ACT MATH PRACTICE (ALGEBRA)

Arithmetic

100

The square root of -(-9)² = ?

A. 9i   B. 9+i   C. 9-i   D. 9   E. -9

A. 9i

200

(x+3)(x-3) = 

A. 2x-9  B. 2x+9  C. x² +6x -9  D. x² - 9  E. x² -6x -9

D. x²-9

300

For f(x) = 4x-3 and g(x) = 10x -12, f(x) + g(x) =

A. 14x - 15  B. 14x +9  C. -6x -15  D. 6x +9  E. 14x+15

A. 14x -15

400

For all nonzero values for x and y, (2xy)(9x³y) / (6x²y) =

A. 2x⁴y²   B. 2x²y  C. 18x⁵y³   D. 3x³y²   E. 3x²y

E. 3x²y

500

Simplify the expression (x²+8x+12) / (6x+36)

A. (x+6)/6  B. (x+6)/(x-6)  C. 8/x  D. (x+2)/6  E. (x+6)/3

D. (x+2)/6

Solving Equations

100

Which of the following is a solution to the equation x² +25x = 0?

A. 50   B. 25   C. 5   D. -5   E. -25

E. -25

200

What is the solution to the following system of equations? 

3x-y=2

6x+2y=5

A. (5,2)  B. (7/9,1/3)  C. (1/4,3/4)  D. (2,5)  E. (3/4,1/4)

E. (3/4,1/4)

300

If the expression g(x) = x + kx - 6 is equal to zero when x = -3, what is the value of k?

A. -3   B. 3   C. 1   D. 2   E. -1

C. 1

400

If x/5 = 2 - x/4, then x =

A. -40  B. -2  C. 2/9  D. 40/9  E. 9

D. 40/9

500

If 2x = 2y-6, then (y-x)⁴ = ?

A. 9  B. 27  C. 36  D. 48  E. 81

E. 81

Functions

100

In a standard coordinate plane, how many times will the graph of the function g(x) = (x-8)(x+3)(x+6) intersect the x-axis?

A. 2  B. 3  C. 4  D.9  E.12

B. 3

200

Find all x-intercepts for the graph of the function f(x)= (x-2)(x²-5x-14)

a. {-2,7}  b. {-2,2,7}  c. {-7,-2,2}  d. {-7,-2,2,7}

b. {-2,2,7}

300

Which of the following statements is true about the parabola y=-2x²-3x

A. It opens upward  B. It opens to the left  C. It has a line of symmetry at x=3/4  D. It has its vertex at the origin  E. It has a line of symmetry at x = -3/4

E. It has a line of symmetry at x = -3/4

400

Given f(x) = x³+5, if f(x)=130, what is the value of x?

A. 5  B. 2  C. 3  D. 1  E. -5

A. 5

500

For the functions f(x) = x²+1 and g(x) = x-5, (f o g)(x) =

A. x²-4  B. x²+25  C. x²+26  D. x²-10x+25  E. x²-10x+26

E. x²-10x+26

Exponents

100

What is the solution to the equation 9^2x+2 =27^x+1 ?

A. -1   B. 1/2   C. 3/7    D. 2    E. 3

A. -1

200

If n = 8 and 16 (2^m) = 4^n-8, then m = ?

A. -4   B. -2   C. 0   D. 1   E. 8

A. -4

300

(27/64)^-2/3 =?

A. -9/16   B. -9/32   C. 9/32   D. 16/9   E. 32/9

D. 16/9

400

If x is a real number such that x³ = 729, then x² + sqrt (x) = ?

A. 9   B. 27   C. 30   D. 84   E. 90

D. 84

500

If (n^x)/(n^y) = n² for all n not equal to zero, which of the following must be true?

A. x+y=2   B. x-y=2   C. xy=2   D. x/y=2  

B. x-y=2

Inequalities

100

What is the largest integer value of z that satisfies the inequality 31/38 > z/27 ?

A. 23   B. 22   C. 21   D. 20   E. 19

B. 22

200

If -x>y and |x| >y, which values for x and y make both statements true? 

l.(0,0)  ll.(-2,3)  lll.(-5,4)  lV.(-2,-3)  V.(5,-5)

A. All except ll   B. All of them  C. lll and lV  D. lV only

C. lll and lV

300

Which coordinate pair is a solution to the inequality 12-3y > 6x+3?

A. (1,1)   B. (2,1)   C. (1,2)   D. (-1,-2)  E. (2, -1)

D.  (-1,-2)

400

Given y = x/(x-1) and x>1, which of the following is a possible value of y?

A. -1.9  B. -0.9  C. 0.0  D. 0.9  E. 1.9

E. 1.9

500

What is the solution to -3a+7 > 2?

A. a>5/3   B. a<5/3   C. a>5   D. a=3 

B. a<5/3