Free Printable PSAT prep 1

1.

Which of the following is an equivalent form of the expression

15x+24ax

a)

$39ax^2$

b)

$39\left(a+2x\right)$

c)

$\left(5+8a\ \right)x$

d)

$\left(15+24a\right)x$

2.

The formula

$d=rt$ is used to calculate the distance an object travels over a period of time, $t$ , at a constant rate, $r$ . Based on this formula, what is the rate,

r

, in terms of

d

and

t

?

a)

$r=\frac{d}{t}$

b)

$r=dt$

c)

$r=\frac{t}{d}$

d)

$r=d-t$

3.

Which of the following ordered pairs $\left(x,y\right)$ satisfies both equations $y=x^2+3x-4$ and $x=y-4$ ?

a)

(0,-4)

b)

(2,6)

c)

(3,14)

d)

(5,9)

4.

Which of the following is a solution to the equation $2x^2+4x=3+3x^2$ ?

a)

-1

b)

0

c)

3

d)

6

5.

-3x-4y=20
x-10y=16

If (x,y) is the solution to the system of equations above, what is the value of x?

a)

-14

b)

-12

c)

-4

d)

16

6.

The equation y=36 + 18x models the relationship between the height y, in inches, of a typical golden delicious apple tree and the number of years, x, after it was planted. If the equation is graphed in the xy-plane, what is indicated by the y-intercept of the graph?

a)

The age, in years, of a typical apple tree when it is planted

b)

The height, in inches, of a typical apple tree when it is planted

c)

The number of years it takes a typical apple tree to grow

d)

The number of inches a typical apple tree grows each year

7.

Giovanni wants to buy shirts that cost $19.40 each and sweaters that cost $24.80 each. An 8% sales tax will be applied to the entire purchase. If Giovanni buys 2 shirts, which equation relates the number of sweaters purchased, p, and the total cost in dollars, y?

a)

1.08(38.80+24.80p)=y

b)

38.80+24.80p=0.92y

c)

38.80+24.80p=1.08y

d)

0.92(38.80+24.80p)=y

8.

A line is graphed in the xy-plane. If the line has a positive slope and a negative y-intercept, which of the following points cannot lie on the line?

a)

(-3,-3)

b)

(-3,3)

c)

(3,-3)

d)

(3,3)

9.

A parachute design uses 18 separate pieces of rope. Each piece of rope must be at least 270 centimeters and no more than 280 centimeters long. What inequality represents all possible values of the total length of rope x, in centimeters, needed for the parachute?

a)

270\le x\le280

b)

$4860\le x\le4870$

c)

$4860\le x\le5040$

d)

$5030\le x\le5040$

10.

A carpenter has $60 with which to buy supplies. The carpenter needs to buy both nails and screws. Nails cost $12.99 per box, and screws cost $14.99 per box. If n represents the number of boxes of nails and s represents the number of boxes of screws, which of the following systems of inequalities models this situation?

a)

{12.99n+14.99s $\ge$ 60
{n+s $\le$ 1

b)

{12.99n+14.99s $\le$ 60

{n+s $\le$ 1

c)

{12.99n+14.99s $\ge$ 60

{n $\ge$ 1
{s $\ge$ 1

d)

{12.99n+14.99s $\le$ 60

{n $\ge$ 1

{s $\ge$ 1

11.

In the figure above, which of the following ratios has the same value as $\frac{AB}{BC}$

a)

\frac{BD}{DC}

b)

$\frac{BC}{AC}$

c)

$\frac{AD}{BD}$

d)

$\frac{DC}{BC}$

12.

$\left(x^2y^3\right)^{\frac{1}{2}}\left(x^2y^3\right)^{\frac{1}{3}}=x^{\frac{a}{3}}y^{\frac{a}{2}}$

If the equation above, where a is a constant, is true for all positive values of x and y, what is the value of a?

a)

2

b)

3

c)

5

d)

6

13.

If the equation y=(x-6)(x+12) is graphed in the xy-plane, what is the x-coordinate of the parabola's vertex?

a)

-6

b)

-3

c)

3

d)

6

14.

21x+14=7(3x+a)

In the equation above, a is a constant. For what value of a does the equation have an infinite number of solutions

(a)

15.

Juliene practiced her dance routine for twice as many minutes on Monday as she did on Tuesday. She practiced her routine those two days for a total of 2 hours and 15 minutes. For how many minutes did Juliene practice her dance routine on Monday?

(a)

16.

In the expression below, a is an integer. $12x^2+ax-20$ If 3x+4 is a factor of the expression above, what is the value of a?

(a)

17.

(ax+by)(cx-dy)

In the expression above, a, b, c, and d are non-zero constants and ad=bc. If ac=18 and bd=50, what is the value of the coefficient of the xy term when the expression is multiplied out and the like terms are collected?

(a)

18.

Probability can only be values between which two numbers?

a)

0 to 2

b)

0 to 10

c)

0 to 5

d)

0 to 1

19.

Find the probability of rolling greater than a 1 on a single die.

a)

6/6

b)

5/6

c)

4/6

d)

1/6

20.

The following M & M colors are in the bowl:

4 yellow, 6 orange, 3 green, 5 blue, 2 brown

What is the probability of selecting a brown candy?

a)

2/18

b)

1/9

c)

1/10

21.

Theoretical P(King)

a)

2/8

b)

1/8

c)

3/8

d)

1/4

22.

What statement does the shaded region represent?

a)

A C∪ B ∩ C

b)

C'

c)

A ∪ B

d)

B ∩ C ∪ A

23.

What is the P(B)?

a)

56/135

b)

52/135

c)

64/135

d)

63/135

24.

The probability of an event occurring, P(A), can be expressed as a fraction, decimal, or percent.

a)

True

b)

False

25.

What statement does the shaded region represent?

a)

A or B

b)

A and not B

c)

Not A

d)

Not A or B

26.

There are 6 boys and 8 girls in a classroom. What is the probability that the teacher randomly selects a boy?

a)

⁸/₆

b)

⁶/₈

c)

3/7

d)

⁸/₁₄

27.

X ∩ Y ∩ Z

a)

{ }

b)

{Phillip}

c)

{Billy, Phillip, Bryan, Perez}

d)

{Billy, Perez, Bryan}

28.

The radius of a given circle is increased by 20%. What is the percent increase of the area of the circle.

a)

20%

b)

40%

c)

44%

d)

100%

e)

144%

29.

A circle is inscribed inside a square. If a point inside the square is selected at random, what is the probability that the point will also be inside the circle?

a)

\frac{\pi}{4}

b)

$\frac{3}{4}$

c)

$\frac{\pi}{6}$

d)

$\frac{5}{6}$

30.

If the center of a circle is at (0, 4) and the diameter of the circle is 6, what is the equation of that circle?

a)

$x^2+\left(y-4\right)^2=36$

b)

$x^2+\left(y-4\right)^2=9$

c)

$x^2+y^2=9$

d)

$\left(x-4\right)^2+y^2=9$

e)

$\left(x-4\right)^2+y^2=36$

31.

What is the radius of a circle with the equation

x\left(x-8\right)+y\left(y-6\right)=24?

a)

4

b)

6

c)

7

d)

8

e)

3

32.

A circle has its origin at (0, 0). The point (5, 7) is on the edge of the circle. What is the radius of the circle?

a)

$r=\sqrt{74}$

b)

$r=4\sqrt{21}$

c)

There is not enough information

d)

$r=6\sqrt{2}$

e)

$r=2\sqrt{18}$

33.

In the figure above, a circle is centered at point C and a line is tangent to the circle at point B. What is the equation of the line?

a)

5x-2y=41

b)

$2x+5y=-1$

c)

$5x+2y=29$

d)

$x+y=4$

e)

$2x-5y=29$

34.

The perimeter of a circle is 36 π. What is the diameter of the circle?

(a)

35.

If the area of a circle is four times larger than the circumference of that same circle, what is the diameter of the circle?

(a)

36.

A circle with an area of 13π in² is centered at point C. What is the circumference of this circle?

a)

\pi\sqrt{13}

b)

$26\pi$

c)

$2\pi\sqrt{13}$

d)

$13\pi$

e)

$\pi\sqrt{26}$

37.

If the equation of a circle is $\left(x-7\right)^2+\left(y+1\right)^2=81$ , what is the area of the circle?

a)

$2\pi$

b)

$81\pi$

c)

$18\pi$

d)

$6561\pi$

e)

$49\pi$

38.

If a circle has a circumference of 16π, what would its area be if its radius were halved?

a)

$4\pi$

b)

$8\pi$

c)

$64\pi$

d)

$16\pi$

39.

Two concentric circles have circumferences of 4π and 10π. What is the difference of the radii of the two circles?

(a)

40.

The length of an arc, S, of a circle is 8π and the radius, r, of the circle is 16. What is the measure in degrees of the central angle, θ, formed by the arc S?

a)

$120\degree$

b)

$45\degree$

c)

$90\degree$

d)

$30\degree$

e)

$60\degree$

41.

The hypotenuse is the diameter of the circle.

Find the area of the circle above.

a)

$6.25\pi$

b)

$5\pi$

c)

$5.5\pi$

d)

$6.75\pi$

e)

$6.5\pi$

42.

The total number of followers of a Mars rover’s social media account is 1,764,000, as summarized by age in the

graph above. Which of the following could be the median age of the followers?

a)

37

b)

29

c)

20

d)

16

43.

A geologist examined the 95 rocks on display at a museum. She recorded the type of rock and whether the rock

has a shiny or dull surface as shown in the two-way table above. If a nonmetamorphic rock from the museum’s display is selected at random, what is the probability that the rock has a shiny surface?

a)

$\frac{17}{53}$

b)

$\frac{17}{45}$

c)

$\frac{28}{45}$

d)

$\frac{18}{25}$

44.

A marketing company surveyed 50 randomly selected residents of a town in order to estimate the age distribution

of residents in the town. The table above shows the results of the survey. What percent of the residents surveyed were age 70 or younger?

a)

13%

b)

26%

c)

74%

d)

87%

45.

On election day, a local news show randomly selected 500 people who voted in a mayoral election. The voters

were asked to report which candidate they voted for, and the results of the survey are shown in the table above. A total of 15,000 people voted in the election. Based on the results of the survey, what is the best estimate for the

total number of votes Maria Hernandez is expected to receive?

a)

3,500

b)

4,850

c)

7,750

d)

8,250

46.

Leta has a large assortment of petunia, rose, and zinnia flowers. All of the flowers in the assortment are either

pink, red, or white. The table above shows the number of flowers by color and type. Leta separates out the white flowers and picks one of them at random. What is the probability that the flower Leta

picks is a rose?

a)

$\frac{1}{3}$

b)

$\frac{9}{24}$

c)

$\frac{1}{2}$

d)

$\frac{4}{9}$

47.

The table above shows the distribution of US states according to whether they have a state-level sales tax and a

state-level income tax. To the nearest tenth of a percent, what percent of states with a state-level sales tax do not have a state-level income tax?

a)

6.0%

b)

10.0%

c)

13.3%

d)

15.5%

48.

A group of 10 students played a certain game. Every player received a score equal to an integer from 1 to 10,

inclusive. For the 10 players, the mean score was 4. If more than half of the players received a score greater

than 5, which of the following is true about the mean score of the remaining players?

a)

It must be less than 4.

b)

It must be equal to 4.

c)

It must be 4 and 5.

d)

It must be greater than 5.

49.

A sample of 600 ninth graders was selected at random and asked how much time they spend on homework each

day. Of the ninth graders selected, 220 spend less than 2 hours on homework each day. If the conclusion was

drawn that “approximately 1.35 million ninth graders spend less than 2 hours on homework each day,” which of

the following is closest to the population, in millions, of ninth graders?

a)

0.368

b)

0.495

c)

3.68

d)

5.84

50.

The energy pyramid above shows four trophic levels in an ecosystem and the direction of energy transfer between

those levels. On average, 10% of the net energy of one trophic level is transferred to the next trophic level in an ecosystem. Based on the energy pyramid, if primary producers have 5,000 joules (J) of energy, approximately how much of this energy, in calories, is transferred to the secondary consumers in this ecosystem? (1 calorie = 4.18 J)

a)

11.96

b)

20.90

c)

119.6

d)

209.0

51.

A magazine article on video game habits in the United States reported that in 2012 gamers spent an average of

5.6 hours per week playing games. The article also reported the average for 2013 to be 6.3 hours per week.

Based on the article, how did the average number of hours that gamers spent playing games per week change

from 2012 to 2013?

a)

It decreased by 12.5%.

b)

It increased by 7.0%.

c)

It increased by 11.1%.

d)

It increased by 12.5%.

52.

What is the equation of the line shown?

a)

y=3x-3

b)

y=-3x+3

c)

y=1/3x-3

d)

y=-1/3x+3

53.

Which ordered pair (x,y) satisfies the system of equations shown below?
2x - y = 6
x + 2y = -2

a)

(-6, 2)

b)

(-2, 2)

c)

(2, -2)

d)

(4, 2)

54.

Which of the following is an equivalent form of the expression

15x+24ax

a)

$39ax^2$

b)

$39\left(a+2x\right)$

c)

$\left(5+8a\ \right)x$

d)

$\left(15+24a\right)x$

55.

Which of the following is an equivalent form of the expression

15x+24ax

a)

$39ax^2$

b)

$39\left(a+2x\right)$

c)

$\left(5+8a\ \right)x$

d)

$\left(15+24a\right)x$

56.

The formula

$d=rt$ is used to calculate the distance an object travels over a period of time, $t$ , at a constant rate, $r$ . Based on this formula, what is the rate,

r

, in terms of

d

and

t

?

a)

$r=\frac{d}{t}$

b)

$r=dt$

c)

$r=\frac{t}{d}$

d)

$r=d-t$

57.

Which of the following ordered pairs $\left(x,y\right)$ satisfies both equations $y=x^2+3x-4$ and $x=y-4$ ?

a)

(0,-4)

b)

(2,6)

c)

(3,14)

d)

(5,9)

58.

-3x-4y=20
x-10y=16

If (x,y) is the solution to the system of equations above, what is the value of x?

a)

-14

b)

-12

c)

-4

d)

16

59.

What is the probability of rolling a cube and having it land as a six?

a)

1/6

b)

5/6

c)

1/3

d)

1/2

60.

A bag contains 5 quarters, 2 dimes, and 4 pennies. What is the probability of picking a quarter?

a)

5/11

b)

5/6

c)

1/3

d)

5

61.

Change this decimal to a percent.
0.528

a)

528%

b)

52.8%

c)

5.28%

d)

52%

62.

If a coin is flipped 3 times, what is the probability that it will land on tails at least twice?

a)

1/8

b)

1/4

c)

1/2

d)

3/4

63.

What type of slope does the graph have?

a)

Positive

b)

Negative

c)

Zero Slope

d)

Undefined

64.

What is the solution to this system?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

65.

Find the value of the missing angle.

a)

27

b)

55

c)

43

d)

137

66.

What is the slope in the equation y=2x + 3?

a)

2

b)

3

c)

5

d)

Cannot be Determined

67.

6) Find the Lateral Surface Area of a Triangular Prism.

a)

72

b)

65

c)

84

d)

18

68.

$Given\ h\left(x\right)=x^2-4\$

What is h (6)?

a)

32

b)

0

c)

-4

d)

77

69.

What is f(2)?

a)

-4

b)

8

c)

0

d)

5

70.

What is the value of f(-5)?

a)

-2

b)

2

c)

4

d)

0

71.

For the function f(x) = 4x + 2, find x such that f(x) = 2.

a)

10

b)

2

c)

-2

d)

0

72.

What is the type of association?

a)

Negative

b)

no association

c)

positive

73.

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books. Use the trend line to predict how many chapters would be in a book with 180 pages.

a)

12 chapters

b)

15 chapters

c)

18 chapters

d)

21 chapters

74.

What type of association does this graph have?

a)

positive

b)

negative

c)

none

d)

all of the above

75.

What type of correlation best describes the scatter plot shown?

a)

positive, weak

b)

positive, strong

c)

negative, weak

d)

no correlation

76.

Solve
3x - 5 = -26

a)

x=-21

b)

x=21

c)

x=-7

d)

x=61

77.

2 + (9²- 4)

a)

16

b)

77

c)

79

78.

(7 + 41) ÷ 2 – 15

a)

19

b)

9

c)

25

d)

3

79.

Solve
s + 9 ≥ -25

a)

s ≥ -18

b)

s ≥ -34

c)

s ≤ 18

d)

s ≥ 34

80.

The graph above shows the student participation for 4 school clubs. Each student is allowed to participate in only one club. If the school has 250 students, how many students are not in a club?

a)

A) 220

b)

B) 90

c)

C) 60

d)

D) 30

81.

What fraction is represented by the shaded part of the image above?

a)

5/6

b)

1/5

c)

1/6

d)

None of the Above

82.

Which fraction is equivalent to 12/15?

a)

6/5

b)

4/5

c)

3/5

d)

2/5

83.

Which equation best represents the relationship between x and y in the table shown?

a)

y=4x-10

b)

y=-1/3x-10

c)

y=-10x+10

d)

y=-3x-10

84.

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

a)

add

b)

subtract

c)

multiply

d)

divide

85.

According to exponent rules, when we multiply two power with the same base we _______ the exponents.
Example: c⁶ ⋅ c⁴

a)

add

b)

subtract

c)

multiply

d)

divide

86.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

87.

Which of the following represents direct variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

88.

Which of the following represents indirect variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

89.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

90.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

91.

If y = 15 when x = 12 find y when x = 32.

a)

40

b)

-40

c)

5

d)

-5

92.

The Height of a wave in California varies directly with the seconds that pass by. At 4 seconds, the wave is 6 feet high. How many seconds will give you a wave that is 10 feet high?

a)

y = 2/3x

b)

6

c)

6.6

d)

7

93.

The width of a rectangle varies inversely with its length. If the width is 6 when the length is 24, give an equation that shows the relationship.

a)

y = 4x

b)

y = 144x

c)

y = 4/x

d)

y = 144/x

94.

Y is directly proportional to the square of z and inversely proportional to w.

a)

y=kz²/w

b)

y=kz/w

c)

y=w/kz²

d)

y=w/kz

95.

The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person whose mass is 75 kg?

a)

50 kg water

b)

72 kg water

c)

94 kg water

d)

150 kg water

96.

Y varies inversely with x, and y is 0.5 when x is 4. Which equation represents this situation?

a)

y=2x

b)

y=2/x

c)

y=4x

d)

y=x/2

97.

y varies directly with the square of x. If y=40 when x=4, find y when x = 7

a)

17.5

b)

70

c)

122.5

98.

The formula d = rt is used to calculate the distance an object travels over a period of time, t, at a constant rate, r. Based on this formula, what is the rate, r, in terms of d and t ?

a)

$r=\frac{d}{t}$

b)

$r=dt$

c)

$r=\frac{t}{d}$

d)

$r=d-t$

99.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

skew lines

d)

intersecting lines

100.

How many solutions does this system of equations have?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

d)

Two Solutions

101.

If a system of linear equations has one solution, what does this mean about the two lines?

a)

Parallel lines

b)

the same line

c)

Intersecting lines

102.

Solve the system of equations by elimination.
-x + y = -13
-8x - 4y = -8

a)

(5, 8)

b)

(5, -8)

c)

(-5, -18)

d)

(-5, 8)

103.

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

a)

yes

b)

no

104.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

105.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

a)

45 minutes

b)

90 minutes
2x + 4y = 315

c)

60 minutes
3x + 4y = 450

d)

30 minutes

106.

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

a)

y = 9.65 + x
y = 8.40 + x

b)

y = 9.65x + 43
y = 8.40x + 58

c)

y =9.65x
y = 8.40x

d)

y = 9.65x - 43
y = 8.40x - 58

107.

Solve for x and y.
y = 2/3x - 2
y = -x + 3

a)

(0,3)

b)

(0,-3)

c)

(3,0)

d)

(-3,0)

108.

Solve for x and y.
y = 2/3x - 2
y = -x + 3

a)

(0,3)

b)

(0,-3)

c)

(3,0)

d)

(-3,0)

109.

Set up the problem.

a)

sin(47) = x/28

b)

cos(47) = x/28

c)

tan(47) = x/28

d)

cos(47) = 28/x

110.

Which Trig function do you use?

a)

Sine

b)

Cosine

c)

Tangent

111.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

112.

Set up the problem so that you can solve for X.

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

113.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

114.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

115.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

116.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

117.

What is the length of u and v in this 30-60-90 triangle?

a)

u = 8 v = 4√3

b)

u = 4√2 v = 8

c)

u = 16 v = 8

d)

u = 4√3 v = 8

PSAT prep 1

Total questions: 117

Worksheet time: 6hrs 33mins

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