Algebra Practice Test

Test your knowledge of introductory Algebra with this Algebra practice exam. Whether you are studying for a school math test or looking to test your math skills, this free practice test will challenge your knowledge of algebra.

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1 -3ab + 4ac - 2ad = -(3ab - 4ac + 2ad)

True

False

Incorrect. Please choose another answer.

-3ab + 4ac - 2ad = -(3ab - 4ac + 2ad)

-3ab + 4ac - 2ad = -3ab + 4ac - 2ad

2 A father gave $500 to his two sons. He gave X dollars to one son. Which of the following expressions correctly shows the amount he gave to the other son.

a. $500 + X

b. $500 ÷ X

c. $500 x X

d. $500 - X

Incorrect. Please choose another answer.

If X represents the amount given to one son, $500 - X represents the amount given to the other son.

3 Solve X where 5X = 20.

a. 4

b. 5

c. 10

d. 15

Incorrect. Please choose another answer.

5X = 20

X = 20 ÷ 5

X = 4

4 Solve X where X - 5 = 15.

a. 10

b. 15

c. 20

d. 25

Incorrect. Please choose another answer.

X - 5 = 15

X = 15 + 5

X = 20

5 Solve X where 3X + 7 - 2 = 8.

a. 1

b. 2

c. 3

d. 4

Incorrect. Please choose another answer.

3X + 7 - 2 = 8

3X + 5 = 8

3X = 3

X = 3 ÷ 3

X = 1

6 Irene is N years old. If Tom is twice as old, which of the following algebraic statements shows his age now?

a. 2N

b. 2N + X

c. 2 - N

d. N - 2

Incorrect. Please choose another answer.

If Irene is N years old and Tom is twice as old as Irene, the algebraic formula to show how old Tom is would be 2 x N or 2N.

7 John has B bats and buys C bats more. He then gives away D bats. Which of the following algebraic statements corretly shows how many bats John has left?

a. D - BC

b. B - C - D

c. B + C - D

d. B + D + C

Incorrect. Please choose another answer.

If John starts with B bats and buys C more bats, the total number of bats John has would be represented by the formula B + C.

When John gives D bats away, the sum of B + C would subtract D bats to determine how many he has left.

So, the formula is B + C - D.

8 What is the representation algebraically of the cost of L feet of lumber at Y dollars per foot?

a. L + Y

b. LY

c. L / Y

d. L - Y

Incorrect. Please choose another answer.

There are a variety of ways to show multiplication, L x Y.

LY
L · Y
(L)(Y)

9 3x + 6x =

a. 3x

b. 9 + 2 x

c. 9x

d. 9x + 2

Incorrect. Please choose another answer.

3x + 6x = 9x

10 5a + 2b - b + 4a =

a. 9a + b

b. a + b

c. 7a - 3b

d. 6a

Incorrect. Please choose another answer.

5a + 2b - b + 4a =

5a + 4a + 2b - b =

9a + b

11 Find the value of 3abc, where a = 2, b = 3 and c = 4.

a. 12

b. 27

c. 72

d. 82

Incorrect. Please choose another answer.

If a = 2, b = 3 and c = 4,

3abc =

3(2)(3)(4) =

6 x 12 = 72

12 The sum of a certain number and 3 times the number is 40. What is the number?

a. 8

b. 9

c. 10

d. 11

Incorrect. Please choose another answer.

8 + 3(8) = 32

9 + 3(9) = 36

10 + 3(10) = 40

11 + 3(11) = 44

13 Joe is lending Frank $500 and Frank has 4 years to pay it back. Joe is charging 6% interest. Frank wants to determine how much interest he'll pay over the 4 years. He sets up the formula, interest (i) = loan amount (l) x rate (r) x time (t). Find i.

a. $12

b. $120

c. $125

d. $1,200

Incorrect. Please choose another answer.

i = l x r x t

l = $500, r = 6% and t = 4 years

l = $500 x .06 x 4

i = $30 x 4

i = $120

14 In V = 2m - 3, V is which of the following?

a. Constant

b. Dependent Variable

c. Independent Variable

d. Exponent

Incorrect. Please choose another answer.

A dependent variable is a variable that depends on one or more other variables. In this equation, V depends on the value of m.

An independent variable is a variable that can have its value chosen without considering the values of other variables. In this equation, m is an independent variable.

15 In B = 3 + 4w, 3 is which of the following?

a. Constant

b. Dependent Variable

c. Independent Variable

d. Coefficient

Incorrect. Please choose another answer.

A constant is a value that does not change. In this equation, 3 is a fixed number that will not change.

A coefficient is a number used to multiple a variable. In this equation, 4 is a coefficient of the independent variable w.

16 V = bdt. Solve the formula for d.

a. d = b/tv

b. d = t/bv

c. d = vbt

d. d = v/bt

Incorrect. Please choose another answer.

v = bdt

v = d
bt

17 B = 1hm. Solve the formula for h.
2

a. h = 1/2Bm

b. h = 2B/m

c. h = 2m/B

d. h = 2Bm

Incorrect. Please choose another answer.

B = 1hm
2

2B = 1hm

2B = h
m

18 The absolute value of -14 is 14.

True

False

Incorrect. Please choose another answer.

The absolute value of a number, even a negative number, is a positive number.

19 - 3 + (-14) =

a. 11

b. -11

c. -17

d. -42

Incorrect. Please choose another answer.

- 3 + (-14) =

- 3 - 14 = - 17

20 20 - (-6) =

a. 14

b. -14

c. 26

d. 120

Incorrect. Please choose another answer.

20 - (-6) =

20 + 6 = 26

21 Add the following: 3x - 2y + 2y + 3z + 2z - 4x - 5y.

a. x - 5y - z

b. x -

c. - x - 5y - z

d. - x - 5y + 5z

Incorrect. Please choose another answer.

3x - 2y + 2y + 3z + 2z - 4x - 5y =

3x - 4x - 2y - 5y + 2y + 3z + 2z =

-x - 5y + 5z

22 6x - 10 = 4(x + 3). Solve for x.

a. x = 9

b. x = 10

c. x = 11

d. x = 12

Incorrect. Please choose another answer.

6x - 10 = 4(x + 3)

6x - 10 = 4x + 12

6x = 4x + 22

2x = 22

x = 11

23 x - 6 = 17. Solve for x.

a. x = 23

b. x = 11

c. x = 102

d. x = 17 / 6

Incorrect. Please choose another answer.

x - 6 = 17

x = 17 + 6

x = 23

24 Which of the following is not a grouping symbol?

a. parentheses

b. braces

c. brackets

d. arrows

Incorrect. Please choose another answer.

Grouping symbols such as parentheses, brackets and braces in math will contain numbers, variables and operations. The grouping symbol tells you to do the operation first. An arrow, on the other hand, is an implicaiton notation to show that both sides of an notation are equal.

25 A minus sign that precedes a parenthesis causes the sign of each term within the parentheses to change when the parentheses are removed.

True

False

Incorrect. Please choose another answer.

If a minus sign appears outside of a parentheses, the minus sign changes the terms within the parentheses when the parentheses is removed. For example,

- (2x - 4y)

-2x + 4y

26 If X equals 5, what is the value of 6X + 2X - X?

a. 25

b. 30

c. 35

d. 40

Incorrect. Please choose another answer.

If x = 5,

6x + 2x - x =

6(5) + 2(5) - 5 =

30 + 10 - 5 = 35

27 If 10 is separated into two parts, one of which is y, represent the second part.

a. 10 / y

b. 10 + y

c. 10 - y

d. y - 10

Incorrect. Please choose another answer.

If 10 is separated into two parts, one of which is y, the second part will be 10 - y.

28 Find 3 consecutive numbers such that 3 times the first is equal to 8 more than the sum of the other two.

a. 8, 9, 10

b. 9, 10, 11

c. 11, 12, 13

d. 12, 13, 14

Incorrect. Please choose another answer.

x = 1st number

x + 1 = 2nd number

x + 2 = 3rd number

3x = x + 1 + x + 2 + 8

3x = 2x + 11

x = 11

29 The ratio of the height of two buildings is 7 to 5. The first building is 210 feet tall. How tall is the second building?

a. 140

b. 145

c. 150

d. 160

Incorrect. Please choose another answer.

7/5 = 210/x

7x = 1,050

x = 150

30 Factor the polynomial 5x - 15.

a. x = 5

b. 5(x - 3)

c. x - 3

d. 5x - 3(5)

Incorrect. Please choose another answer.

When factoring, look to see what you can take out of a parentheses to put out front of it. It is the opposite of distributing in polynomial expressions.

The first term 5x can be factored (5)(x).

The second term 15 can be factored (5)(3).

5 is the only factor common to both terms. Divide out the 5 from the terms and move the common factor to the front of the parentheses.

Remember, when dividing 15 by 5, a 3 is left over.

5x/5 - 15/5 = x - 3

Move the common factor to the front.

5(x - 3)