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More Lessons for ACT Math

Math Worksheets

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

Example:

If a - b = 14 and 2a + b = 46, then b =?

F. 6

G. 16

H. 20

J. 30

K. 40

**ACT Math Algebra Problem**

Complex numbers

Example:

In the complex number system, i^{2} = -1. What does (4 - i)(-2 + 5i) equal?

A. -3 + 7i

B. -3 + 22i

C. 3 + 7i

D. -8i

E. -8 + 7i

**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)

**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 4x^{2} = 2y and y^{2} = 8z?

A. z = 1/4 x^{3}

B. z = 1/2 x^{2}

A. z = 1/4 x^{4}

A. z = 1/2 x^{4}

A. z = 4 x^{3}

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 x^{3}y and x^{2}y^{3} 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

More Lessons for ACT Math

Math Worksheets

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

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

Complex numbers

Example:

In the complex number system, i

A. -3 + 7i

B. -3 + 22i

C. 3 + 7i

D. -8i

E. -8 + 7i

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)

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 4x

A. z = 1/4 x

B. z = 1/2 x

A. z = 1/4 x

A. z = 1/2 x

A. z = 4 x

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 x

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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