Full-Length PSAT 10 Math Practice Test

☐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

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☐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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