Free Printable PSAT Practice Test ALL (no calculator)

1.

A babysitter earns $8 an hour for babysitting 2 children and an additional $3 tip when both children are put to bed on time. If the babysitter gets the children to bed on time, what expression could be used to determine how much the babysitter earned?

a)

8 + 3x, where x is the number of hours

b)

3 + 8x, where x is the number of hours

c)

x(8 + 2) + 3, where x is the number of children

d)

3 + (8 + 2)x, where x is the number of children

2.

$3\left(x+y\right)=y$

If (x,y) is a solution to the equation above and y ≠ 0, what is the ratio $\frac{x}{y}$ ?

a)

$-\frac{4}{3}$

b)

$-\frac{2}{3}$

c)

$\frac{1}{3}$

d)

$\frac{2}{3}$

3.

$\frac{1}{2}x-\frac{1}{4}y=10$

$\frac{1}{8}x-\frac{1}{8}y=19$

Which ordered pair (x,y) satisfies the system of equations above?

a)

(-112, -264)

b)

(64, 88)

c)

$\left(\frac{232}{3},\frac{224}{3}\right)$

d)

(288, 536)

4.

Triangle ABC above is isosceles with AB = AC and BC = 48. The ratio of DE to DF is 5 : 7. What is the length of $\overline{DC}$ ?

a)

12

b)

20

c)

24

d)

28

5.

In a certain game, a player can solve easy or hard puzzles. A player earns 30 points for solving an easy puzzle and 60 points for solving a hard puzzle. Tina solved a total of 50 puzzles playing this game, earning 1,950 points in all. How many hard puzzles did Tina solve?

a)

10

b)

15

c)

25

d)

35

6.

$n=456-3T$
The equation above is used to model the relationship between the number of cups, n, of hot chocolate sold per day in a coffee shop and the average daily temperature, T, in degrees Fahrenheit. According to the model, what is the meaning of the 3 in the equation?

a)

For every increase of 3°F, one more cup of hot chocolate will be sold.

b)

For every decrease of 3°F, one more cup of hot chocolate will be sold.

c)

For every increase of 1°F, three more cups of hot chocolate will be sold.

d)

For every decrease of 1°F, three more cups of hot chocolate will be sold.

7.

A truck enters a stretch of road that drops 4 meters in elevation for every 100 meters along the length of the road. The road is at 1,300 meters elevation where the truck entered, and the truck is traveling at 16 meters per second along the road. What is the elevation of the road, in meters, at the point where the truck passes $t$ seconds after entering the road?

a)

$1,300-0.04t$

b)

$1,300-0.64t$

c)

$1,300-4t$

d)

$1,300-16t$

8.

If $f(x-1)=2x+3$ for all values of $x$ , what is the value of $f(-3)$ ?

a)

-7

b)

-5

c)

-3

d)

-1

9.

Which of the following is equivalent to $\left(s-t\right)\left(\frac{s}{t}\right)$

a)

$\frac{s}{t}-s$

b)

$\frac{s}{t}-st$

c)

$\frac{s^2}{t}-s$

d)

$\frac{s^2}{t}-\frac{s}{t^2}$

10.

For what value of h is

$24=\frac{h}{10}-6$ ?

(a)

11.

What is the value of a if

(2a + 3) - (4a - 8) = 7?

(a)

12.

If $x$ is not equal to zero, what is the value of $\frac{4\left(3x\right)^2}{\left(2x\right)^2}$ ?

(a)

13.

If x - 2 is a factor of x²- bx + b, where b is a constant, what is the value of b?

(a)

14.

$2x^2+7x-15=0$
If r and s are two solutions of the equation above and r > s , which of the following is the value of r − s?

a)

$\frac{15}{2}$

b)

$\frac{13}{2}$

c)

$\frac{11}{2}$

d)

$\frac{3}{2}$

15.

To cut a lawn, Allan charges a fee of $15 for his equipment and $8.50 per hour spent cutting a lawn. Taylor charges a fee of $12 for his equipment and $9.25 per hour spent cutting a lawn. If x represents the number of hours spent cutting a lawn, what are all the values of x for which Taylor’s total charge is greater than Allan’s total charge?

a)

$x>4$

b)

$3\le x\le4$

c)

$4\le x\le5$

d)

$x<3$

16.

$p(x)=3(x^2+10+5)-5(x-k)$

In the polynomial p(x) defined above, k is a constant. If p(x) is divisible by x, what is the value of k ?

a)

-3

b)

-2

c)

0

d)

3

17.

In the xy-plane, if the parabola with equation $y=ax^2+bx+c$ , where a, b, and c are constants, passes through the point (−1, 1), which of the following must be true?

a)

a - b = 1

b)

-b + c = 1

c)

a + b + c = 1

d)

a - b + c = 1

18.

If $\frac{1}{2}x+\frac{1}{3}y=4$ , what is the value of $3x+2y$ ?

(a)

19.

$x^2+y^2-6x+8y=144$

The equation of a circle in the xy-plane is shown above. What is the diameter of the circle?

(a)

20.

Which of the following is an equivalent form of the expression 15x + 24ax ?

a)

39ax²

b)

39(a + 2x)

c)

(5 + 8a)x

d)

(5 + 8a)3x

21.

What are the coordinates of the vertex in the equation below?

y=2x^2−12x+13

a)

(4,5)

b)

(-4,5)

c)

(3,-5)

d)

(-3,5)

22.

Solve for the roots of this equation:

y=2x^2+3x−9

a)

$x=-\frac{3}{2}$ and $x=3$

b)

$x=\frac{3}{2}$ and $x=-3$

c)

$x=0$ and $x=-\frac{3}{2}$

d)

$x=0$ and $x=\frac{3}{2}$

23.

Which of these equations will show the parabola with the widest opening when graphed?

a)

$y=-\frac{3}{4}x^2+x-\frac{1}{2}$

b)

$y=2x^2-5x+8$

c)

$y=\frac{1}{2}x^2+3x+5$

d)

$y=x^2+2x-3$

24.

The function f(r) = r² + 3 is shifted 4 units down and 5 units to the right. Which function shows this transformation?

a)

g(r) = (r + 5)² - 1

b)

g(r) = r² - 5r - 4

c)

g(r) = r² - 10r + 24

d)

g(r) = (r - 4)² + 5

25.

Determine which line is perpendicular to:

$\frac{y}{2}-1=3\left(x+1\right)$

a)

$x=-3\left(-5+2y\right)$

b)

$6x=-y+15$

c)

$y=6x-4$

d)

$\frac{1}{2}\left(y-3\right)=3\left(x-5\right)$

26.

The sine of angle B in the right triangle ABC is $\frac{4}{5}$ . What is cos (B)?

(a)

27.

The equation of a circle is given as:

$\left(x-5\right)^2+\left(y-12\right)^2=r^2$

What is r, if it is twice the distance from the center of the circle to the origin?

(a)

28.

Simplify: $\frac{a^2b^{\frac{1}{2}}b}{a^{\frac{1}{2}}ab^2}$

a)

$\frac{b^{\frac{1}{2}}}{a^{\frac{1}{2}}}$

b)

$\frac{a}{b}$

c)

$\frac{ab}{b}$

d)

$\frac{a^{\frac{1}{2}}}{b^{\frac{1}{2}}}$

29.

What is 1 radian equal to in degrees?

a)

$\frac{\pi}{90}$

b)

$\frac{180}{\pi}$

c)

$\frac{90}{\pi}$

d)

$2\pi$

30.

Which linear equation shows the relationship between variables x and y, if (0, -2), (1, 1), and (5, 13) are points on the line?

a)

3x - y = 2

b)

x = 3y - 2

c)

y = x + 12

d)

y = 5x - 13

31.

Which of these statements describes the graph of the inequality:

$y>2x-1$

a)

a dashed line passing through ( $\frac{1}{2}$ , 0) and (0, -1) with shaded area above the line

b)

a heavy line passing through ( $\frac{1}{2}$ , 0) and (0, -1) with shaded area above the line

c)

a dashed line passing through (2, 0) and (0, -1) with shaded area below the line

d)

a heavy line passing through (2, 0) and (0, -1) with shaded area below the line

32.

Express y in terms of x in this inequality:

$9x+3\ge1-3y$

a)

$y>-3x+\frac{4}{3}$

b)

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

c)

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

d)

$y\le-3x+\frac{4}{3}$

33.

Solve this inequality and give your answer as an interval:

$\left|5x-2\right|<13$

a)

$\left(-\frac{11}{5},3\right)$

b)

$\left(-\frac{2}{5},\frac{13}{5}\right)$

c)

$-\frac{11}{5}<x<3$

d)

$\left[5,13\right]$

34.

Josh usually drives at an average of 30 miles per hour. How much must he increase his usual speed if he needs to travel 300 miles in 6 hours. Give your answer in miles per hour.

(a)

35.

In this data set:

{4, 4, 6, 6, 6, 7, 7, 8, 8, 9},

two measures of center are equal in value. What is this value?

(a)

36.

What is the value of x + 3 in this equation, if y = 3?

$3x+9=18-y$

(a)

37.

Annie is 10 years old, while Emma is 16. If x represents Annie’s age, and y Emma’s age, which pair of equations will you use to solve for the age of Emma when she was twice as old as Annie?

a)

y + 6 = x and y = 2x

b)

y = x + 6 and y = 2x

c)

y = x + 6 and 2y = 2

d)

y = x - 6 and y = 2x

38.

Which of the following describes the solutions to this system of two equations?

$y=3x+14$
$y-3=x^2$

a)

only one solution

b)

two real solutions

c)

infinite number of solutions

d)

no real solution

39.

The table provides information concerning the amounts saved by Albert and Bernard for the months from January to June, inclusive. In which month did Albert’s accumulated savings become six times the initial amount he saved?

a)

May

b)

April

c)

June

d)

March

40.

If this data on the table were to be plotted using line graphs, with the x-axis representing the months and the y-axis representing accumulated savings, whose savings will have a steeper line graph for the period January-April?

a)

cannot be determined

b)

Bernard's

c)

Albert's

d)

lines would have the same slope

41.

Which of the following is an equivalent form of the expression 15x + 24ax ?

a)

39ax²

b)

39(a + 2x)

c)

(5 + 8a)x

d)

(5 + 8a)3x

42.

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)

$r=d-t$

43.

Which of the following is a solution to the equation 2x² + 4x = 3 + 3x²?

a)

-1

b)

0

c)

3

d)

6

44.

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

45.

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

46.

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 ≤ x ≤ 280

b)

4,860 ≤ x ≤ 4,870

c)

4,860 ≤ x ≤ 5,040

d)

5,030 ≤ x ≤ 5,040

47.

In the equation below, a is a constant, for what value of a does the equation have an infinite number of solutions?

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

(a)

48.

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)

49.

In the equation below, a is an integer.

12x² + ax - 20

If 3x + 4 is a factor of this expression, what is the value of a?

(a)

50.

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

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

51.

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)

52.

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)

b)

c)

d)

53.

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)

$\frac{DC}{BC}$

54.

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

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

a)

2

b)

3

c)

5

d)

6

55.

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

56.

$(ax+by)(cx-dy)$
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)

57.

$\frac{5\left(k+2\right)-7}{6}=\frac{13-\left(4-k\right)}{9}$

In the equation above, what is the value of k?

a)

$\frac{9}{17}$

b)

$\frac{9}{13}$

c)

$\frac{33}{17}$

d)

$\frac{33}{13}$

58.

$4x-y=3y+7$
$x+8y=4$

Based on the system of equations above, what is the value of the product xy?

a)

$-\frac{3}{2}$

b)

$\frac{1}{4}$

c)

$\frac{1}{2}$

d)

$\frac{11}{9}$

59.

$\frac{1}{x}+\frac{2}{x}=\frac{1}{5}$

Anise needs to complete a printing job using both of the printers in her office. One of the printers is twice as fast as the other, and together the printers can complete the job in 5 hours. The equation above represents the situation described. Which of the following describes what the expression

\frac{1}{x}

represents in this equation?

a)

The time, in hours, that it takes the slower printer to complete the printing job alone

b)

The portion of the job that the slower printer would complete in one hour

c)

The portion of the job that the faster printer would complete in two hours

d)

The time, in hours, that it takes the slower printer to complete $\frac{1}{5}$ of the printing job

60.

The graph of y = (2x – 4)(x – 4) is a parabola in the xy-plane. In which of the following equivalent equations do the x- and y-coordinates of the vertex of the parabola appear as constants or coefficients?

a)

y = 2x² – 12x + 16

b)

y = 2x(x – 6) + 16

c)

y = 2(x – 3)² + (–2)

d)

y = (x – 2)(2x – 8)

61.

Andrew is hosting a party and books a catering company that charges $14.95 per person plus a $40 cleanup fee. He has a coupon for a 15% discount off the entire cost of the booking. Which of the following models Andrew's total cost, in dollars, of catering his party for p people?

a)

0.85(14.95p) + 40

b)

0.85(14.95p + 40)

c)

0.15(14.95 + 40)p

d)

0.15p(14.95 + 40)

62.

Bora is a summer volunteer at the public library. At 9:30 a.m., the head librarian asks Bora to scan and reshelve a stack of returned library books. Bora can scan 20 books in one minute, and it takes him at least 1.5 minutes to reshelve each book. Which inequality below models the number of books, b, that Bora can scan and reshelve before his 12:00 p.m. lunch break?

a)

$1.55b≥270$

b)

$20b+1.5b≤270$

c)

$\frac{31b}{20}\ge150$

d)

$\frac{b}{20}+\frac{3b}{2}\le150$

63.

If the value of twice a number, k, plus 7 is between 3 and 23, then which of the following must also be true of k?

a)

$\left|k-4\right|<4$

b)

$\left|k-3\right|<5$

c)

$\left|k-5\right|<3$

d)

$\left|k-6\right|<2$

64.

$\frac{x}{2}+\frac{y}{4}+3=5$

From the equation above, which of the following is the value of 2x + y?

a)

2

b)

8

c)

20

d)

32

65.

Which expression below is equivalent to the difference of the sum and product of (3m + 1) and (m – 5)?

a)

$-3m^2+10m+1$

b)

$3m^2-10m-9$

c)

$3m^2-18m-9$

d)

$-3m^2+18m+1$

66.

Lines l, k, and m above divide the xy-plane into seven regions as shown. Which regions should be shaded to show the solution to this system of inequalities?

y\ge\frac{1}{4}x-3

y\le-\frac{1}{2}x+1

a)

II and III

b)

I and V

c)

VI and VII

d)

I and VI

67.

If 3(2x – 5) = 4(6 – x), then what is $\frac{3}{4}$ in terms of x?

a)

$\frac{2x-5}{6-x}$

b)

$\frac{6-x}{2x-5}$

c)

$\frac{5-2x}{x-6}$

d)

$\frac{x-6}{5-2x}$

68.

$2^{3k}=1,073,741,824$

Which of the following is the value of k?

a)

8

b)

9

c)

10

d)

11

69.

The rational expression $\frac{3x^3y^{-2}z^a}{x^2y^{-4}z^2}$ simplifies to a monomial degree of 2. What is the value of a?

(a)

70.

$S\left(t\right)=-16t^2+128t$

In the function above, S is the altitude in feet of a model rocket t seconds after launch. How many seconds, to the nearest second, does it take for the rocket to reach its maximum height?

(a)

PSAT Practice Test ALL (no calculator)

Total questions: 70

Worksheet time: 1hrs 9mins

Similar Resources on Wayground