ColorMathPink.com – Diagnostic Testing Center: Pre-Algebra

Pre-Algebra Diagnostic Test
By Lynette Long Copyright Lynette Long (2000)

Print a copy of this diagnostic test. Solve each problem and circle the correct answer. When you have finished the entire test, click on the answer icon, so that you can grade your test and find out what you know and don't know about pre-algebra.

Competency 1
Do you know how to add a negative number to a positive number?

What is (+5) + (-3)?
a. 2
b. -2
c. 8
d. -8

What is (+12) + (-15)?
a. -3
b. 3
c. 27
d. -27

Competency 2
Do you know how to add a positive number to a negative number?

What is (-6) + (+5)?
a. -1
b. 1
c. -11
d. 11

What is (-20) + (+2)?
a. -18
b. 18
c. -22
d. 22

Competency 3
Do you know how to add a negative number to a negative number?

What is (-7) + (-8)?
a. -1
b. 1
c. 15
d. -15

What is (-15) + (-9)?
a. - 6
b. 6
c. - 24
d. 24

Competency 4
Do you know how to subtract a positive number from a negative number?

What is (- 4) - (+5)?
a. -1
b. 1
c. -9
d. 9

What is (-8) - (+2)?
a. -6
b. 6
c. -10
d. 10

Competency 5
Do you know how to subtract a negative number from a negative number?

What is (-6) - (-8)?
a. -2
b. 2
c. -14
d. 14

What is (-15) - (-10)?
a. -25
b. -5
c. 5
d. 25

Competency 6
Do you know how to subtract a negative number from a positive number?

What is (+2) - (-3)?
a. -1
b. 1
c. -5
d. 5

What is (+6) - (-4)?
a. -2
b. 2
c. -10
d. 10

Competency 7
Do you know how to multiply a negative number times a positive number?

What is (-4) times (+8)?
a. -4
b. 4
c. -32
d. 32

What is (-5) times (20)?
a. -15
b. 15
c. -100
d. 100

Competency 8
Do you know how to multiply a positive number times a negative number?

What is (2) times (-3)?
a. -5
b. 5
c. -6
d. 6

What is (+10) times (-6)?
a. -4
b. 4
c. -60
d. 60

Competency 9
Do you know how to multiply a negative number by a negative number?

What is (-3) times (-8)?
a. -5
b. -11
c. -24
d. 24

What is (-4) times (-5)?
a. -1
b. -9
c. -20
d. 20

Competency 10
Do you know how to divide a negative number by a positive number?

What is (- 40) divided by (+5)?
a. 8
b. -8
c. 200
d. -200

What is (-12) divided by (+3)?
a. 4
b. -4
c. 36
d. -36

Competency 11
Do you know how to divide a positive number by a negative number?

What is (+50) divided by (-2)?
a. 100
b. -100
c. 25
d. -25

What is (+80) divided by (-10)?
a. -8
b. 8
c. -800
d. 800

Competency 12
Do you know how to divide a negative number by a negative number?

What is (-4) divided by (-2)?
a. 2
b. -2
c. 1/2
d. -1/2

What is (-12) divided by (-24)?
a. -1/2
b. -2
c. 1/2
d. 2

Competency 13
Do you know how to square a whole number?

What is 6 squared?
a. 12
b. 36
c. -12
d. -36

What is 17 squared?
a. 34
b. 144
c. 289
d. 4913

Competency 14
Do you know how to find the square root of a number?

What is the square root of 16?
a. 4
b. 8
c. 16
d. 256

What is the square root of 81?
a. 3
b. 9
c. 81
d. 6561

Competency 15
Do you know how to cube a number?

What is (3)³?
a. -9
b. 9
c. -27
d. 27

What is (-2)³?
a. 6
b. -6
c. 8
d. -8

Competency 16
Do you know how to square a decimal?

What is (.01)²?
a. .1
b. .01
c. .001
d. .0001

What is (.2)²?
a. .4
b. .04
c. .08
d. .008

Competency 17
Do you know how to find the cube root of a number?

What is the cube root of 64?
a. 2
b. 4
c. 8
d. -8

What is the cube root of 125?
a. 5
b. 25
c. -5
d. -25

Competency 18
Do you know how to find the square root of a decimal?

What is the square root of .01?
a. .1
b. .01
c. .5
d. .0001

What is the square root of 1.44?
a. .012
b. .12
c. 1.2
d. 12

Competency 19
Do you know how to square a proper fraction?

What is 1/9 squared?
a. 1/3
b. 1/18
c. 2/9
d. 1/81

What is 2/5 squared?
a. 4/5
b. 2/25
c. 4/25
d. 2/7

Competency 20
Do you know how to find the square root of a proper fraction?

What is the square root of 1/4?
a. 1/16
b. 1/2
c. 1
d. 1/8

What is the square root of 9/16?
a. 3/16
b. 3/4
c. 9/4
d. 81/16

Competency 21
Do you know how to solve simple algebraic expressions using addition and subtraction?

Solve for x: x + 15 = 30
a. x = 15
b. x = 30
c. x = 45
d. x = 60

Solve for x: x - 4 = 10
a. x = 6
b. x = 10
c. x = 14
d. x = 40

Competency 22
Do you know how to solve simple algebraic expressions using multiplication and division?

Solve for x: 3x = 15
a. x = 5
b. x = 12
c. x = 18
d. x = 45

Solve for x: 1/2 x = 10
a. x = 5
b. x = 9 1/2
c. x = 10 1/2
d. x = 20

Competency 23
Do you know how to solve an equation using ratios when the variable is in the numerator?

Solve for x: 1/4 = x /12
a. x = 1/48
b. x = 3
c. x = 4
d. x = 48

Solve for x: 1/3 = x /4
a. x = 3/4
b. x = 4/3
c. x = 3
d. x = 4

Competency 24
Do you know how to solve an equation using ratios when the variable is in the denominator?

Solve for x: 3/8 = 6/x
a. x = 3
b. x = 6
c. x = 12
d. x = 16

Solve for x: 5/6 = 15/x
a. x = 5
b. x = 6
c. x = 15
d. x = 18

Competency 25
Do you know how to use the Order of Operations?

What is 3(6 + 2) - 5?
a. 15
b. 16
c. 19
d. 21

What is 7 x 4 - 2 x 3 + 1?
a. 20
b. 23
c. 41
d. 56

Now that you've completed taking the Pre-Algebra Diagnostic Test, find out the answers so that you can grade your test. Each competency is tested by two questions. You need to get both questions correct in order to pass a competency. Review the questions you missed. Go look at the Algebra FAQ's to find out how to do the competencies you've failed.

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