Algebra test generator. Unlimited practices. Sharpen your algebra skills! Answers and solutions.
Time
02 : 30 : 00

# Algebra test generator

Name _____________________                                        Date:_____________________

current difficulty level: Choose test difficulty:         Easy              Challenging
(current difficulty level: Easy)

Solve the following problems:

Important instructions

1.   Multiply:   12 and 9? 108

2.   Add:   -14 and -16? -30

3.   Divide:   -11 and -1? 11

4.   Substract:   10 and -4? 14

5.   Calculate: |2 · 11 + -11| 11

6.   Simplify the following expressions:
• -9 – -1x + -1x -9

• -3y – 9 – 16y – -12y -9-7y

• -19x – 2 + -4x – -17x – -19 + 13 30-6x

• x12 × y6 x12 × y6

• x-1
x9
x-10

• (9x3)6 531441x18

7.   Which of the following expressions show the associative property?
• -1 + 1 = 1 + -1
• 7( 8 + 4 ) = 7×8 + 7×4
• ( 4 × 5 ) × 6 = 4 × ( 5 × 6 )
• 7 × ( x + 9 + 4 ) = 7×x + 7×9 + 7×4
C

8.   Which properties are illustrated by the following three expressions?
• ( f + 0 ) + e = f + ( 0 + e )
• 9 × 3 + x = x + 9 × 3
• 1 × 77 = 77
• Identity property of multiplication, Associative property of multiplication and Commutative property of addition
• Associative property of addition, Commutative property of addition and Identity property of multiplication
• Associative property of addition, Associative property of multiplication and Distributive property
• Commutative property of addition, Identity property of multiplication and Commutative property of multiplication
B

9.   Solve the following equations for x:
• -x · 28 = 28 x = -1

• -
4
27
= -
1
27
x x = 4

• 8 = 97 + 89x x = -1

• -e + b = ax x = (-e+b)/a

10.   Solve the following inequalities. Then graph a) on the number line
• -35x + -38 ≤ -3 x ≥ -1

• x ≠ -381
• 38 ≥ x ≥ -54
• -
27
9
x > -
18
6
x < 1

11.   Convert the following numbers into scientific notation:
• 0.0000615 6.15 × 10-5

• 233000000000 2.33 × 1011

• -12z9 + -4z4 + 12z1 + 14  and  2z10 + 6z9 + -4z1 + -1
2z10 + -6z9 + -4z4 + 8z1 + 13

• -1z13 + 2z6 + -6z3 + -3z2 + -12  and  12z13 + 3z3 + -8z2 + -4 11z13 + 2z6 + -3z3 + -11z2 + -16

13.   Multiply the following polynomials and simplify:
• (7x5 - 5)2
14x5 - 10

• (7x5 + x)(10x5 - 4)
70x10 + 10x6 - 28x5 - 4x

14.   Divide:
• 10x3 + 20x2 + 4x + 8 / 2x + 4
5x2 + 2

15.   Find the greatest common factor of the following terms:
• 72, 60, 33
3

• 75x3y8, 39x3
3x3

16.   Factor the following polynomials:
• 24x3 - 21x2 - 54x
24x(x +
9
8
)(x - 2)

• x2 - 2x - 48
(x + 6)(x - 8)

• x7 + x6 - 12x5
x5(x - 3)(x + 4)

17.   For question 16, exercises b) and c), solve for x:
• x =
-6
and
8

• x =
0
,
3

and
-4

18.   You are seating 3 people on 3 chairs. How many different ways can those people sit?
• 6

19.   Use the following data to construct a box and whiskers plot:
• 15, 12, 14, 21, 39, 38, 11, 16, 37, 34

20.   A bag contains 2 blue balls, 6 red balls, and 2 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
20.00%

• A blue ball or red ball?
80.00%

• Two red balls?
36.00%

• A blue ball and a white ball?
4.00%

21.   Solve and graph the following systems of linear equations:
• x + y = 2
x - y = 19
A(10.5,-8.5)

• 4x - 8y = -20
4x + 4y = -6

B(-2.67,1.17)

22.   Write the following fractions in simplest form:
• 6x6y9
3x8y6
2y3
x2

• x5 + 8x4 + 15x3
x6(x + 5)
(x + 3)
x3

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 - 22 = -9x
x1 = -11,   x2 = 2

24.   Convert the following repeating decimal into a fraction:
• x = 6.310
6304
999

25.   Solve the following equation:
• 28
x
= 2
x = 7

26.   Rationalize the denominator of each fraction below:
• 21
10
21
10
10

27.   Use a trigonometric ratio to find x:
x = 34.64 cm

28.   The sum of two consecutive even integers is 58. What are the integers? (Hint: use 2x as the first even integer)
a=28, b=30

29.   After you leave your house, you walk 12 blocks east and 16 blocks south. How far are you from your house?
• I am
20
blocks from my house.

30.   The length of a rectangle is 2 less than 2 times the width. What are the dimensions of the rectangle if the area is 264m2?
• width = 12,  length = 22