SAT Math Practice Test Questions

SAT Math Practice Test Questions is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.

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:

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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Official source: what the SAT covers, how it is structured and how it is scored are published by the College Board, which writes and administers the test, at satsuite.collegeboard.org.