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# Algebra test generator

Name _____________________                                        Date:_____________________

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(current difficulty level: Challenging)

Solve the following problems:

Important instructions

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1.   Multiply:   100 and 42? 4200

2.   Add:   77 and -75? 2

3.   Divide:   64 and 2? 32

4.   Substract:   8 and 89? -81

5.   Calculate: |-73 + 79 · -88| 7025

6.   Simplify the following expressions:
• -31x – 36 – -4 -32-31x

• 78 – -10x – -77 – 52x 155-42x

• 98z + -28x + 69y + 68 – -87x – 78y 68+59x-9y+98z

• x57 × x4 x61

• x72
x-79
x151

• (6x2)8 1679616x16

7.   Which of the following expressions show the associative property?
• a + b = b + a
• 0 + -4x = -4x
• ( 8 + 3 ) + 6 = 8 + ( 3 + 6 )
• ( -7 + 1 ) × 8 = 8 × ( -7 + 1 )
C

8.   Which properties are illustrated by the following three expressions?
• ( m × n ) × l = m × ( n × l )
• 1 × 69 = 69
• ( w + x ) + v = w + ( x + v )
• Associative property of multiplication, Identity property of multiplication and Associative property of addition
• Identity property of multiplication, Distributive property and Identity property of addition
• Identity property of addition, Identity property of multiplication and Commutative property of addition
• Commutative property of addition, Identity property of multiplication and Associative property of addition
A

9.   Solve the following equations for x:
• -78 – x = -55 x = -23

• -
16
14
=
2
7
x x = -4

• 14 – -46x = 60 x = 1

• -g + a = ex x = (-g+a)/e

10.   Solve the following inequalities. Then graph a) on the number line
• -17x – 27 > -10 x < -1

• x ≠ -128
• -38 ≥ x ≤ 14
• -
6
3
x ≤ -24 x ≥ 12

11.   Convert the following numbers into scientific notation:
• 0.000719 7.19 × 10-4

• 70100000000 7.01 × 1010

12.   Add the following polynomials:
• 5z7 + -13z1 + 7  and  -11z7 + 11z4 + 6z1 + -15
-6z7 + 11z4 + -7z1 + -8

• 35z18 + -43z7 + -22z1 + -49  and  -17z18 + -12z7 + -11z1 + 5 18z18 + -55z7 + -33z1 + -44

13.   Multiply the following polynomials and simplify:
• (7x3 + 10x2 + 10x)8x5
56x8 + 80x7 + 80x6

• (4x5 - 6)(10x2 + 5)
40x7 + 20x5 - 60x2 - 30

14.   Divide:
• 25x3 - 35x2 + 15x + 8 / 5x - 7
(5x2 + 3) with a remainder of 29

15.   Find the greatest common factor of the following terms:
• 495, 360, 245
5

• 117x3y5, 480x5y6, 39x7y4
3x3y4

16.   Factor the following polynomials:
• 32x4 + 0x3 - 2x2
32x2(x -
1
4
)(x +
1
4
)

• x2 - 5x - 50
(x - 10)(x + 5)

• x5 + 18x4 + 72x3
x3(x + 12)(x + 6)

17.   For question 16, exercises b) and c), solve for x:
• x =
10
and
-5

• x =
0
,
-12

and
-6

18.   You have 4 pants, 4 shirts, and 4 shoes. How many different ways can you dress?
• 64

19.   Use the following data to construct a box and whiskers plot:
• 19, 8, 38, 20, 29, 18, 9, 17, 4, 37

20.   Suppose you toss a coin and spin a spinner numbered 1 through 9
• What is the probability of getting heads and 4?
5.56%

• What is the probability of getting tails and an odd number?
22.22%

• What is the probability of getting tails and a multiple of 4?
11.11%

• What is the probability of getting heads and a prime number?
22.22%

• What is the probability of not tails and not 5?
44.44%

• What is the probability of getting not heads 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 = -1
x - y = 10
A(4.5,-5.5)

• x - 3y = 12
9x + 2y = -9

B(-0.1,-4.03)

22.   Write the following fractions in simplest form:
• 44x4y7
11x6y10
4
x2y3

• x3(x + 3)
x3 + 2x2 - 3x
x2
(x - 1)

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 + 30 = 13x
x1 = 10,   x2 = 3

24.   Convert the following repeating decimal into a fraction:
• x = 0.5
5
9

25.   Solve the following equation:
• -
2x - 4
+ 18 = 8
x = 52

26.   Rationalize the denominator of each fraction below:
• 14
4
2
21
2
21
3

27.   Use a trigonometric ratio to find x:
x = 29.44 cm

28.   The sum of two consecutive even integers is 14. What are the integers? (Hint: use 2x as the first even integer)
a=6, b=8

29.   After you leave your house, you walk 12 blocks west and 9 blocks north. How far are you from your house?
• I am
15
blocks from my house.

30.   Each side of a square is lengthened by 5 ft. This makes the area of the square 361ft2. What is the original length of a side of the square?
• 14 ft

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