Free Printable MATHEMATICS ACHIEVEMENT TEST(MAT)

1.

The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.

a)

y = 8x + 50

b)

C = 50m +8

c)

y = 50x + 8

d)

C = 8m + 50

2.

Your four-month bill for the gym comes to $221. That includes the cost per month of $50 plus the one-time membership fee. How much is the membership fee?

a)

$21

b)

$171

c)

$4.42

d)

$15.50

3.

A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. Interpret the y-intercept in context.

a)

The additional fee of $8.

b)

The initial fee of $25.

c)

The additional fee of $25.

d)

The initial fee of $8.

4.

A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. Interpret the y-intercept in context.

a)

The additional fee of $8.

b)

The initial fee of $25.

c)

The additional fee of $25.

d)

The initial fee of $8.

5.

Linda bought a Bloodgood Japanese Maple tree. In two years, the tree was 7' tall and in 10 years the tree grew to its mature height of 15'. Write an equation in slope-intercept form that shows the number of years, t, it takes to reach a certain height, h.

a)

h = - t + 9

b)

h = t + 5

c)

h = t - 9

d)

h = -t + 5

6.

Derrick started up a charity for the local animal shelters. He started selling handmade dog leashes for $5. It cost him $120 to get the supplies to make the leashes. Write an equation for the amount of money he raises, A, if he sells x amount of leashes.

a)

A = 120 + 5x

b)

A = 120x + 5

c)

A = -120 + 5x

d)

A = 120 - 5x

7.

Write an equation in slope-intercept for of the line between the points: (-2, 8) and (3, -12)

a)

y = -(4/5)x + (32/5)

b)

y = -4x

c)

y = -4x + 16

d)

y = 4x

8.

Find the slope between the points
(8, 5) and (-9, 5)

a)

Zero

b)

Undefined

c)

-10/17

d)

-10/1

9.

Given $A=\frac{b}{c}$ , what happens to A as b increases and why?

a)

A decreases because b is in the denominator.

b)

A increases because b is in the denominator.

c)

A decreases because b is in the numerator.

d)

A increases because b is in the numerator.

10.

Given $A=\frac{b}{c}$ , what happens to A as c increases and why?

a)

A decreases because c is in the denominator.

b)

A increases because c is in the denominator.

c)

A decreases because c is in the numerator.

d)

A increases because c is in the numerator.

11.

11 011₂=

a)

17₁₀

b)

27₁₀

c)

33₁₀

d)

37₁₀

12.

Given that x₅ = 35_10,then x =

a)

10

b)

12

c)

20

d)

120

13.

101₂+ 111₂=

a)

1000₂

b)

1001₂

c)

1011₂

d)

1100₂

14.

Which of the following is false?

a)

101₂+ 11₂ = 1000₂

b)

101₂- 11₂ = 10₂

c)

101 110₂ = 56₈

d)

234₈ = 1 011 100₂

15.

Given that 43₅< x₁₀< 34_8,which of the following is not a possible value of x?

a)

25

b)

26

c)

27

d)

28

16.

Given that X₁₀= 11₂+ 11₅+ 11_8, find the value of X.

a)

15

b)

16

c)

17

d)

18

17.

110 100₂ - 11 011₂=

a)

10 000₂

b)

10 001₂

c)

11 001₂

d)

11 011₂

18.

Given that 4x5³+ 2x5²+ 5y = 4230_5,find the value of y.

a)

0

b)

2

c)

3

d)

6

19.

1. 100111₂ = ...................₈

a)

47

b)

67

c)

77

d)

11

20.

Which of the following is false?

a)

101₂+ 11₂ = 1000₂

b)

101₂- 11₂ = 10₂

c)

101 110₂ = 56₈

d)

234₈ = 1 011 100₂

21.

What is a⁸÷a³

a)

a³

b)

a⁴

c)

a⁵

d)

a⁶

22.

What is b³xb⁴÷b²?

a)

b⁷

b)

b⁵

c)

b⁶

d)

b^2.5

23.

What is x⁵÷x

a)

x⁵

b)

x⁴

c)

x³

d)

x²

24.

If 8^x = 32^1.5, What is the value of x?

a)

1.5

b)

2.5

c)

3

d)

4

25.

Evaluate 8^1/3* 4^-1/2

a)

8

b)

4

c)

2

d)

1

26.

Evaluate 27^-1/3 * 49^-1/2* 125⁰

a)

210

b)

21

c)

1/21

d)

1

27.

If 5ⁿ= 125 find n.

a)

25

b)

1/3

c)

-3

d)

3

28.

Simplify 27^1/3- 16 ^-1/4

a)

6

b)

5

c)

4

d)

3

29.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

30.

How many significant figures are there in 0.0054 grams?

a)

1

b)

2

c)

3

d)

4

31.

How many significant figures are there in 10.020 moles?

a)

2

b)

3

c)

4

d)

5

32.

What is 6.7 × 10⁴ written

as an ordinary number?

a)

67000

b)

6700

c)

670000

d)

0.00067

33.

What is 45,000 written in standard form?

a)

45 × 10³

b)

4.5 × 10⁴

c)

4.5 × 10³

34.

What is 0.00051

written in standard form?

a)

5.1 × 10^-4

b)

51 × 10^-4

c)

5.1 × 10^-5

35.

What is 3a+5b if a=4, b=6

a)

40

b)

42

c)

44

d)

46

36.

How many significant figures are there in 0.0054 grams?

a)

1

b)

2

c)

3

d)

4

37.

How many significant figures are there in 10.020 moles?

a)

2

b)

3

c)

4

d)

5

38.

Find the value of "?" using approximation :

√(2300) × √(240) = ?

a)

685

b)

705

c)

745

d)

815

e)

635

39.

Find the value of "?" using approximation :

-(4.99)³ + (29.98)² - (3.01)^{4 = ?}

a)

550

b)

590

c)

620

d)

650

e)

690

40.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

41.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

42.

Write in logarithmic form

2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

43.

Solve for x:
log_x25 = 2

a)

5

b)

-5

c)

1/5

d)

-1/5

44.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

45.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

46.

State the property (s) used to simplify the expression

6log 2 = log 64

a)

Product Property

b)

Quotient Property

c)

Power Property

d)

Product and Power Property

47.

State the property (s) used to simplify the expression

log₄20 - 3log₄x = log₄(20/x³)

a)

Power Property

b)

Quotient Property

c)

Quotient and Power Property

d)

Product and Power Property

48.

Write the logarithm expression as a single logarithm

log₆25 - log₆5

a)

log₆125

b)

log₅20

c)

log₆5

d)

log₆30

49.

Write as one logarithm. Simplify, if possible.

log₃9 + log₃27

a)

log₃3

b)

log₃243

c)

log₃1/3

d)

not possible

50.

Expand the logarithm expression

log 6x³y

a)

log 6x³ + log y

b)

log 6 + log x³ + log y

c)

3 log 6 + log x + log y

d)

log 6 + 3log x + log y

51.

Write as one logarithm. Simplify, if possible.

log₃9 + log₃27

a)

log₃3

b)

log₃243

c)

log₃1/3

d)

not possible

52.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

53.

Evaluate the following logarithm:

log₄16

a)

1

b)

-2

c)

2

d)

¹/₂

54.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

55.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

56.

Write as a single logarithm:

log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

57.

A polygon has a sum of interior angle measures equal to 1620°. How many sides does the polygon have?

a)

9

b)

11

c)

13

d)

7

58.

A regular polygon has an EXTERIOR angle with a measure of 60. How many sides does it have?

a)

6

b)

120

c)

3

d)

60

59.

A regular polygon has an INTERIOR angle with a measure of 60. How many sides does it have?

a)

6

b)

120

c)

3

d)

60

60.

What is the SUM of the angle measures in a triangle (3 sides)?

a)

60°

b)

90°

c)

120°

d)

180°

61.

What is the sum of the interior angles for a 24-gon

a)

3960

b)

360

c)

15

d)

4280

62.

What is the SUM of the angle measures in a nonagon (9 sides)?

a)

1440°

b)

900°

c)

1080°

d)

1260°

63.

How do you find the sum of the exterior angles of a polygon?

a)

180(n-2)

b)

180

c)

(180(n-2))/n

d)

360

64.

What is the name of a 12-sided polygon?

a)

Dodecahedron

b)

Polygon

c)

Decagon

d)

Dodecagon

65.

The sum of 5 angles of a hexagon is 600^o^. What is the measure of the 6th angle?

a)

90^o

b)

120^o

c)

100^o

d)

60^o

66.

What is the sum of the measures of the interior angles of an 11-gon?

a)

1080 degrees

b)

900 degrees

c)

1620 degrees

d)

1980 degrees

67.

The graph of a quadratic function is called

a)

a line

b)

a hyperbola

c)

a parabola

d)

a cubic

68.

Standard form of a quadratic equation

a)

y=x²

b)

y=ax²+bx+c

c)

y=mx+b

d)

y=x

69.

Which of the following is NOT a quadratic function

a)

f(x) = -3x²

b)

f(x) = -5x - x²

c)

y = 3x³- 4x + 5

d)

A = pi.r²

70.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

71.

Find the roots of this equation
x²+ x - 6 = 0

a)

4, -1

b)

3, -2

c)

-6, 1

d)

2, -3

72.

The Equation (x² + 1)² - x² = 0 has ___

a)

four real roots

b)

two real roots

c)

no real roots

d)

one real root

73.

Roots of the quadratic equation of the type ax² + bx = 0 is _____

a)

x = 0

b)

ax + b = 0

c)

x = 0 and ax + b = 0

d)

Not possible to find

74.

The non-zero root of the equation 3x - 5x² = 0 is_____

a)

3⁄5

b)

5⁄3

c)

-3⁄5

d)

-5⁄3

75.

What is a second degree polynomial equation?

a)

Linear Equations

b)

Quadratic Inequalities

c)

Quadratic Equations

d)

Quadratic Functions

76.

What is the other term for quadratic equations?

a)

Equation of degree 3

b)

Equation of degree 0

c)

Equation of degree 2

d)

None of the above

77.

Which of the following is an example of quadratic equations?

a)

x + 9 = 0

b)

x + y =12

c)

x³ + 5x² - 14 =0

d)

x² - 2x = 7

78.

Which of the following is NOT an example of quadratic equations?

a)

2x² - 3 = 2x

b)

-8x - 15 = -x²

c)

x + 3y = 45

d)

x² + 7x + 10 = 0

79.

x - 12 = -x² is an example of quadratic equation.

a)

True

b)

False

80.

Check all the examples of quadratic equations.

a)

y² - 8y + 16 = 0

b)

x = 15

c)

x² - 12 = 4x

d)

y - 6 = y²

81.

What is the standard form of 9x - 16 = 3x - x²?

a)

x² +12x -16 = 0

b)

2x² + 9x -16 = 0

c)

x² + 6x -16 = 0

d)

-x² + 6x - 16= 0

82.

Find x if 5, 9, 11, 12, 13, 14, 17 and x have a mean of 12.

a)

15

b)

16

c)

17

d)

18

83.

A sample of 10 measurements has a mean of 15.7 and a sample of 20 measurements has a mean of 14.3. Find the mean of all 30 measurements.

a)

16.3

b)

14.8

c)

17.1

d)

21.4

84.

A basketball team scored
43, 55, 41 and 37
points in their first four matches.
Determine the mean number of points scored for the first four matches and hence calculate What score will the team need to shoot in the next match so that they maintain the same mean score?

a)

52

b)

44

c)

35

d)

27

85.

The mean of four numbers is 71.5. If three of the numbers are 58, 76, and 88, what is the value of the fourth number?

a)

64

b)

55

c)

48

d)

60

86.

The mean of eight numbers is 41. The mean of two of the numbers is 29 What is the mean of the other six numbers?

a)

34

b)

55

c)

45

d)

72

87.

From January to September, the mean number of car accidents per month was 630. From October to December, the mean was 810 accidents per month. What was the mean number of car accidents per month for the whole year?

a)

700

b)

675

c)

760

d)

812

88.

What is the commonly used measure of central tendency?

a)

Mode

b)

Median

c)

Mean

89.

Which measure of central tendency is greatly affected by extreme scores?

a)

Mode

b)

Median

c)

Mean

d)

none of these

90.

Jade has grades of 91 and 90 in Math. What grade must she obtain on the third quarter to get an average of 91?

a)

90

b)

91

c)

92

d)

93

91.

On a treasure map, the actual distance is directly related to the scaled distance. If 15 miles is represented by 3 centimeters, then how many centimeters on the treasure map are equivalent to 135 miles?

a)

27 cm

b)

675 cm

c)

529 cm

d)

32 cm

92.

The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

$2

b)

$308

c)

$1.57

d)

$265

93.

If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k?

a)

121

b)

4

c)

100

d)

6

94.

a varies inversely as the square of b. If a is 1 when b is 3, find a when b is 5.

a)

0.36

b)

9

c)

25

d)

36

95.

The cost per person to rent a mountain cabin is inversely proportional (varies inversely) to the number of people who share the rent. If the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?

a)

$22.50

b)

$57.60

c)

$1.11

d)

$12.50

96.

The cost per person to rent a mountain cabin is inversely proportional (varies inversely) to the number of people who share the rent. If the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?

a)

$22.50

b)

$57.60

c)

$1.11

d)

$12.50

97.

What type of variation does this scenario represent?
The grade you earn in a class
and the number of assignments you complete
and the number of hours you study

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

98.

What type of variation does this scenario represent?
The outside temperature
and the number of layers of clothes you need to wear outside to feel comfortable

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

99.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

100.

The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

$2

b)

$308

c)

$1.57

d)

$265

101.

If y varies inversely as x, and y = 32 when x = 3, find x when y = 15.

a)

3/5

b)

8/5

c)

16/5

d)

32/5

102.

The current in a simple electrical circuit is inversely proportional to the resistance. If the current is 80 amps when the resistance is 50 ohms, find the current when the resistance is 22 ohms.

a)

90 amps

b)

100 amps

c)

105 amps

d)

120 amps

103.

If y varies inversely as x, and y = 14 when x = 8, find y when x = 7.

a)

16

b)

20

c)

24

d)

28

104.

Choose the correct answer from the given four options:
In an AP, if d = –4, n = 7, a_n = 4, then a is

a)

6

b)

7

c)

20

d)

28

105.

Choose the correct answer from the given four options:
In an AP, if a = 3.5, d = 0, n =101 ,then a_n will be

a)

0

b)

3.5

c)

-3.5

d)

1

106.

Which term of the AP: 21, 42, 63, 84,... is 210?

a)

9^th

b)

10^th

c)

11^th

d)

12^th

107.

The 4th term from the end of the AP: –11, –8, –5, ..., 49 is

a)

37

b)

40

c)

43

d)

58

108.

If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is

a)

0

b)

5

c)

6

d)

15

109.

The sum of first five multiples of 3 is

a)

45

b)

55

c)

15

d)

30

110.

The sum of first 100 natural number is

a)

5005

b)

5500

c)

5050

d)

1010

111.

Find the derivative of f(x) = 2x²+3.

a)

4x

b)

4x²

c)

3

d)

4x+3

112.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

113.

Find the derivative of the given equation
f(x) = 1/x²

a)

1/2x

b)

-2x

c)

2x

d)

-2x^-3

114.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

115.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

116.

Find the derivative
f(t) = (t² + 2t)⁵

a)

f'(t) = 5(2t+2)⁴

b)

f'(t) = 5(t² + 2t)⁴

c)

f'(t) = 5(t² + 2t)⁴(2t)

d)

f'(t) = 5(t² + 2t)⁴(2t + 2)

117.

Find the derivative.
y = x²/ (3x-1)

a)

y' = 9x²- 12
y' = (3x-1) / (3x-1)²

b)

y' = (3x² - 2x) / (3x-1)²

c)

y' = (6x+1)²/ 3

118.

f (x) = 5x³ + x² + 4, f '(x) = ?

a)

$5x^2+2x$

b)

$15x^3+2x$

c)

$15x^2$

d)

$15x^2+2x$

119.

Solve 24 > -3r > -9

a)

-8 < r < 3

b)

-8 > r > 3

c)

r > - 8 and r > 3

d)

r > -8 or r < 3

120.

|−2n| = −75

a)

{5,6}

b)

{75/2,-75/2}

c)

{-5,5}

d)

No Solution

121.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

122.

When you graph an inequality, you used a closed dot when you use which symbols?

a)

≤, ≥

b)

<, >

123.

The side of a cube whose surface area is 600 cm² is____

a)

10 cm

b)

10 cm²

c)

60 cm

d)

6 cm

124.

The area of a rhombus whose diagonals are 9 cm and 7 cm is ______

a)

16 cm²

b)

63 cm²

c)

63 cm²

d)

16 cm²

125.

If the base of the triangle is doubled and height is halved, its area will be _____

a)

Doubled

b)

Halved

c)

one-fourth

d)

Same

126.

Two cubes with 9 cm edge are joined end to end. Find the length of the newly formed solid.

a)

18 cm

b)

9 cm

c)

27 cm

d)

None of the above

127.

A solid sphere of radius x cm is melted and cast into a shape of a solid cone of same radius height of the cone is

a)

3x

b)

X

c)

4x

d)

2x

128.

Choose the correct answer to find the area of a circle

a)

$\pi r^2$

b)

$2\pi r^2$

c)

$2\pi r$

129.

The ratio of the volume of a cube to that of a sphere which exactly fits into the cube is…

a)

π : 1

b)

4 : 3

c)

6 : π

d)

π : 6

130.

If the surface area of a sphere is 100π cm² then its diameter is equal to

a)

25 cm

b)

50 cm

c)

5 cm

d)

10 cm

131.

1.A parallelogram has one side 18 cm and its distance from the opposite side is 8 cm. The area of the parallelogram is

a)

120cm2^{ }

b)

$72\ cm^2$

c)

$144\ cm^2$

d)

$100\ cm^2$

132.

2 .sum of parallel sides of a trapezium is 26m and its area is 156 square metres , then distance between the parallel side of the trapezium is

a)

14 m

b)

13 m

c)

12 m

d)

11 m

133.

Simplify

\sqrt{88}

a)

$4\sqrt{2}$

b)

$2\sqrt{4}$

c)

$4\sqrt{11}$

d)

$2\sqrt{22}$

134.

\sqrt{48}

a)

$3\sqrt{4}$

b)

$4\sqrt{3}$

c)

$3\sqrt{12}$

d)

$4\sqrt{4}$

135.

Simplify fully:
√32

a)

4√8

b)

16√2

c)

4√2

d)

4√4

136.

Simplify fully:
√32 + 5√32

a)

6√32

b)

24√8

c)

24√2

d)

6√8

137.

Simplify fully:
2√45 - 5√45 + 9√16

a)

-9√5 + 36

b)

-3√45 + 144

c)

6√16

d)

6√106

138.

Simplify as much as possible:
10√10 ÷ 2√5

a)

5√2

b)

2√5

c)

5√50

d)

5√5

139.

Simplify fully:
√32 + 5√32

a)

6√32

b)

24√8

c)

24√2

d)

6√8

140.

Simplify

\sqrt{18}+2\sqrt{50}

a)

$3\sqrt{5}$

b)

$13\sqrt{2}$

c)

$-4\sqrt{2}$

d)

$7\sqrt{5}-3\sqrt{3}$

141.

Expand and simplify.....

√5(4√2 - 2√5)

a)

4√10 - 10

b)

4√10 - 2√25

c)

2√20 - 2√25

d)

2√20 - 10

142.

What is 7 mod 3?

a)

1 mod 3

b)

2 mod 3

c)

3 mod 3

d)

0 mod 3

143.

What is 57 mod 7?

a)

0 mod 7

b)

1 mod 7

c)

7 mod 7

d)

-1 mod 7

144.

What is 5 mod 4?

a)

1

b)

2

c)

3

d)

4

145.

What is 18 mod 4?

a)

0

b)

1

c)

2

d)

4

146.

What is 14 mod 12?

a)

1

b)

2

c)

3

d)

4

147.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

148.

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

a)

{-4, -3, -2, -1, 0, 1, 2, 3}

b)

{-3, -2, -1, 1, 2, 3}

c)

{-4, -3, -2, -1, 1, 2, 3, 4}

d)

{-4, -3, -2, -1, 1, 2, 3}

149.

What does this symbol ( ∪ ) represent in set theory?

a)

Union

b)

Intersection

c)

Disjointed

d)

Subset

150.

The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?

a)

{-4, -3, -2, -1, 0, 1, 2, 3}

b)

{-3, -2, -1, 1, 2, 3}

c)

{-4, -3, -2, -1, 1, 2, 3, 4}

d)

{-4, -3, -2, -1, 1, 2, 3}

MATHEMATICS ACHIEVEMENT TEST(MAT)

Total questions: 150

Worksheet time: 5hrs 1mins

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