Free Printable Practice Test

1.

If x = 3, then what is the value of $(x^2−3)−2(x^3−5x)$ ?

a)

0

b)

-18

c)

-16

d)

24

e)

54

2.

A student's GPA is determined by assigning each letter grade a certain number and taking the average of those numbers. If a certain high school determines that A's are worth 4.0, B's are worth 3.0, C's are worth 2.0, D's are worth 1.0, and F's are worth 0 and that a student gets 6 A's, 2 B's, and 2 C's over the entire school year, what is the student's GPA for that year?

a)

3.4

b)

3.0

c)

3.7

d)

4.0

e)

4.2

3.

A single shipping truck can transport either a maximum of 500 boxes with a volume of 30 cubic inches each or a maximum of 2 tons of weight. If a customer needs to ship 300 boxes, each with a volume of 30 cubic inches and weighing 6 pounds, how many shipping trucks will they need to use? (Note that 1 ton is equivalent to 2000 pounds)

a)

A) 1

b)

B) 2

c)

C) 5

d)

D) 10

e)

E) 150

4.

If x and y are both real numbers, which of the following is equivalent to (2x + 3y)(2x - 3y)?

a)

A) 4x² + 6xy + 9y²

b)

B) 4x² + 12xy + 9y²

c)

C) 4x² + 12xy - 9y²

d)

D) 4x² + 9y²

e)

E) 4x² - 9y²

5.

What is the x-intercept of a line that passes through (3,7) and (0,13)?

a)

A) 6

b)

B) 6.5

c)

C) 7

d)

D) 7.5

e)

E) 8

6.

|5 − 15|³ + |15 − 5|² = ?

a)

-900.00

b)

-750.00

c)

900.00

d)

1,000.00

e)

1,100.00

7.

Julie is baking 4 loaves of banana bread for her math club bake sale, using a recipe that requires 2 $\frac{1}{3}$ cups of flour per loaf and 3 $\frac{1}{4}$ cups of sugar per 2 loaves. What is the total amount of sugar and flour, in cups, that Julie will need to bake these 4 loaves?

a)

6 $\frac{1}{2}$

b)

9 $\frac{1}{3}$

c)

15 $\frac{1}{3}$

d)

15 $\frac{5}{6}$

e)

20 $\frac{2}{3}$

8.

The square of a certain positive integer lies between 133 and 150. What is this positive integer?

a)

9

b)

10

c)

11

d)

12

e)

13

9.

30% of 60 is 45% of what number?

a)

35

b)

40

c)

45

d)

65

e)

70

10.

Annie is currently one third of her mother's age. 10 years ago, her mother was 5 times as old as Annie.

How old is Annie?

a)

10

b)

20

c)

30

d)

40

e)

50

11.

Which of the following inequalities is equivalent to 4 - 2x > -6 ?

a)

x > -10

b)

x < -5

c)

x < 5

d)

x < 10

e)

x > 10

12.

Which of the following is equivalent to $\left(8^{\frac{2}{3}}\right)^2$

a)

2

b)

4

c)

8

d)

16

e)

32

13.

Given the system of equations: x + y = 10 x − y = 0 What is a possible solution to this system of equations?

a)

(0,0)

b)

(5,0)

c)

(0,5)

d)

(5,-5)

e)

(5,5)

14.

There are two non-intersecting lines, which of the following three statements must be true about these lines?I. The two lines are parallel.
II. The two lines have the same slope.
III. The two lines exist in the same plane.

a)

I. Only

b)

II. Only

c)

I. and II. Only

d)

I., II., and III.

e)

None of the statements must be true

15.

A local movie theater has tickets with dimensions as shown. If the shape of the ticket is a rectangle with quarter-circles removed from the corners, what is the total area in square millimeters of one ticket?

a)

56

b)

$200-\frac{9}{4}\pi$

c)

$200-9\pi$

d)

191

e)

200

16.

The function f is defined as f(x) = (3x)³ - 4x² + 26. Which of the following is equivalent to f(2)?

a)

178

b)

200

c)

216

d)

226

e)

264

17.

The result of multiplying 5 consecutive integers is 120.

What is the largest of these integers?

a)

3

b)

4

c)

5

d)

9

e)

10

18.

How many real solutions are there to the following system of equations?

$y=x^2-10x+30$

$y=2x-6$

a)

0

b)

1

c)

2

d)

3

e)

Infinitely Many

19.

What is the length of leg AB, given that sinθ = $\frac{3}{5}$ ?

a)

6

b)

7

c)

8

d)

9

e)

10

20.

The greatest common factor of 111 and 148 is 13 less than x. What is the value of x?

a)

3

b)

37

c)

50

d)

74

e)

111

21.

Two airplanes are flying simultaneously.

Relative to Airplane 1, Airplane 2 is currently 4 miles East, 5 miles North, and 0.5 miles higher.

What is the approximate distance, in miles, between the two planes at this point in time?

a)

6

b)

6.1

c)

6.2

d)

6.3

e)

6.4

22.

Given that ABCD is a square with a side length of 4 inches and E, F, G, H, I, J, K, and L are midpoints of their respective line segments, what is the ratio of shaded area to unshaded area?

a)

1:3

b)

5:16

c)

1:4

d)

1:8

e)

7:16

23.

I can water 1 acre of land with 1000 gallons of water. To the nearest quart, how much water do I need to water 100 square feet of land? (Note: There are 43,560 square feet in an acre)

a)

2

b)

3

c)

4

d)

8

e)

9

24.

Which of the following would model a population that grows at a constant rate of 3.5% annually, using t as our variable for time and P for our current population?

a)

$P\left(t\right)=p\left(1.35\right)t$

b)

$P\left(t\right)=p\left(1.35\right)^t$

c)

$P\left(t\right)=p\left(1.035\right)t$

d)

$P\left(t\right)=p\left(1.035\right)^t$

e)

$P\left(t\right)=t\left(1.035\right)^p$

25.

Given that the point (2,3) is an endpoint on a line segment and the point (5,9) is the midpoint of that line segment, what is the other endpoint of the line segment?

a)

(7,12)

b)

(8,15)

c)

(9,12)

d)

(9,15)

e)

(10,18)

26.

What is the perimeter of a regular hexagon with an area of $54\ \sqrt[]{3}$ ?

a)

6

b)

12

c)

36

d)

$48\ \sqrt[\ ]{3}$

e)

$50\ \sqrt[]{3}$

27.

What are the values of x that satisfy the equation $x=1+\frac{1}{x}$ ?

a)

$0$

b)

$1$

c)

$\frac{1+\sqrt[]{5}}{2}$

d)

$\frac{1-\sqrt[]{5}}{2}$

e)

$\frac{1+\sqrt[]{5}}{2},\frac{1-\sqrt[]{5}}{2}$

28.

Lines I and m are parallel in the following diagram.

Which of the following is the value of x?

a)

80

b)

100

c)

110

d)

130

e)

160

29.

Jessica, Sarah, and Eliza are Girl Scouts selling cookies to raise money for their troop. The table shows how many boxes each girl sold of each variety of cookie. If Thin Mints cost $3 a box, Samoas cost $4 a box, Tagalongs cost $2.50 a box, and Do-si-dos cost $2.75 a box,

how much money worth of cookies did Eliza sell?

a)

$18

b)

$40

c)

$45

d)

$63

e)

$74

30.

Jessica, Sarah, and Eliza are Girl Scouts selling cookies to raise money for their troop. The table shows how many boxes each girl sold of each variety of cookie. What is the probability that if you randomly choose a customer of Jessica, Sarah, or Eliza, they bought either Samoas or Do-si-dos?

a)

13/72

b)

19/72

c)

4/9

d)

1/2

e)

5/9

31.

Jessica and Eliza decide to combine their total cookies sold in order to beat Sarah. Over the next two weeks, if Jessica and Eliza sell another 10 boxes of cookies each, how many more boxes will Sarah need to sell in order to have sold more cookies than Jessica and Eliza?

a)

22

b)

32

c)

33

d)

62

e)

63

32.

There is a circle with equation (x − 3)² + y² = 16. Which of the following points could lie on the perimeter of the circle?

a)

(-1,0)

b)

(0,0)

c)

(3,-3)

d)

(3,3)

e)

(7,1)

33.

If the measure of inscribed angle EBD is 42 degrees, what is the measure of central angle EOD in degrees?

a)

21

b)

42

c)

84

d)

105

e)

126

34.

A cube has edge lengths of 4 inches. What is the surface area of this cube in square inches?

a)

16

b)

32

c)

64

d)

96

e)

128

35.

For which of the following values of x is $\frac{\left(x^4-5x^3\right)}{\left(3x-x^2\right)}$ undefined?

a)

1

b)

2

c)

3

d)

4

e)

5

36.

What is the mean of the following 8 scores? 23, 54, 62, 71, 36, 95, 40, 76

a)

57

b)

57.125

c)

57.5

d)

58

e)

457

37.

Which of the following could be a value of x in the equation $\log_4\left(x\right)=\log_3\left(27\right)$ ?

a)

16

b)

32

c)

64

d)

128

e)

256

38.

There are a total of 72 students enrolled in either biology or physics at a certain school. If 40 students take biology and 40 students take physics, how many students are enrolled in both biology and physics?

a)

2

b)

4

c)

6

d)

8

e)

10

39.

The area of a circle is $28\pi$ more than $1\frac{1}{2}$ times its circumference. What is the radius of this circle?

a)

4

b)

7

c)

8

d)

14

e)

28

40.

What is the value of x in the following figure?

a)

6

b)

7

c)

8

d)

9

e)

10

41.

At what angle does the line y = x intersect the x-axis?

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

e)

120 degrees

42.

There are two internet service providers that a certain school district is deciding between.

The first internet service provider (ISP 1) charges a one-time $100 base setup fee and then charges $40 per month for continued service.

The second internet service provider (ISP 2) charges half as much for their base setup fee and 25% more per month.

If the school district is going to sign a 12-month contract with their chosen internet service provider, which plan will be cheaper and by how much?

a)

ISP 1, $60

b)

ISP 1, $70

c)

ISP 2, $50

d)

ISP 2, $60

e)

They cost the same amount

43.

What is the x-intercept of $f\left(x\right)=64\left(4\right)^{\left(1-x\right)}-8$ ?

a)

-5/2

b)

-3/2

c)

1/2

d)

3/2

e)

5/2

44.

Simplify $\frac{5}{\left(12+5i\right)}$

a)

$\frac{60+25i}{119}$

b)

$\frac{60-25i}{119}$

c)

$\frac{60+25i}{169}$

d)

$\frac{60-25i}{169}$

e)

$\frac{60-25i}{13}$

45.

Given that the period of y = sin(x) is 2π, what is the period of y = 4sin(x − 2π) + 3?

a)

0

b)

π

c)

2π

d)

3

e)

4

46.

If vector $v=<1,2,5>$ , vector $u=<5,x,8>$ , and $3v-u=<-2,2,7>$

what is the value of x?

a)

2

b)

4

c)

6

d)

8

e)

10

47.

Given that chord AC has a length of 18 and that OC = 15, what is the radius of the smaller circle?

a)

4

b)

8

c)

12

d)

16

e)

18

48.

If OB has a length of 6 and BC has a length of 8, what is the ratio of the circumference of the smaller circle to the circumference of the larger circle?

a)

1:5

b)

2:5

c)

1:2

d)

3:5

e)

3:4

49.

If chord AC has a length of 10, what is the area of the shaded region?

a)

5π

b)

10π

c)

15π

d)

20π

e)

25π

50.

If there is a group of 8 people or more at a certain restaurant, then the restaurant will automatically include a 15% tip for the waiter before any discounts are used. If the price of the food alone for a group of 10 people is $135 after applying a coupon for 40% off, then how large is the tip the waiter is guaranteed?

a)

$15.50

b)

$20.25

c)

$33.75

d)

$42.00

e)

$42.50

51.

What is the value of $\log\left(125\right)+\log\left(8\right)$ ?

a)

2

b)

3

c)

4

d)

5

e)

8

52.

A baseball is thrown upwards from the roof of a building and its height can be modeled as an equation of height (h feet) in terms of time (t seconds) as follows, $h\left(t\right)=-4t^2+24t+27$ . The vertex form of this equation reveals that the baseball reaches which of the following heights at its maximum height?

a)

15

b)

24

c)

27

d)

53

e)

63

53.

How many ways are there to choose three textbooks from a locker that contains twelve textbooks in total?

a)

4

b)

6

c)

9

d)

220

e)

1320

54.

What is the length of side AF?

given that AB = BC = CD = DE = EF = 1 and all right angles are indicated?

a)

1

b)

$\sqrt[]{2}$

c)

$\sqrt[]{3}$

d)

2

e)

$\sqrt[]{3}$

55.

Jonathan is rolling a weighted six-sided die with the following weights: $P\left(1\right)=\frac{1}{6},\ P\left(2\right)=\frac{1}{12},\ P\left(3\right)=\frac{1}{2},\ P\left(4\right)=\frac{1}{12},\ P\left(5\right)=\frac{1}{12},\ P\left(6\right)=\frac{1}{12}.$ What is the difference between the expected value of Jonathan's weighted die and an unweighted die?

a)

1/12

b)

1/4

c)

5/12

d)

1/2

56.

What is the units digit of $2^{57}$ ?

a)

0

b)

2

c)

4

d)

6

e)

8

57.

What is $\tan\left(\cos^{-1}\left(\frac{12}{13}\right)\right)?$

a)

5/12

b)

5/13

c)

12/13

d)

12/5

e)

13/5

58.

Which of the following is equivalent to $\left|4+3i\right|,$ where $i=\sqrt[]{\left(-1\right)}?$

a)

3

b)

4

c)

5

d)

6

e)

7

59.

If the distance between the center of circle A and circle B is 10, circle A has a radius of 8, and circle B has a radius of 2, what is the area of quadrilateral ABCD?

a)

16

b)

18

c)

24

d)

28

e)

40

60.

What is the value of x in the following equation?

a)

4

b)

$\frac{\sqrt[]{5}}{2}$

c)

$\frac{\sqrt[]{5}+1}{2}$

d)

$\frac{\sqrt[]{5}+3}{2}$

e)

6

Practice Test

Total questions: 60

Worksheet time: 5hrs 0mins

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