ACT Questions: Intermediate Algebra

Videos, examples, solutions, activities and worksheets to help ACT students review some intermediate algebra questions.

ACT Math Algebra Problem
Complex numbers
Example:
In the complex number system, i² = -1. What does (4 - i)(-2 + 5i) equal?
A. -3 + 7i
B. -3 + 22i
C. 3 + 7i
D. -8i
E. -8 + 7i

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ACT Math Solutions
Rational Equations
For all nonzero x and y, 1/(2x) + 1/(3y) = ?
A. 6/(2xy)
B. (y + 2x)/(6xy)
C. 6/(2x + 3y)
D. (3x + 2y)/(6xy)
E. (2x + 3y)/(6xy)

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ACT Math - Intermediate Algebra Worksheet
Solving Systems of Equations
Examples:

1. If x - y = 5 and x + y = 5, the y =?
   A. -5
   B. 0
   C. 1/5
   D. 5
   E. -1/5
   
   
2. Given that x is an integer, for which of the following values of x is x + 1/4x > 14 and x + 1 < 14
   A. 10
   B. 11
   C. 12
   D. 13
   E. 14
   
   
3. Which of the following equations expresses z in terms of x for all real numbers x,y, and z such that 4x² = 2y and y² = 8z?
   A. z = 1/4 x³
   B. z = 1/2 x²
   A. z = 1/4 x⁴
   A. z = 1/2 x⁴
   A. z = 4 x³
   
   
4. If 5x + 4y = 19 and 2x - 3y = 3, what is the value of x + y?
   A. 4
   B. 6
   C. 3/2
   D. 22/3
   E. 14
   
   
5. If x = 4y and y = 1/3 z, which of the following is the value of 2z - x?
   A. 4/3 z
   B. 3/4 z
   C. 2/3 z
   D. z
   E. 3/2 z
   
   
6. If x an y are positive integers such that the greatest common factor of x³y and x²y³ is 64, then which of the following could x equal?
   A. 3
   B. 4
   C. 5
   D. 16
   E. 64
   
   
7. A large sphere has a radius that is 3 times larger than the radius of a small sphere. How many times larger is the volume of the larger sphere than the volume of the smaller sphere?
   A. 3
   B. 4/3
   C. 9
   D. 12
   E. 27
   
   
8. If x = 3t -6 and y = 3 - 2t, which of the following expresses y in terms of x?
   A. y = 1 - 2x
   B. y = 9 - x
   C. y = -2/3 x - 1
   D. y = 2/3 x + 1
   E. y = x - 9
   
   
9. Three friends are going to rent a house to live in. If they split the rent 3 ways, each one of them pays $650 each month. They were hoping to each pay $400 or less. How many more people have to live in the house for each one of them to pay $400 or less?
   A. 6
   B. 5
   C. 4
   D. 3
   E. 2
   
   
10. Ten players from the high school soccer team and 8 players from the football team donate money for a senior class gift. The soccer players each donated half as much as each football player and together they raised $260. How much did each football player donate?
    A. $10
    B. $15
    C. $12
    D. $20
    E. $22
    

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ACT Math: Algebra Problem
Try this typical ACT-style Algebra problem
Example:
If a - b = 14 and 2a + b = 46, then b =?
F. 6
G. 16
H. 20
J. 30
K. 40

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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