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# Algebra test generator

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   -38 and -72? 2736

2.   Add:   41 and 75? 116

3.   Divide:   -65 and 13? -5

4.   Substract:   -37 and 52? -89

5.   Calculate: |12 · -14 + -95| 263

6.   Simplify the following expressions:
• 51x + 51x – -74 74+102x

• -68 + 91 – -24x + -14x 23+10x

• 76 – -12y – -16x + -58 – -38z 18+16x+12y+38z

• y-57 × y-60 × x-87 × y86 x-87 × y-31

• x33
x-45
x78

• (5x4)8 390625x32

7.   Which of the following expressions show the associative property?
• ( m × n ) + 4 = 4 + ( m × n )
• ( 5 + 6 ) + 4 = 5 + ( 6 + 4 )
• 5 + 3z + 10
• d × ( e + 3 ) = de + 3e
B

8.   Which properties are illustrated by the following three expressions?
• 5 × (7 + x) = (7 + x) × 5
• r + s + 0 = r + s
• y × ( z + 1 ) = y × z + y × 1
• Associative property of multiplication, Commutative property of multiplication and Identity property of multiplication
• Associative property of addition, Associative property of multiplication and Commutative property of multiplication
• Commutative property of multiplication, Identity property of addition and Distributive property
• Distributive property, Associative property of multiplication and Commutative property of multiplication
C

9.   Solve the following equations for x:
• -x · -11 = -33 x = -3

• 1
22
x =
1
22
x = 1

• 54 = 56 + -2x x = 1

• gx = -fx – e x = (-e)/(g+f)

10.   Solve the following inequalities. Then graph a) on the number line
• x – 29 < -2 x < 27

• x ≠ 801
• -94 ≤ x ≥ -62
• 36
12
x ≤ -33 x ≤ -11

11.   Convert the following numbers into scientific notation:
• 0.000000000117 1.17 × 10-10

• 338000000 3.38 × 108

• 15z10 + 6z6 + -9z5 + -19z4 + -8z1  and  17z7 + 13z6 + 20z5
15z10 + 17z7 + 19z6 + 11z5 + -19z4 + -8z1

• -23z20 + 15z14 + -35z9 + -46z6 + -20z3  and  -36z17 + 16z14 + -33z9 + -37z3 -23z20 + -36z17 + 31z14 + -68z9 + -46z6 + -57z3

13.   Multiply the following polynomials and simplify:
• (3x3 + 8x2 + 10x)7x2
21x5 + 56x4 + 70x3

• (1x5 + 4x2 + 8x)(9x3 + 3x2)
9x8 + 3x7 + 36x5 + 84x4 + 24x3

14.   Divide:
• 2x2 - 6x - 20 / x - 5
2x + 4

15.   Find the greatest common factor of the following terms:
• 75, 200
25

• 120y, 288x6y
24y

16.   Factor the following polynomials:
• 11x4 - 22x3 + 11x2
11x2(x - 1)(x - 1)

• x2 - x - 20
(x - 5)(x + 4)

• x5 + 6x4 - 72x3
x3(x + 12)(x - 6)

17.   For question 16, exercises b) and c), solve for x:
• x =
5
and
-4

• x =
0
,
-12

and
6

18.   How many ways can 6 people wait in line?
• 720

19.   Use the following data to construct a box and whiskers plot:
• 28, 13, 7, 34, 10, 32, 27 20.   Suppose you toss a coin and spin a spinner numbered 1 through 14
• What is the probability of getting heads and 13?
3.57%

• What is the probability of getting tails and an odd number?
25%

• What is the probability of getting heads and a multiple of 6?
7.14%

• What is the probability of getting heads and a prime number?
21.43%

• What is the probability of not heads and not 2?
46.43%

• What is the probability of getting not tails and not a whole number?
0%

• What is the probability of heads or tails and a whole number?
100%

• What is the probability of getting tails?
50%

21.   Solve and graph the following systems of linear equations:
• x + y = 8
x - y = -13
A(-2.5,10.5)

• 7x - 8y = -15
x + 10y = -19

B(-3.87,-1.51)

22.   Write the following fractions in simplest form:
• 88x6y7
22x8y5
4y2
x2

• (x2 + 6x + 9)
(x + 3)
x + 3

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• -10x = x2 + 21
x1 = -3,   x2 = -7

24.   Convert the following repeating decimal into a fraction:
• x = 0.796
796
999

25.   Solve the following equation:
• 24
x
= 2
x = 6

26.   Rationalize the denominator of each fraction below:
• 7
14
+ 3
7
14
- 21
5

27.   Use a trigonometric ratio to find x: x = 24.00 cm

28.   The sum of two consecutive odd integers is 28. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=13, b=15

29.   After you leave your house, you walk 5 blocks west and 12 blocks north. How far are you from your house?
• I am
13
blocks from my house.

30.   A rectangle has a width that is 5 m less than its length. The area of the rectangle is 336m2. What are the dimensions of the rectangle?
• width = 16,  length = 21

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