}{7}$

b)

$\frac{15-2\sqrt{2}}{7}$

186.

Which of these is the WRONG rule of surds?

a)

$𝑎\sqrt{x}+𝑏\sqrt{x}=(𝑎+𝑏)\sqrt{x}\$

b)

$\sqrt{a+b}=\sqrt{a}+\sqrt{b}$

c)

$\sqrt{a}×\sqrt{b}=\sqrt{ab\ }\ \$

d)

$\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$

187.

Rationalize the denominator. Simplify the answer. $\frac{5\ -\ \sqrt{21}}{\sqrt{3}\ -\ \sqrt{7}}$

a)

$\frac{\sqrt{3}\ +\sqrt{7}}{2}$

b)

$\frac{\sqrt{3}+7}{-2}$

c)

$\frac{\sqrt{3}-\ \sqrt{7}}{2}$

d)

$\frac{\sqrt{3}\ -2\sqrt{7}}{10}$

188.

Simplify $\frac{3^n\times9^{n+1}}{3^{n-1}\times9^{n-1}}$ .

a)

3

b)

27

c)

81

d)

243

189.

Given log₅(4x − 7) = log₅(x + 5).

Find the value of x.

a)

3

b)

4

c)

7

d)

12

190.

a)

A

b)

B

c)

C

d)

D

191.

Rationalise $\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{2}-1}$

a)

$-2\sqrt{2}$

b)

$2\sqrt{2}$

c)

$3+\sqrt{2}$

d)

$3+2\sqrt{2}$

192.

Solve

\sqrt{x-3}=2

a)

4

b)

5

c)

6

d)

7

193.

Solve

3\sqrt{1-x}=x+3

a)

-15, 0

b)

-15

c)

0

d)

no solutions

194.

In order to solve

3\sqrt{1-x}=x+3

, do you need to do recheck?

a)

Yes

b)

No

195.

Solve for x.

a)

$\frac{\log6-3\log3}{4\log3-2\log6}$

b)

$\frac{\log6+3\log3}{4\log3-2\log6}$

c)

$\frac{2\log6+\log6}{4\log3-3\log3}$

d)

no solution

196.

$2\log_4x^{ }=\log_43+\log_4\left(x+6\right)$

Solve this equation

a)

$x=6$

b)

$x=6,\ x=-3$

c)

$x=-18$

d)

no solutions

197.

Solve
$\ln14+\ln\left(2-x\right)=\ln x+\ln\left(x-11\right)$

a)

4

b)

4 and -7

c)

-7

d)

no solutions

198.

Solve
$\log_8\ x-\log_8\left(x-1\right)=1$

a)

$\frac{8}{7}$

b)

No Solution

c)

$-\frac{7}{64}$

d)

$\frac{55}{6}$

199.

Solve for x: $9^x=60$

a)

1.748

b)

x = 6.667

c)

x = 0.537

d)

x = 1.863

200.

$125^x\cdot25^{2x+1}=\left(\frac{1}{5}\right)^{x+6}$

Solve.

a)

$-\frac{18}{6}$

b)

-1

c)

1

d)

$\frac{18}{6}$

201.

Solve $4^{\left(x-\frac{1}{2}\right)}-9\left(2^{\left(x-2\right)}\right)+1=0$

(You can choose more than 1 answer)

a)

2

b)

$\frac{1}{2}$

c)

4

d)

-1

202.

In order to solve

\sqrt{x-3}=2

, do we need to do recheck?

a)

No

b)

Yes

RANDOM REVISION

Total questions: 202

Worksheet time: 5hrs 0mins

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