SAT Math Practice Test Questions

B. \(\frac{5}{30}\)

C. \(\frac{6}{30}\)

D. \(\frac{11}{30}\)

5- What is the value of \(x\) in the following system of equations?
\(5x+2y=3\)
\(y=x\)

A. \(\frac{3}{7}\)

B. \(\frac{1}{3}\)

C. \(\frac{2}{3}\)

D. \(\frac{4}{3}\)

6- If \(y=nx+2\), where n is a constant, and when \(x=6, y=14\), what is the value of y when \(x=10\)?

A. 10

B. 12

C. 18

D. 22

7- Which of the following numbers is NOT a solution to the inequality \(2x-5≥3x-1\)?

A. \(-2\)

B. \(-4\)

C. \(-5\)

D. \(-8\)

8- \(4x^2+6x-3, 3x^2-5x+8\)
Which of the following is the sum of the two polynomials shown above?

A. \(5x^2+3x+4\)

B. \(4x^2−6x+3\)

C. \(7x^2+x+5\)

D. \(7x^2+5x+1\)

9-The table above shows some values of linear function \(g(x)\). Which of the following defines \(g(x)\)?

A. \(g(x)=2x+1\)

B. \(g(x)=2x−1\)

C. \(g(x)=−2x+1\)

D. \(g(x)=x+2\)

10- If \(\frac{6}{5}=\frac{3}{2}\), what is the value of \(y\)?

A. \(\frac{5}{6}\)

B. \(\frac{5}{4}\)

C. \(\frac{4}{5}\)

D. \(\frac{3}{2}\)

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Answers:

1- C
When 5 times the number \(x\) is added to 10, the result is
\(10 + 5x\). Since this result is equal to 35, the equation \(10 + 5x = 35\) is true.
Subtracting 10 from each side of \(10 + 5x = 35\) gives \(5x=25\),
and then dividing both sides by 5 gives \(x=5\).
Therefore, 3 times \(x\) added to 6, or
\(6 + 3x\), is equal to \(6 + 3(5) = 21\).

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2- B
Since \(f(x)\) is linear function with a negative slop, then when \(x=-2, f(x)\) is maximum and when \(x = 3, f(x)\) is minimum. Then the ratio of the minimum value to the maximum value of the function is:
\(\frac{f(3)}{f(-2)}=\frac{-3(3)+1}{-3(-2)+1}=\frac{-8}{7}=-\frac{8}{7}\)

3- D
The description \(8+2x\) is 16 more than 20 can be written as the equation \(8+2x=16+20\), which is equivalent to \(8+2x=36\).
Subtracting 8 from each side of \(8+2x=36\) gives \(2x=28\).
Since \(6x\) is 3 times \(2x\), multiplying both sides of \(2x=28\) by 3 gives \(6x = 84\)

4- D
Of the 30 employees, there are 5 females under age 45 and 6 males age 45 or older. Therefore, the probability that the person selected will be either a female under age 45 or a male age 45 or older is: \(\frac{5}{30} + \frac{6}{30} = \frac{11}{30}\)

5- A
Substituting \(x\) for \(y\) in first equation.
\(5x+2y=3\)
\(5x+2(x)=3\)
\(7x=3\)
Divide both side of \(7x = 3\) by 3 gives \(x =\frac{3}{7}\)

6- D
Substituting 6 for \(x\) and 14 for \(y\) in \(y = nx+2\) gives \(14=(n)(6)+2\),
which gives \(n=2\). Hence, \(y=2x+2\).
Therefore, when \(x = 10\), the value of \(y\) is
\(y=(2)(10)+2 = 22\)

7- A
Subtracting \(2x\) and adding 5 to both sides of \(2x – 5 ≥ 3x – 1\) gives \(-4 ≥ x\).
Therefore, x is a solution to \(2x – 5 ≥ 3x – 1\) if and only if \(x\) is less than or equal to \(-4\) and x is NOT a solution to \(2x – 5 ≥ 3x – 1\) if and only if \(x\) is greater than \(-4\).
Of the choices given, only \(-2\) is greater than \(-4\) and, therefore, cannot be a value of \(x\).

8- C
The sum of the two polynomials is \((4x^2+6x-3)+(3x^2-5x+8)\)
This can be rewritten by combining like terms:
\((4x^2+6x-3)+(3x^2-5x+8)=(4x^2+3x^2 )+(6x-5x)+(-3+8)=
7x^2+x+5\)

9- C
Plugin the values of \(x\) in the choices provided. The points are \((1,-1)\),\((2,-3)\),and \((3,-5)\)
For \((1,-1)\) check the options provided:
A. \(g(x)=2x+1→−1=2(1)+1→−1=3A.g(x)=2x+1→−1=2(1)+1→−1=3\) This is NOT true.
B. \(g(x)=2x−1→−1=2(1)−1=1B.g(x)=2x−1→−1=2(1)−1=1\) This is NOT true.
C. \(g(x)=−2x+1→−1=2(−1)+1→−1=−1C.g(x)=−2x+1→−1=2(−1)+1→−1=−1\) This is true.
C. \(g(x)=x+2→−1=1+2→−1=3C.g(x)=x+2→−1=1+2→−1=3\) This is NOT true.

10- B
To solve the equation for \(y\), multiply both sides of the equation by the reciprocal of \(\frac{6}{5}\), which is \(\frac{5}{6}\),
this gives \(\frac{5}{6}× \frac{6}{5}y=\frac{3}{2} ×\frac{5}{6}\), which simplifies to
\(y=\frac{15}{12}=\frac{5}{4}\)

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