More Lessons for ACT Math
Videos, examples, solutions, activities and worksheets to help ACT students review some intermediate algebra questions.
ACT Math: Algebra Problem
Try this typical ACT-style Algebra problem
If a - b = 14 and 2a + b = 46, then b =?
ACT Math Algebra Problem
In the complex number system, i2
= -1. What does (4 - i)(-2 + 5i) equal?
A. -3 + 7i
B. -3 + 22i
C. 3 + 7i
E. -8 + 7i
ACT Math Solutions
For all nonzero x and y, 1/(2x) + 1/(3y) = ?
B. (y + 2x)/(6xy)
C. 6/(2x + 3y)
D. (3x + 2y)/(6xy)
E. (2x + 3y)/(6xy)
ACT Math - Intermediate Algebra Worksheet
Solving Systems of Equations
1. If x - y = 5 and x + y = 5, the y =?
2. Given that x is an integer, for which of the following values of x is x + 1/4x > 14 and x + 1 < 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
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?
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
E. 3/2 z
6. If x an y are positive integers such that the greatest common factor of x3
y and x2
is 64, then which of the following could x equal?
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?
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?
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?
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