PSAT 10 Math Practice Test Questions

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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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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