PSAT 10 Math Practice Test Questions
Are you preparing for your PSAT 10 Math test? Review these free PSAT 10 Math Practice questions to help you learn more about the PSAT 10 Math test. Reviewing practice questions is the best way to brush up on your Math skills. Here, we walk you through solving 10 common PSAT 10 Math practice problems covering the most important math concepts on the PSAT 10 Math test. For additional educational resources, visit the U.S. Department of Education website.
These PSAT 10 Math practice questions are designed to be similar to those found on the real PSAT 10 Math test. They will assess your level of preparation and will give you a better idea of what to study for your exam.
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wing system of equations?
\(x+4y=10\)
\(5x+10y=20\) For education statistics and research, visit the National Center for Education Statistics.
A. \(x=3,y=2\) For education statistics and research, visit the National Center for Education Statistics.
B. \(x=2,y=-3\) For education statistics and research, visit the National Center for Education Statistics.
C. \(x=-2,y=3\) For education statistics and research, visit the National Center for Education Statistics.
D. \(x=3,y=-2\) For education statistics and research, visit the National Center for Education Statistics.
3- If \(a ≠ 0\) and \(6b=5a\sqrt{3}\), then what is the value of \(\frac{2b \sqrt{3}}{4a}\) ? For education statistics and research, visit the National Center for Education Statistics.
A. \(\frac{5}{4}\) For education statistics and research, visit the National Center for Education Statistics.
B. \(\frac{5}{4}a\) For education statistics and research, visit the National Center for Education Statistics.
C. \(2a\) For education statistics and research, visit the National Center for Education Statistics.
D. \(2a\sqrt{3}\) For education statistics and research, visit the National Center for Education Statistics.
4- If a gas tank can hold 25 gallons, how many gallons does it contain when it is \( \frac{2}{5} \) full? For education statistics and research, visit the National Center for Education Statistics.
A. 50 For education statistics and research, visit the National Center for Education Statistics.
B. 125 For education statistics and research, visit the National Center for Education Statistics.
C. 62.5 For education statistics and research, visit the National Center for Education Statistics.
D. 10 For education statistics and research, visit the National Center for Education Statistics.
5- In the \(xy\)-plane, the point \((4,3)\) and \((3,2)\) are on line \(A\). Which of the following equations of lines is parallel to line \(A\)? For education statistics and research, visit the National Center for Education Statistics.
A. \(y = 3x\) For education statistics and research, visit the National Center for Education Statistics.
B. \(y = \frac{x}{2}\) For education statistics and research, visit the National Center for Education Statistics.
C. \(y = 2x\) For education statistics and research, visit the National Center for Education Statistics.
D. \(y = x\) For education statistics and research, visit the National Center for Education Statistics.
6- In the following graph, which of the data point is farthest from the line of best fit (not shown)? For education statistics and research, visit the National Center for Education Statistics.
A. (6,1)
B. (5,4)
C. (3,3)
D. (2,2)
7- A football team won exactly \(80\%\) 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. 49
B. 35
C. 12
D. 32
8- If \(x\) is greater than 0 and less than 1, 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. \(\sqrt {(x^{2} )}+1< \sqrt{(x^{2}+1) }< x\)
9- If \(x\) is directly proportional to the square of \(y\), and \(y=2\) when \(x=12\), then when \(x=75 y=\) ?
A. \(\frac{1}{5}\)
B. 1
C. 5
D. 12
10- Jack earns $616 for his first 44 hours of work in a week and is then paid 1.5 times his regular hourly rate for any additional hours. This week, Jack needs $826 to pay his rent, bills, and other expenses. How many hours must he work to make enough money this week?
A. 40
B. 48
C. 53
D. 54
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Answers:
1- B
Use the formula of areas of circles.
Area of a circle = \(πr^2→64 π=πr^2→64=r^2→r=8\)
The radius of the circle is 8. Now, use the circumference formula:
Circumference \(= 2πr = 2π (8) = 16π\)
2- C
\(x+4y=10\)
\(5x+10y=20\)
Multiply the top equation by -5 then,
\(-5x-20y=-50\)
\(5x+10y=20\)
\(Add \space two \space equations\)
\(-10y=-30→y=3 \) plug in the value of y into the first equation
\(x+4y=10→x+4(3)=10→x+12=10\)
Subtract 12 from both sides of the equation. Then:
\(x+12=10→x=-2\)
3- A
\(6b=5a\sqrt3→b= \frac{5a\sqrt3}{6}\)
\(Therefore:\)
\(\frac{2b\sqrt3}{4a}=\frac{2× \frac{5a\sqrt3}{6}×\sqrt3}{4a}=\frac{2×5a×3}{4×6a}=\frac{5}{4}\)
4- D
\( \frac{2}{5} ×25= \frac{50}{5} =10\)
5- D
The slop of line A is:
\(\frac{y_{2} – y_{1}}{x_{2} – x_{1}} = \frac{3-2}{4-3}=1 \)
Parallel lines have the same slope and only choice \(D (y=x)\) has slope of 1.
6- A
Line AB is the best fit line.
Then, point (6,1) is the farthest from line AB.
7- B
Choices \(A, C\) and \(D\) is incorrect because \(80\%\) of each of the numbers is a non-whole number.
\(49, 80 \% \ of \ 49 = 0.80×49=39.2\)
\(35, 80 \% \ of \ 35=0.80×35=28\)
\(12, 80 \% \ of \ 12=0.80×12=9.6\)
\(32, 80 \% \ of \ 32=0.80×32=25.6\)
8- A
Let \(x\) be equal to 0.5, then: \(x = 0.5\)
\(\sqrt{(x^2+1)}=\sqrt{(0.5^2+1)}=\sqrt{1.25}≈1.12\)
\(\sqrt{(x^2 )+1}=\sqrt{(0.5^2 )}+1=0.5+1=1.5\)
Then, option A is correct.
\(x<\sqrt{(x^2+1)}<\sqrt{(x^2 )}+1\)
9- C
\(x\) is directly proportional to the square of \(y\). Then:
\(x=cy^2\)
\(12=c(2)^2→12=4c→c=\frac{12}{4}=3\)
The relationship between \(x\) and y is:
\(x=3y^2\)
\(x=75\)
\(75= 3y^2 →y^2 = \frac{75}{3} = 25→y=5\)
10- D
The amount of money that jack earns for one hour:
\(\frac{$616}{44} =$14\)
Number of additional hours that he work to make enough money is:
\(\frac{$826-$616}{1.5×$14}=10\)Number of total hours is: \(44 + 10 = 54\)
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