Algebra I 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 algebra.



Competency 1
Do you know how to add two like expressions?

What is 3x + 7x?
a. 10 + 2x
b. 10x
c. 10x2
d. 4x

What is 4xy +2xy + xy?
a. 6xy
b. 6x3y3
c. 7xy
d. 7x3y3


Competency 2
Do you know how to subtract two algebraic expressions?

What is 10y - y?
a. 9
b. 9y
c. 10
d. 10y

What is 15yz - 3yz - 11yz?
a. 12yz
b. 23yz
c. yz
d. 7yz


Competency 3

Do you know how to multiply two algebraic expressions together?

What is 2(6x)?
a. 8x
b. 12x
c. 12x2
d. 12(2x)

What is (4a)(6a)?
a. 10a
b. 10a2
c. 24a
d. 24a2


Competency 4
Do you know how to divide two algebraic expressions?

What is 9a divided by a?
a. 8a
b. 9
c. 9a2
d. 10a

What is 12ab2 divided by 4b?
a. 3
b. 3a
c. 3ab
d. 3ab2


Competency 5
Do you know how to add negative algebraic expressions?

What is 3xy + (-5xy) + (-xy)?
a. -2xy
b. -2
c. -3xy
d. 9xy

What is -10xy + (-10xy)?
a. 0
b. 20xy
c. -20xy
d. -20


Competency 6
Do you know how to subtract negative algebraic expressions?

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

What is -9x - (-10x)?
a. 19x
b. x
c. -19x
d. -x

Competency 7
Do you know how to multiply negative algebraic expressions?

What is (-6x)(-2x)?
a. 12xy
b. 12x2
c. -12x
d. -12x2

What is (-a)(-6a)(-5)?
a. 30a
b. 30 - 2a
c. -30a2
d. -30 - 6a2


Competency 8
Do you know how to multiply a polynomial by a monomial?

What is 6x(x + 3)?
a. 21x
b. 18x2 + 18
c. 6x2 + 18x
d. 18x2

What is -5y(2y - 7)?
a. -25y
b. 10y -35
c. -10y2 -35
d. -10y2 + 35y


Competency 9
Do you know how to divide a polynomial by a monomial?

What is (16x2 - 6x - 4) divided by -2?
a. 8x2 - 3x - 2
b. -8x2 - 3x - 2
c. 8x - 3x + 2
d. -8x2 + 3x + 2

What is (20a2b2 - 15ab) divided by (-5a)?
a. 4ab + 3ab
b. 4ab2 + 3b
c. - 4ab2 - 3b
d - 4ab2 + 3b


Competency 10
Do you know how to simplify an algebraic expression?

Simplify 3xy + 7x + 5x - 2xy + 6 -2x + 4
a. 5xy +12x + 10
b. xy +10x +10
c. 21x2y
d. 10x2y + 3y -2x +10

Simplify 3x - 2(4x -6) + 7
a. 3x - 8x - 5
b. -5x - 5
c. -5x + 1
d. -5x + 19


Competency 11
Do you know how to solve an equation using multiplication?

Solve 3x = -15
a. x = -5
b. x = 5
c. x = 45
d. x = -45

Solve - 4/5x = 12
a. x = 48/5
b. x = -48/5
c. x = 15
d. x = -15


Competency 12
Do you know how to solve an equation using addition?

Solve x - 6 = 10
a. x = 4
b. x = - 4
c. x = -16
d. x = 16

Solve a + 1/3 = 1/2
a. a = 5/6
b. a = 2/3
c. a = 1/6
d. a = -1/6


Competency 13
Do you know how to solve an equation using both addition and multiplication?

Solve 7x -2 = 19
a. x = 17/7
b. x = -3
c. x = 3
d. x = 10

Solve 1/2x + 5 = 10
a. x = 5/2
b. x = 5
c. x = 10
d. x = 15


Competency 14
Do you know the number properties?

What property is illustrated by the problem 3 + 2 = 2 + 3?
a. Additive Identity Property
b. Associative Property of Addition
c. Commutative Property of Addition
d. Distributive Property

What property is illustrated by 6(3a) = (6 x 3)a
a. Additive Identity Property
b. Associative Property of Multiplication
c. Commutative Property of Multiplication
d. Distributive Property


Competency 15
Do you know the number systems?

What type of number is 3/5?
a. Integer
b. Whole
c. Rational
d. Irrational

What type of number is (-7)?
a. Natural
b. Whole
c. Integer
d. Irrational


Competency 16
Do you know how to solve an inequality using addition?

Solve x - 2 > - 2?
a. x > -2
b. x > 0
c. x < 0
d. x > 4

Solve y + 7 < 4?
a. y > -3
b. y < -3
c. y > 11
d. y < -11


Competency 17
Do you know how to solve an inequality using multiplication?

Solve 2x < -10
a. x < -5
b. x > -5
c. x > -20
d. x < -20

Solve -3c > -1/3
a. c > 3
b. c < 3
c. c > 1/9
d. c < 1/9


Competency 18
Do you know how to solve an inequality using a several step process?

Solve 2x -5 > 15
a. x > 10
b. x < 10
c. x > 20
d. x < 20

Solve -1/2 x + 4 < 0
a. x > - 4
b. x < -2
c. x < 8
d. x > 8


Competency 19
Do you know how to multiply two binomial expressions together?

What is (x + 5)(x - 1)?
a. x2 + 5x -1
b. x2 + 6x - 5
c. x2 + 4x + 5
d. x2 + 4x - 5

What is (2x - 4)(x - 2)?
a. 2x2 - 4x - 2
b. 2x2 - 6x + 8
c. 2x2 -8x + 8
d. 2x2 -8x -8


Competency 20
Do you know how to factor quadratic equations?

Factor x2 - 2x + 1 = 0
a. (x + 1)(x - 1) = 0
b. (x + 1)(x + 1) = 0
c. (x - 1)(x - 1) = 0
d. (x -2)(x - 1/2) = 0

Factor 2x2 + 5x + 2 = 0
a. (x + 1)(2x + 2) = 0
b. (2x + 1)(x + 2) = 0
c. (x - 1)(2x - 2) = 0
d. (x - 2)(2x - 1) = 0


Competency 21
Do you know how to solve quadratic equations using factoring?

What are the possible solutions to the equation x2 - 9 = 0?
a. x = 9
b. x = 1 and -9
c. x = -3 and 3
d. x = 0

What are the possible solutions to the equation 2x2 + 7x + 3 = 0?
a. x = 3 and 7
b. x = 1/2 and 3/7
c. x = -1/2 and -3
d. x = 3/2 and 1


Competency 22
Do you know how to solve quadratic equations using the quadratic formula?

If you were using the quadratic formula to solve 3x2 - 2x + 5 = 0 what would you use to substitute for a, b, and c?
a. a = 3, b = 2, c = 5
b. a = -3, b = -2, c = 5
c. a = 3, b = -2, c = 5
d. a = -2, b = 3, c = 5

If a = 1, b = 5, and c = 4, what is the solution to the quadratic equation?
a. 1, 4
b. - 4, -1
c. -25
d. 9, -9


Competency 23
Do you know how to solve simultaneous equations using addition?

Solve 3x - 2y = 1 and 2x + 2y = 4
a. x = 3, y = -2
b. x = 2, y = 2
c. x = 1, y = 1
d. x = 1, y = -1

Solve 2x + 6y = 10 and 4x + 2y = 10
a. x = 1, y = -3
b. x = 1, y = -1
c. x = 2, y = 1
d. x = 5, y = 0


Competency 24
Do you know how to solve simultaneous equations using substitution?

What would you substitute to solve these two simultaneous equations?
X + 2y = 6 and 4x - y = 10
a. y = 4x - 10
b. y = 1/2x + 3
c. x = y
d. x = 2y + 6

Which of these is the correct substitution for these two equations?
2x - y = 12 and 3x + 2y = -1
a. 2x - (3x -2y) = 12
b. 3x + 2(2x -12) = -1
c. 3(y + 12) + 2y = -1
d. 2(-2y -1) -y = 12


Competency 25
Do you know how to find the slope of a line?

What is the slope of y = - 3x + 2
a. -3
b. 2
c. 1
d. -3/2

What is the slope of 10x - 2y = 8
a. 5
b. -5
c. -2
d. 10


Competency 26
Do you know how to find the y-intercept of a line?

What is the y intercept of the line y = 3x - 4?
a. 1
b. -3/4
c. 3
d. -4

What is the y intercept of the line 2y = 4x.
a. 0
b. 1/2
c. 2
d. 4


Competency 27
Do you know how to find the equation of a line given two points?

What is the equation of the line through (1, -3) and (2, 4)?
a. y = 7x -10
b. 2x + 4y = 10
c. x - 3y = 0
d. 7x + 2y = 4

What is the equation of the line through (5, 5) and (-1, -1)?
a. 5x + 5y = -1
b. -x - y = 5
c. 5x - y = -6
d. x = y


Competency 28
Do you know how to put an equation in slope/intercept form?

Which of the following equations is in slope intercept form?
a. 2x + 3y = 0
b. x = 5y - 1
c. 2y = 6x - 2
d. y = x + 4

Change 4x - 2y = 6 to slope intercept form.
a. 4x -2y - 6 = 0
b. 4x - 6 = 2y
c. y = 2x - 3
d. x = 6 - 2y


Competency 29
Do you know how to square an algebraic expression?

What is (-7ab2)2?
a. 49ab2
b. 49a2b2
c. -49a2b4
d. 49a2b4

What is (2x - 3)2?
a. 4x2 + 9
b. 4x2 - 6x +9
c. 36x2
d. 4x2 -12x + 9


Competency 30
Do you know how to find the square root of an algebraic expression?

What is the square root of 4x2y6?
a. 2x2y6
b. 4xy3
c. 2xy3
c. 2xy2

What is the square root of 16x2y2?
a. 12xy
b. 2y(3x)
c. 6xy2
d. 4xy


Now that you've completed taking the Algebra I 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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