Free Printable Optional Maths Exam 2078

1.

Formed by the intersection of two lines, the horizontal axis and the vertical axis.

a)

Coordinate Plane

b)

Quadrants

c)

Discrete Graph

d)

Relation

2.

The horizontal axis on a coordinate plane is called......

a)

the origin

b)

the y-axis

c)

the x-axis

d)

the range

3.

The vertical axis on a coordinate plane is called......

a)

the origin

b)

the y-axis

c)

the x-axis

d)

the range

4.

The four regions into which the x- and y- axis separate the coordinate plane

a)

Coordinates

b)

Zeros

c)

Input

d)

Quadrants

5.

the POINT at which the x- and y-axis intersect on the coordinate plane

a)

the range

b)

the domain

c)

the origin

d)

the relation

6.

a set of ordered pairs

a)

relation

b)

mapping

c)

function

d)

input

7.

The set of y-values in the ordered pair in a relation

a)

domain

b)

range

c)

coordinates

d)

origin

8.

The set of x-values in the ordered pair in a relation

a)

domain

b)

range

c)

coordinates

d)

origin

9.

Illustrates how each element of the domain is paired with an element of the range.

a)

function notation

b)

relation

c)

function

d)

mapping

10.

A relation in which each element of the domain is paired with exactly one element of the range

a)

function notation

b)

relation

c)

function

d)

mapping

11.

A way to name a function that is defined by an equation. "Replace "y" with "f(x)"

a)

function notation

b)

relation

c)

function

d)

mapping

12.

If any vertical line posses through the graph of a relation no more than once, then its a function

a)

Domain

b)

Range

c)

Vertical Line Test

d)

Mapping

13.

Let R be a relation on N given by R={(x,y):x=y-2, y>6}, then

a)

(2,4)∈R

b)

(3,8)∈R

c)

(8,7)∈R

d)

(6,8)∈R

14.

If A={a,b,c} theen R={(b,c)}, then R is

a)

Reflexive only

b)

Symmetric only

c)

Transitive only

d)

equivalence relation

15.

For real numbers x and y define xRy iff x-y+√2 is an irrational number. then R is

a)

reflexive

b)

symmetric

c)

transitive

d)

none of these

16.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

17.

Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is

a)

Reflexive and Symmetric

b)

Transitive and symmetric

c)

Equivalence

d)

Reflexive, transitive but not symmetric

18.

Let the function be defined by f(x) = 5x² + 2 for all x ϵ R. Then f is

a)

onto function

b)

one-one, onto function

c)

one-one, into function

d)

many –one , into function

19.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

20.

What is the domain?

a)

the set of all x-values

b)

the set of all y-values

21.

What is the domain?

a)

the set of all x-values

b)

the set of all y-values

22.

What is the range?

a)

the set of all x-values

b)

the set of all y-values

23.

List the ordered pairs

a)

Input and Output

b)

(0,12), (2,10), (4,8), (6,6)

c)

(12,0), (10,2), (8,4), (6,6)

d)

(6,6)

24.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

25.

What is the degree of this polynomial?

2x⁴- 3x⁵+ x

a)

-3

b)

2

c)

4

d)

5

26.

What is the constant of this polynomial?

2x³- 8x²+ 3x - 7

a)

2

b)

-8

c)

3

d)

-7

27.

Simplify the Expression:

3x + 6 - 2x +7

a)

14

b)

14x

c)

x + 13

d)

x - 13

28.

The number in front of the variable is called the....

a)

exponent

b)

base

c)

coefficient

d)

fronter

29.

Which pair is an example of like terms?

a)

2a and 2b

b)

x and x²

c)

3k and 3k³

d)

y² and 2y²

30.

Simplify by combining like terms:
4x² - 3x + 11 -2x

a)

4x² - 5x + 11

b)

11x + 11

c)

16x² - 5x + 11

d)

10x²

31.

Find the product:
(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

32.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

33.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 4y²- y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

34.

The next two terms of the sequence 8,4,2,1, 1/2 are

a)

1/3 and 1/4

b)

1/4 and 1/8

c)

1/8 and 1/6

d)

1/5 and 1/7

35.

In an arithmetic sequence if a₁₅ =108 and d=7, find a₁.

a)

14

b)

101

c)

206

d)

10

36.

Identify the common difference.
97, 86, 75, 64, ...

a)

8

b)

11

c)

-11

d)

-8

37.

The next two terms of the sequence 4,7,10,13 are ....

a)

16 and 19

b)

15 and 19

c)

16 and 18

d)

15 and 18

38.

Expand: $\sum_{k=3}^6\left(2k-1\right)$

a)

4, 6, 8, 10

b)

4, 6, 8

c)

5, 7, 9, 11

d)

5, 7, 9

39.

What must be true in order to ADD two matrices?

a)

They must be square.

b)

The dimensions must be equal.

c)

The determinant can't equal 0.

d)

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

40.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

41.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

42.

What is a Matrix?

a)

An equation of over 5 numbers or symbols

b)

A set of numbers in rows and columns

c)

A method of finding the n^th value of a series

d)

A complicated number system

43.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

44.

How many rows are in a 7 x 3 matrix?

a)

7

b)

3

c)

21

d)

10

45.

How many columns are in a 5 x 4 matrix?

a)

5

b)

4

c)

20

d)

9

46.

When a 3x6 matrix is multiplied by a 6x5 matrix, what will the dimensions of the product be?

a)

6x6

b)

3x6

c)

3x5

d)

5x6

47.

What is the value of element a₃₄?

a)

2

b)

-3

c)

6

d)

1

48.

Find the product.

a)

b)

c)

d)

No Product Exists

49.

How would a scalar multiplication be carried out for a matrix?

a)

Add the Scalar to every element in the matrix

b)

Dot product the rows of one matrix with the columns of the other matrix

c)

Multiply every element with the scalar to create a new matrix

d)

subtract the elements in the first matrix from the elements of the second matrix

50.

Find the co-ordinates of the point which divides the line segment joining the points (6,3) and (-4,5) in the ratio 3:2 internally.

a)

(0 , 5)

b)

(1 , 21/5)

c)

(0 , 21/5)

d)

(1 , 5)

51.

How is the distance formula correctly written:

a)

$d\ =\ \sqrt{\left(y_{1\ }-\ y_2\right)^2\ -\left(x_{2\ }-\ x_1\right)^2}\$

b)

$d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2_{\ }}-\ y_1\ \right)2}$

c)

$d\ =\ \sqrt{\left(y_{1\ }-\ y\ _2\right)^2\ +\ \left(x_{2\ }-\ x_1\right)}^2$

d)

d = $\sqrt{\left(x\right)^2-\ \left(y\right)^2}$

52.

What is the center of MN given M(3, -1) and N(7, -5)

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

53.

The centroid is the point of concurrency of the 3 ____ of a triangle.

a)

Medians

b)

Midsegments

c)

Perpendicular Bisectors

d)

Angle Bisectos

54.

Find the coordinates of the centroid of the triangle whose vertices are V(-7, -6), T(-8, 0) and W(0,0)

a)

(-3, -7)

b)

(-5, -2)

c)

(-3, -9)

d)

(-5, -2.5)

55.

Find the equation of the straight line with slope 2 passing through (-3, 4) .

a)

$2x-y-2=0$

b)

$2x-y-10=0$

c)

$2x-y+2=0$

d)

$2x-y+10=0$

56.

Find the equation of the straight line with slope -7 and y-intercept 4 .

a)

$4x-y-7=0$

b)

$7x+y-4=0$

c)

$x-4y+7=0$

d)

$x+7y-4=0$

57.

Find the equation of the straight line passing through A(10, -2) and B(4, 1) .

a)

$x+2y-6=0$

b)

$x+2y-9=0$

c)

$x+14y+12=0$

d)

$x+14y+18=0$

58.

Straight line $3x-9y-k=0$ passes through A(2, 1) . Find the value of $k$ .

a)

-15

b)

-3

c)

3

d)

15

59.

What does 'b" represent in y=mx+b

a)

y-intercept

b)

macaroni

c)

nothing

d)

slope

60.

What line goes through (1,4) and has gradient 2

a)

y=2x+2

b)

y=x+1

c)

y=4x-1

d)

y=2x+4

61.

Find the x-intercept of straight line $3x-7y+21=0$ .

a)

$-7$

b)

$-\frac{3}{7}$

c)

$\frac{7}{3}$

d)

$3$

62.

The y-intercept of straight line $3x-6y+5k=0$ is -2. Find the value of k.

a)

$\frac{12}{5}$

b)

$\frac{6}{5}$

c)

$-\frac{6}{5}$

d)

$-\frac{12}{5}$

63.

The equation of a straight line is 2x +5y =7. Find the gradient of the line

a)

-2

b)

-5/2

c)

-2/5

d)

5

64.

Which of the following points is the point of intersection of the lines y = 2x + 1 and y = - x + 7

a)

(-2, 9)

b)

(8, -1)

c)

(2, 5)

d)

(6, 13)

65.

Determine whether the following straight lines

3y = -6x + 3 and y + 2x = 14

are parallel or not.

a)

Yes

b)

No

66.

What is the y-intercept in the equation

y= - 2x

a)

-2

b)

-2x

c)

0

d)

1

67.

A moving point P maintains an equal distance from two parallel lines. Which of the following does the locus of P belong to?

a)

A circle

b)

A straight line

c)

Two parallel lines

d)

Two perpendicular lines

68.

Let A, B be two points. P is a point such that PA perpendicular to PB. What is the locus of P?

a)

The locus of P is a circle with diameter AB

b)

The locus of P is a circle with centre A and diameter AB

c)

The locus of P is the perpendicular bisector of AB

d)

The locus of P is a pair of lines parallel to AB.

69.

What is the perimeter (in units) of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

a)

65

b)

8.06

c)

14

d)

19.06

70.

What is the area (in square units) of the triangle formed by the points (-3,1), (-3,5), and (4,1)?

a)

19.06

b)

14

c)

28

d)

8.06

71.

Square ABCD has vertices A(-2,-3), B(4, -1), C(2, 5), and D(-4, -3)and . What is the area of the square?

a)

$2\sqrt{10}$

b)

$4\sqrt{10}$

c)

40

d)

20

72.

Choose the points between I and G.

a)

A

b)

E

c)

B

d)

H

e)

D

73.

Vector is a quantity with:

a)

magnitude and direction

b)

magnitude

c)

direction

d)

none of the above

74.

Given points A(2, 1) and B(-4, 1). Explain why the vector AB is parallel to the x-axis

a)

because vector AB is a multiple of the unit vector i

b)

because vector AB is a multiple of the unit vector j

c)

because vector AB is a multiple of the unit vector k

75.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

76.

If vector a= (4, -5) and vector b= (-7, 4) Find a+b

a)

(3, 9)

b)

(-3, -1)

c)

(11, 1)

d)

(-3, -9)

77.

If vector a= (4, -5) and vector b= (-7, 4) Find a-b

a)

(-11, -9)

b)

(11, 9)

c)

(11, -9)

d)

(-3, -1)

78.

Let vector a= (5, -7) and vector b= (-12, 2) Find 2b-4a

a)

(44, -32)

b)

(-4, 24)

c)

(-44, 32)

d)

(4, -24)

79.

Reflect the point (2, -4) over the y-axis.

a)

(-4, 2)

b)

(-2, 4)

c)

(-2, -4)

d)

(2, 4)

80.

Reflect (6, -3) over the line x-axis.

a)

(6, 3)

b)

(-6, -3)

c)

(-3, 6)

d)

(3, -6)

81.

B(-2, -4)
Reflect over the line y = x

a)

(2, -4)

b)

(-4, 2)

c)

(-4, -2)

d)

(4, 2)

82.

Dilate point A by a scale factor of 3. What are the coordinates of A'?
A(3,3)

a)

A'(9,9)

b)

A'(6,6)

c)

A'(0,0)

d)

(1,1)

83.

A dilation is which of the following:

a)

An enlargement

b)

A reduction

c)

Either an enlargement or a reduction

d)

Neither an enlargement or a reduction

84.

What is the only rule that will flip the order of x and y?

a)

180 degree rotation

b)

90 degree or 270 degree rotation

c)

Reflection over the y-axis

85.

What is the rule for a 270 degree clockwise rotation?

a)

(x, y) --> (-y, x)

b)

(x, y) --> (y, -x)

c)

(x, y) --> (-x, -y)

86.

What is the rule for a 90 degree counterclockwise rotation?

a)

(x, y) --> (-y, x)

b)

(x, y) --> (y, -x)

c)

(x, y) --> (y, x)

87.

What is the rule for a 180 degree clockwise rotation?

a)

(x, y) --> (-y, x)

b)

(x, y) --> (y, -x)

c)

(x, y) --> (-x, -y)

88.

What is the image of J (8, -6) after a rotation of 180° counterclockwise?

a)

J' (8, 6)

b)

J' (-6, 8)

c)

J' (-8, 6)

d)

J ' (-8, -6)

89.

Triange ABC is translated to image A’B’C’. In this translation, A(5,1) maps to A’(6,-2). The coordinates of B’ are (-1,0). What are the coordinates of B?

a)

B( 2 , -3)

b)

B( -2 , -3)

c)

B( 2, 3)

d)

B(-2 , 3 )

90.

What transformation is happening?
(x, y) ----> (x + 2, y - 3)

a)

slide up 2, left 3

b)

slide right 2, up 3

c)

slide right 2, down 3

d)

slide left 3, right 2

91.

A slide is also called a _________.

a)

Translation

b)

Reflection

c)

Rotation

d)

Transformation

92.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

93.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

94.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

95.

What is the ratio for Sine?

a)

Hyp/Opp

b)

Opp/Hyp

c)

Opp/Adj

d)

Adj/Opp

96.

What is the ratio for Tangent

a)

Opp/Adj

b)

Adj/Opp

c)

Opp/Hyp

d)

Hyp/Opp

97.

Sin X

a)

¹⁵/₁₇

b)

⁸/₁₅

c)

¹⁷/₈

d)

¹⁵/₈

98.

*

a)

cos x

b)

csc x

c)

sec x

d)

cot x

99.

*

a)

csc x

b)

sec x

c)

cot x

d)

tan x

100.

*

a)

csc² x

b)

sec² x

c)

cot² x

d)

tan² x

101.

sin(90⁰-θ) =

a)

cosθ

b)

cscθ

c)

secθ

d)

tanθ

102.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

103.

Rewrite tan(x) in terms of sin(x) and cos(x).

a)

tan(x) = cos(x)/sin(x)

b)

tan(x) = 1/cot(x)

c)

tan(x) = sin(x)/cos(x)

d)

tan(x) = opp/adj

104.

Which expression is equivalent to the trigonometric expression $\frac{\sin^2\left(\theta\right)+\cos^2\left(\theta\right)}{\sin\left(\theta\right)}$ ?

a)

$\sec\left(\theta\right)$

b)

$1$

c)

$\csc\left(\theta\right)$

d)

$\csc^2\left(\theta\right)$

105.

Which expression is equivalent to the trigonometric expression $\csc^2\left(\theta\right)-\cot^2\left(\theta\right)+\tan^2\left(\theta\right)$ ?

a)

$\sec^2\left(\theta\right)$

b)

$\sec\left(\theta\right)$

c)

$\csc\left(\theta\right)$

d)

$\csc^2\left(\theta\right)$

106.

Select the MOST SIMPLIFIED answer for:

$\frac{\sin^2x}{\sin x\cos x}$

a)

$\cot x$

b)

$\frac{\cos x}{\sin x}$

c)

$\frac{\sin x}{\cos x}$

d)

$\tan x$

107.

Select the MOST SIMPLIFIED answer for:

$\frac{\tan x}{\sin x}$

a)

$\csc x$

b)

$\frac{1}{\cos x}$

c)

$\sec x$

d)

$\frac{1}{\sin x}$

108.

$\sin30\degree=$

a)

$\frac{1}{2}$

b)

$\frac{\sqrt{2}}{2}$

c)

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

d)

$\sqrt{3}$

109.

$\sin60\degree=$

a)

$\frac{1}{2}$

b)

$\frac{\sqrt{2}}{2}$

c)

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

d)

$\sqrt{3}$

110.

$\tan30\degree=$

a)

$\frac{\sqrt{3}}{3}$

b)

$\frac{\sqrt{2}}{2}$

c)

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

d)

$\sqrt{3}$

111.

$\sin45\degree=$

a)

$\frac{\sqrt{3}}{3}$

b)

$\frac{\sqrt{2}}{2}$

c)

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

d)

$1$

112.

Which of the following are the trigonometric special angles?

a)

$45^{\degree},\ 20^{\degree},\ 0^{\degree},\ 90^{\degree},\ 60^{\degree}$

b)

$50^{\degree},\ 20^{\degree},\ 0^{\degree},\ 80^{\degree},\ 60^{\degree}$

c)

$\ 0^{\degree},\ 90^{\degree},\ 60^{\degree},\ 35^{\degree},\ 45^{\degree}$

d)

$\ 0^{\degree},\ 90^{\degree},\ 60^{\degree},\ 30^{\degree},\ 45^{\degree}$

113.

What is the mean?

a)

# happening the most

b)

the number in the middle

c)

biggest-smallest

d)

the average

114.

Find the mean of this data set:

2, 57, 38, 42, 6

a)

29

b)

38

c)

50

d)

145

115.

Find the median of this data set:

4, 2, 7, 4, 3

a)

2

b)

5

c)

7

d)

4

116.

Find the mode of this data set:

67, 74, 95, 98, 98, 99, 102

a)

90.4

b)

35

c)

92

d)

98

117.

A technique that divide a set of data into ten equal parts.

a)

Quartile

b)

Decile

c)

Percentile

118.

A technique that divide a set of data into one hundred equal parts.

a)

Quartile

b)

Decile

c)

Percentile

119.

$Q_1$ is always equal to $P_3$

a)

True

b)

False

120.

A company manufactures computer terminals. The following data give the number of computer terminals produced at the company for a sample of 5 days. What is the third decile? 23 24 27 32 33

a)

23

b)

24

c)

27

d)

32

121.

A company manufactures computer terminals. The following data give the number of computer terminals produced at the company for a sample of 5 days. What is the seventy-fifth percentile? 23 24 27 32 33

a)

23

b)

24

c)

27

d)

32

122.

This fractile divides the set into 4 equal parts.

a)

Median

b)

Quartile

c)

Decile

d)

Percentile

123.

Angie ranks 10th in a class of 40. Her percentile is

a)

75

b)

90

c)

10

d)

25

124.

Rochelle got a score of 55 which is equivalent to 70th percentile in a mathematics test. Which of the following is not true?

a)

She scored above 70% of her classmates

b)

Thirty percent of the class got scores of 55 and above

c)

If the passing mark is the first quartile, she passed the test

d)

Her score is below the 5th decile

125.

33, 25, 42, 25, 31, 37, 46, 29, 38

What is the third quartile (Upper Quartile) of the data using Mendenhall and Sincich method?

a)

37

b)

38

c)

40

d)

46

126.

Which of the following is the mean absolute deviation for the set of data?
2.50 3.75 1.25 2.25 3.00

a)

3.3

b)

0.66

c)

2.50

d)

2.55

127.

What is the first step when calculating the Mean Absolute Deviation?

a)

Find the distance each value is from the mean

b)

Find the mean of the distances

c)

Find the mean of the data

128.

Which mean absolute deviation would be more consistent? 4.2 or 8.5?

a)

4.2

b)

8.5

129.

True or false? :The larger the Mean Absolute Deviation the more consistent the data is.

a)

True

b)

False

130.

What is the standard deviation for the data given:

5, 10, 7, 12, 0, 20, 15, 22, 8, 2

a)

6.89

b)

10.1

c)

7.26

d)

9

131.

All of the below sets have the same mean.
Set 1-Standard Deviation=3.1
Set 2-Standard Deviation=4.9
Set 3-Standard Deviation=1.7
Set 4-Standard Deviation=3.2
Which set of data probably has the points closest to the mean?

a)

1

b)

2

c)

3

d)

4

132.

What does this symbol represent?

a)

Standard Deviation

b)

Variance

c)

Mean Absolute Deviation

d)

Sigma

133.

What is the variance for the data given:
5, 10, 7, 12, 0, 20, 15, 22, 8, 2

a)

47.47

b)

102.01

c)

52.77

d)

81

134.

Which of the following is a measure of variability?

a)

mean

b)

median

c)

mode

d)

standard deviation

135.

What does variance represent?

a)

How many different variations are in the data set.

b)

How the population varies compared to the sample.

c)

How spread out each data value is from the mean.

d)

The range, but with a bunch of other stuff going on.

136.

How do you calculate the standard deviation?

a)

Divide the variance by 2.

b)

Its a long process and I can't explain it right now.

c)

Find the mean and multiply it by the variance.

d)

Take the square root of the variance.

137.

If the standard deviation of a data set is 10, what is the variance?

a)

20

b)

100

c)

2.5

d)

10

Optional Maths Exam 2078

Total questions: 137

Worksheet time: 2hrs 17mins

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