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:   -10 and 2? -20

2.   Add:   15 and -8? 7

3.   Divide:   8 and -8? -1

4.   Substract:   -10 and -12? 2

5.   Calculate: |-16 · -10 + 5 · 13| 225

6.   Simplify the following expressions:
• 17x + 14x + 10x 41x

• -4y – 19x – -11y – 3y -19x+4y

• 11x – 20x + -3y – -11x – 18x – 20x -36x-3y

• y-5 × x17 x17 × y-5

• x-14
x-16
x2

• (10x3)4 10000x12

7.   Which of the following expressions show the associative property?
• ( x + y ) × 5 = 5 × ( y + x )
• 2 × ( x + 7 + 4 ) = 2×x + 2×7 + 2×4
• ( x + y ) + z = x + ( y + z )
• 9 + 10u + 4
C

8.   Which properties are illustrated by the following three expressions?
• g + ( h + 0 ) = ( g + h ) + 0
• 6 × ( 15 × -4 ) = ( 6 × 15 ) × -4
• 1 × (t + 11) = t + 11
• Associative property of addition, Associative property of multiplication and Identity property of multiplication
• Distributive property, Commutative property of multiplication and Identity property of multiplication
• Identity property of multiplication, Distributive property and Commutative property of addition
• Associative property of addition, Associative property of multiplication and Identity property of addition
A

9.   Solve the following equations for x:
• 94 + x = 95 x = 1

• 28
19
= -
1
19
x x = -28

• -47 = 8 – 5x x = 11

• bx = a x = a/b

10.   Solve the following inequalities. Then graph a) on the number line
• -x + -26 > 36 x < -62

• x ≠ -796
• -22 > x > 24
• -
40
20
x ≥
36
3
x ≤ -6

11.   Convert the following numbers into scientific notation:
• 0.000000816 8.16 × 10-7

• 90800000 9.08 × 107

• -11z3 + 2z2  and  -14z5 + 6z3
-14z5 + -5z3 + 2z2

• -5z14 + 9z6 + 2z4 + -11  and  9z14 + 1z6 + -1z5 + -2z4 + -6 4z14 + 10z6 + -1z5 + -17

13.   Multiply the following polynomials and simplify:
• (7x4 + x3 + 3x)(9x4 + x2)
63x8 + 9x7 + 7x6 + 28x5 + 3x3

• (8x5 + 9x2 + 2x)(2x5 + 3x2)
16x10 + 42x7 + 4x6 + 27x4 + 6x3

14.   Divide:
• x2 - 36 / x + 6
x - 6

15.   Find the greatest common factor of the following terms:
• 54, 72, 9
9

• 55x4y9, 30x8y
5x4y

16.   Factor the following polynomials:
• 6x5 + 4x4 - 2x3
6x3(x + 1)(x -
1
3
)

• x2 - 7x - 18
(x + 2)(x - 9)

• x4 + 9x3 - 52x2
x2(x - 4)(x + 13)

17.   For question 16, exercises b) and c), solve for x:
• x =
-2
and
9

• x =
0
,
4

and
-13

18.   You can purchase your ice cream in a cup or a cone. Orders can be one, two, or three scoops. Flavors can be chocolate or vanilla. How many choices do you have?
• 12

19.   Use the following data to construct a box and whiskers plot:
• 28, 3, 21, 33, 27, 2, 31, 22, 29

20.   A bag contains 5 blue balls, 2 red balls, and 4 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
36.36%

• A blue ball or red ball?
63.64%

• Two red balls?
3.31%

• A blue ball and a white ball?
16.53%

21.   Solve and graph the following systems of linear equations:
• x + y = -9
x - y = -19
A(-14,5)

• 9x - 8y = -11
4x + 6y = 9

B(0.07,1.45)

22.   Write the following fractions in simplest form:
• 6xy4
24xy4
1
4

• x8 - 9x7 + 20x6
x(x - 4)
x5(x - 5)

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• -8x + 12 = -x2
x1 = 6,   x2 = 2

24.   Convert the following repeating decimal into a fraction:
• x = 0.9158
9067
9900

25.   Solve the following equation:
• -8
x
+ 18 = -6
x
- 10
x = 196

26.   Rationalize the denominator of each fraction below:
• 5
3
6 +
10
30
3
- 5
30
26

27.   Use a trigonometric ratio to find x:
x = 9.24 cm

28.   The sum of two consecutive even integers is 26. What are the integers? (Hint: use 2x as the first even integer)
a=12, b=14

29.   After you leave your house, you walk 6 blocks east and 8 blocks north. How far are you from your house?
• I am
10
blocks from my house.

30.   A rectangle has a length 10 m greater than its width. The area of the rectangle is 144m2. What are the length and width of the rectangle?
• width = 8,  length = 18

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   10 and -17? -170

2.   Add:   2 and -1? 1

3.   Divide:   -20 and 2? -10

4.   Substract:   -16 and 1? -17

5.   Calculate: |13 · -19 + -6| 253

6.   Simplify the following expressions:
• 6 + 4 + -2x 10-2x

• 8x + -10x + -12 – 15y -12-2x-15y

• -13y + -1z + -2y – -9z + -15x -15x-15y+8z

• x-1 × x-10 × x-18 × y-11 x-29 × y-11

• x8
x10
x-2

• (10x3)10 10000000000x30

7.   Which of the following expressions show the associative property?
• ( m + n ) × 5 = 5 × ( m + n )
• b × ( c + 5 ) = bc + 5c
• 2 + -9 = -9 + 2
• ( x + y ) + z = x + ( y + z )
D

8.   Which properties are illustrated by the following three expressions?
• 4x + 14 = 14 + 4x
• ( z + 0 ) × y = z × y + 0 × y
• 0 + b + c + d = b + c + d
• Commutative property of addition, Distributive property and Identity property of addition
• Associative property of multiplication, Identity property of addition and Commutative property of addition
• Associative property of multiplication, Commutative property of addition and Associative property of addition
• Distributive property, Associative property of multiplication and Commutative property of addition
A

9.   Solve the following equations for x:
• x · 35 = -35 x = -1

• 14
4
= -
7
4
x x = -2

• -5x + 58 = 98 x = -8

• -c = bx + fx x = (-c)/(b+f)

10.   Solve the following inequalities. Then graph a) on the number line
• x – -23 < -18 x < -41

• x ≠ 239
• -19 ≤ x ≥ 45
• -
16
8
x >
20
10
x < -1

11.   Convert the following numbers into scientific notation:
• 0.00000000611 6.11 × 10-9

• 396000000 3.96 × 108

• -6z10 + 8z6 + 11z5  and  -14z10 + -9z8 + -5z6 + -6z5 + -8
-20z10 + -9z8 + 3z6 + 5z5 + -8

• -9z19 + 10z12 + -7z10  and  14z19 + -3z10 + 9z10 5z19 + 10z12 + -1z10

13.   Multiply the following polynomials and simplify:
• 6x2(7x5 + 10x4 + 10x)
42x7 + 60x6 + 60x3

• (5x5 + 6x3 + 9x2)(5x4 + x3 + 2)
25x9 + 5x8 + 30x7 + 51x6 + 19x5 + 12x3 + 18x2

14.   Divide:
• 16x2 + 12x - 40 / 4x - 5
4x + 8

15.   Find the greatest common factor of the following terms:
• 75, 42
3

• 78x9y7, 13x8y8, 60x10
x8

16.   Factor the following polynomials:
• 8x3 + 44x2 - 24x
8x(x -
1
2
)(x + 6)

• x2 + 3x - 18
(x - 3)(x + 6)

• x6 - 10x5 - 75x4
x4(x + 5)(x - 15)

17.   For question 16, exercises b) and c), solve for x:
• x =
3
and
-6

• x =
0
,
-5

and
15

18.   You are seating 4 people on 4 chairs. How many different ways can those people sit?
• 24

19.   Use the following data to construct a box and whiskers plot:
• 7, 36, 8, 20, 4, 21, 13, 19, 11, 32

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 even 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 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 heads?
50%

21.   Solve and graph the following systems of linear equations:
• x + y = -8
x - y = -19
A(-13.5,5.5)

• 5x - 4y = -18
3x + 7y = 5

B(-2.26,1.68)

22.   Write the following fractions in simplest form:
• 10x4y6
40x6y3
y3
4x2

• x5 - 9x4 - 10x3
x6(x - 10)
(x + 1)
x3

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• -5x - 36 = -x2
x1 = 9,   x2 = -4

24.   Convert the following repeating decimal into a fraction:
• x = 0.13
13
99

25.   Solve the following equation:
• 4x + 5
+ 2 = 9
x = 11

26.   Rationalize the denominator of each fraction below:
• 7
25
7
5

27.   Use a trigonometric ratio to find x:
x = 15.56 cm

28.   The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)
a=26, b=28

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 4 more than twice its width. The area of the rectangle is 30ft2. What is the length and width of the rectangle?
• width = 3,  length = 10

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