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

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