Algebra practice test
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Name _____________________ Date:_____________________
Solve the following problems
1. What is the product of 10 and +5? ____________
2. Add: 10 + 5 ____________
3. What is the quotient of 16 and 4? _____________
4. Subtract: 1 − 8 ______________
5. Calculate: 6 × 2 + 4 × 3 ___________
6. Simplify the following expressions:
a) 4x + 5 + 2x ____________
b) 6x + 4z + 3x − 10z ____________
c) 10y − 2y − 3z − 9z − 6y ____________
d) x
^{5} × y
^{4} × x
^{7} × y
^{10} ______________
e) x
^{8} ÷ x
^{2} ____________
f) (4x)
^{3} _________________
g) (5c)
^{4} _________________
7. Which of the following expressions show the associative property?
A. 5 × 7 + 2 = 2 + 5 × 7
B. 5 + 7 = 7 + 5
C. (5 × 7) × 2 = 5 × (7 × 2)
D. 2 + 7x
8. Which properties are illustrated by the following three expressions?
a) 1 × 7 + 2 = 2 + 1 × 7
b) 9 * 1 = 9
c) 4 × ( 2 + 6) = 4 × 2 + 4 × 6
A. Identity property of addition, distributive property, and commutative property of addition
B. Identity property of addition, distributive property, and associative property of addition
C. Identity property of multiplication, distributive property, and commutative property of addition
D. Identity property of multiplication, distributive property, and commutative property of multiplication
9. Solve the following equations for x:
a) x − 2 = 7
b) x − 2 = 7
c) (2/3)x = 6
d) 2x + 5 = 11
e) ax + b = e
10. Solve the following inequalities. Then graph a) on the number line
a) 3x  2 > 11
b) x ≠ 5
c) 1 ≤ x < 4
d) 5f < 10
11.
Convert the following numbers into scientific notation:
a) 0.0000000000245 _______________
b) 890000000 ______________
12. Add the following polynomials:
a) 9z
^{8} + 2z
^{5} + 4z
^{2} + 2 and 5z
^{8} + 6z
^{5} + 4z
^{2} + 1z
^{} + 8
b) z
^{6} + 5z
^{4} + 10z
^{3} + 7 and z
^{6} + 8z
^{4} + 4z
^{3} − 8
13. Multiply the following polynomials and simplify
a ) 4x
^{3}( 2x
^{2} + x − 5) _______________
b) (4x
^{3} + 4x )( 2x
^{2} + x − 5)_________________
14. Divide: x
^{3}  6x
^{2} + 5x  30 / x  6 ________________
15. Find the greatest common factor of the following expressions:
a) 15, 30
b) 15x
^{3}, 30x
^{2}
16. Factor the following polynomials
a) 12x
^{2} + 24x
^{3} +  18x ________________
b) x
^{2} − 3x − 18 ________________
c) x
^{6} + 13x
^{5} + 42x
^{4} _________________
17. For question 16, exercises b) and c), solve for x
b) x = ___________ and ____________
c) x = ___________, _____________, and, _______________
18. How many ways can you and 3 other friends sit on 4 chairs? _____________
19. Use the following data to construct a box and whiskers plot:
12, 5, 2, 20, 7, 24, 10, 21
20. Solve and graph the following inequality: 2x + 5 > 12
A bag contains 2 blue balls, 5 red balls, and 3 white balls.
You pick a ball from the bag and put in your pocket. What is the probability of picking:
a) a white ball?_______________
b) a blue ball
or a red ball? _______________
c) two red balls? ________________
d) a blue ball
and a white ball
21. Solve and graph the following systems of linear equations:
a)
x + y = 9
x − y = 7
b)
4x  3y = 10
8x + 5y = 10
22. Write the following fractions in simplest form:
a) (25x
^{6} 36 z
^{7}) / (50x
^{8} 6z
^{5})
b) (x
^{6} + 13x
^{5} + 42x
^{4}) / x
^{3} (x + 6)
23.
Solve the equation below: two different ways.
First, solve using the
quadratic formula:
Second, solve it by
completing the square
x
^{2} = 3x + 10
24.
Convert the following repeating decimal into a fraction
x = 1.01255555555555
25. Solve the following equation:
3  √(x  2) = 1
26. Rationalize the denominator of each fraction below:
a) 2 / √( 5)
b) 4 / (√( 5)  2)
27.
Use a trigonometric ratio to find x:
Word problems
28.
The sum of two consecutive even integers is 18. What are the integers? (Hint: use 2x as the first even integer)
The integers are _______________ and ________________
29.
After you leave your house, you walk 10 blocks east and 6 blocks south. How far are you from your house?
I am __________________ blocks from my house
30.
The length of a rectangle is two more than the width. The area is 35. Find the length and the width (Hint: Let x be the width).
Width = ______________ length = ___________________
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This algebra practice test is an attempt to measure most skills taught in algebra. Keep in mind that this algebra practice test is not an exhaustive list
However, if you can answer most question comfortably, you have definitely mastered most important skills taught in algebra.
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The solution will not only show you how to do the problems, but it will also teach you lots of important algebra concepts that will help you succeed in algebra.
Who should definitely master this algebra practice test:
 You are about to take a test in algebra
 You are trying to understand algebra
 You struggle with algebra
 You are about to take an algebra class and you want to prepare yourself to thrive
 You are a student and you are about to take a state test like the MCAS and it is a requirement for graduation
 You want to brush up your algebra skills
 You have been trying to learn algebra and failed many times
 Basically, anyone who needs a solid foundation in algebra needs this algebra practice test
Teachers!!! Use this algebra practice as a pretest, as a test, or as a final exam!
This algebra practice test should take about 3 hours or 4 hours to complete
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