Full-Length PSAT 10 Math Practice Test

Full-Length PSAT 10 Math Practice Test: work through realistic questions in the same format and difficulty as the real test, then check every answer against a full step-by-step solution so you can see where you lost marks and what to review next.

☐A. (frac{5}{39})

☐B. (frac{6}{39})

☐C. (frac{6}{13})

☐D. (frac{5}{6})

9- If a parabola with equation (y=ax^2+6x+16), where a is constant, passes through point ((-2, 8)), what is the value of (a^2)?

☐A. 1

☐B. 2

☐C. 3

☐D. 4

10- If (a, b) and c are positive integers and (4a=6b=10c), then the value of (2a+3b-4c) is how many times the value of a?

☐A. 2.4

☐B. 2.6

☐C. 3.5

☐D. 4.2

11- What is the length of AB in the following figure if AE=10, CD=16, and BC=20?

☐A. 3.8

☐B. 8.8

☐C. 12.5

☐D. 24.6

12- What is the solution of the following system of equations? (begin{cases}frac{x}{3}+frac{4y}{6}=1 y-x=6 end{cases})

☐A. (x=5,y=-3)

☐B. (x=-3,y=5)

☐C. (x=-3,y=3)

☐D. (x=3,y=3)

13- John buys a pepper plant that is 4 inches tall. With regular watering, the plant grows 8 inches a year. Writing John’s plant’s height as a function of time, what does the intercept represent?

☐A. The (y)-intercept represents the rate of growth of the plant, which is 8 inches

☐B. The (y)-intercept represents the starting height of 6 inches

☐C. The (y)-intercept represents the rate of growth of a plan,t which is 4 inches per year

☐D. There is no (y)-intercept

14- The length of a rectangle is 8 meters greater than 2 times its width. The perimeter of the rectangle is 88 meters. What is the area of the rectangle in meters? __________

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15- In the following equation, what is the value of (y-4x)? ___________
(frac{2y}{9}=x-frac{1}{9}x+4)

16- What is the value of (x) in the following equation?
(frac{x^2-4}{x+2}+4(x+3)=20)

17- If(x≠0), what is the value of (frac{(6(x)(y^3 ))^2}{x^2 (3y^2)^3})? _____________

PSAT 10 Math Practice Test

Section 2 (Calculator)
31 questions
Total time for two parts: 70 Minutes

18- A football team won exactly 72% of the games it played during the last session. Which of the following could be the total number of games the team played last season?

☐A. 40

☐B. 50

☐C. 55

☐D. 60

19- If a gas tank can hold 30 gallons, how many gallons does it contain when it is (frac{5}{6}) full?

☐A. 20

☐B. 25

☐C. 62.5

☐D. 100

20- In the??-plane, the point ((-2,4)) and ((6,20)) are on line A. Which of the following equations of lines is parallel to line A?

☐A. (y= frac{x}{2})

☐B. (y=x)

☐C. (y=2x)

☐D. (y=3x)

21- If (y=nx+4), where n is a constant, and when (x=3), (y=22), what is the value of y when (x=4)?

☐A. 10

☐B. 24

☐C. 28

☐D. 32

22- If (4+4x) is(8) more than (12), what is the value of (8x)?

☐A. 32

☐B.38

☐C. 62

☐D. 84

23- If (x) is greater than(-1) and less than (1) and(x≠0), which of the following is true?

☐A. (x>sqrt{x^2+1})>sqrt{x^2}+1)

☐B.(x<sqrt{x^2}+1<sqrt{x^2+1})

☐C. (sqrt{x^2+1})<x<sqrt{x^2}+1)

☐D.(sqrt{x^2}+1>sqrt{x^2+1}>x)

24- The sum of eight different negative integers is (-100). If the smallest of these integers is (-16), what is the largest possible value of one of the other five integers?

☐A. (-14)

☐B. (-9)

☐C. (, 5)

☐D. (-1)

25- The capacity of a red box is (40%) bigger than the capacity of a blue box. If the red box can hold (35) equal-sized books, how many of the same books can the blue box hold?

☐A. 20

☐B.22

☐C. 25

☐D.30

Questions 9 and 11 are based on the following data

26- If a is the mean (average) of the number of cities in each pollution type category, b is the mode, and c is the median of the number of cities in each pollution type category, then which of the following must be true?

☐A. (a<b<c)

☐B. (b<a<c)

☐C. (a=c)

☐D. (b<c=a)

27- What percent of cities are in the type of pollution A, C, and E respectively?

☐A. (60%, 40%, 90%)

☐B.(30%, 40%, 90%)

☐C. (30%, 40%, 60%)

☐D. (80%, 70%, 50%)

28- How many cities should be added to the type of pollution E until the ratio of cities in the type of pollution E to cities in the type of pollution D will be 0.8?

☐A. 2.2

☐B.3.5

☐C. 4.2

☐D.5.1

29- What is the ratio of the minimum value to the maximum value of the following function?
(-4≤x≤5)
(f(x)=-2x+2)

☐A. (-1)

☐B. (frac{-4}{5})

☐C. (frac{6}{10})

☐D.(frac{8}{7})

30- In the following right triangle, if the sides AB and AC become one-third shorter, what will be the ratio of the perimeter of the triangle to its area?

☐A. (frac{1}{2})

☐B. 1

☐C. 2

☐D. 3

31- The ratio of boys and girls in a class is 5:9. If there are 84 students in the class, how many more boys should be enrolled to make the ratio 1:1?

☐A. 12

☐B.18

☐C. 24

☐D.30

Questions 15 to 17 are based on the following data

32- What’s the maximum ratio of women to men in the four cities?

☐A. 0.88

☐B. 0.91

☐C. 0.96

☐D.0.98

33- What’s the ratio of percentage of men in city A to percentage of women in city C?

☐A. 0.9

☐B. 0.95

☐C. 1.23

☐D. 1.38

34- How many women should be added to city D until the ratio of women to men will be 1.4?

☐A. 470

☐B. 480

☐C. 495

☐D. 500

35- If (f(x)=-2x+2(2x+3)+1) then (f(-3x)=)?

☐A. (5x)

☐B. (-6x+4)

☐C. (-6x+7)

☐D. (6x-7)

36- If a car has 60-liter petrol and after one hour driving the car use 7.5-liter petrol, how much petrol will remain after -hours driving?

☐A. (60+7.5x)

☐B. (60-7.5x)

☐C. (60×7.5x)

☐D. (60÷7.5x)

37- In the triangle below, if the measure of angle is 43 degrees, then what is the value of? (figure is NOT drawn to scale)

☐A. 89

☐B. 90

☐C. 91

☐D. 96

38- The following graph shows the mark of six students in mathematics. What is the mean (average) of the marks?

☐A. 10

☐B. 12

☐C. 14

☐D. 15

39- In the rectangle below if (y > 10) cm and the area of rectangle is 96 cm(^2) and the perimeter of the rectangle is 40 cm, what is the value of and respectively?

☐A. 6, 12

☐B. 8, 10

☐C. 8, 11

☐D. 8, 12

40- If (frac{a-b}{2b}=frac{5}{9}), then which of the following must be true?

☐A. (frac{a}{b}=frac{11}{21})

☐B. (frac{a}{b}=frac{21}{11})

☐C. (frac{a}{b}=frac{21}{10})

☐D. (frac{a}{b}=frac{19}{9})

41- Given the right triangle ABC bellow, sec((β)) is equal to?

☐A. (frac{a}{b})

☐B. (frac{a}{sqrt{a^2+b^2}})

☐C. (frac{sqrt{a^2+b^2}}{a})

☐D. (frac{b}{sqrt{a^2+b^2}})

42- Solve the following inequality.

☐A. (|frac{2x}{3}-4x-6|<4)

☐B. (frac{6}{-10}>x>-3)

☐C. (frac{10}{3}<x<10)

☐D. (-10<x<-frac{10}{3})

43- If (x) is directly proportional to the square of (y), and (y=3) when (x=18), then when (x=288, y= )?

☐A. (frac{1}{5})

☐B. (1)

☐C. (5)

☐D. (12)

27- Which of the following values for (x) and (y) satisfy the following system of equations?
(begin{cases}2x+4y=6 \x+3y=-20 end{cases})

☐A. (x=33,y=-18)

☐B. (x=49,y=-23)

☐C. (x=72,y=-23)

☐D. (x=83,y=-18)

28- If (x+4y=frac{-8y^2+12}{2x}), what is the value of ((x+2y)^2)? ((x≠0))

29- A ladder leans against a wall forming a 45ᵒ angle between the ground and the ladder. If the bottom of the ladder is 10 feet away from the wall, how many feet is the ladder?

30- The volume of cube A is (frac{1}{4}) of its surface area. What is the length of an edge of cube A?

31- (f(x)=ax^2+bx+c) is a quadratic function where a, b and c are constant. The value of x of the point of intersection of this quadratic function and linear function (g(x)=x+2) is (3). The vertex of (f(x)) is at ((-3, 11)). What is the product of a, b and c?

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