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) x⁵ × y⁴ × x^-7 × y¹⁰ ______________

e) x⁸ ÷ x² ____________

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) 9z⁸ + 2z⁵ + 4z² + 2 and 5z⁸ + -6z⁵ + -4z² + -1z + -8

b) z⁶ + 5z⁴ + -10z³ + -7 and -z⁶ + 8z⁴ + 4z³ − 8


13. Multiply the following polynomials and simplify

a ) 4x³( 2x² + x − 5) _______________

b) (4x³ + 4x )( 2x² + x − 5)_________________

14. Divide: x³ - 6x² + 5x - 30 / x - 6 ________________


15. Find the greatest common factor of the following expressions:


a) 15, 30

b) 15x³, 30x²


16. Factor the following polynomials

a) 12x² + 24x³ + - 18x ________________

b) x² − 3x − 18 ________________

c) x⁶ + 13x⁵ + 42x⁴ _________________


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) (25x⁶ 36 z⁷) / (50x⁸ 6z⁵)

b) (x⁶ + 13x⁵ + 42x⁴) / x³ (x + 6)


23.

Solve the equation below: two different ways.

First, solve using the quadratic formula:

Second, solve it by completing the square

x² = -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 = ___________________

Things to keep in mind about the algebra practice test

To print this algebra practice test, click here.

This algebra practice test is an attempt to measure most skills taught in algebra such as the ones mentioned below:

• Add and subtract integers
• Scientific notation
• Solving equations and inequalities
• Add polynomials
• Solving system of equations using the substitution method or the elimination method
• Solving quadratic equations
• Using the Pythagorean theorem to solve problems.

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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
  
  
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• 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
  
  
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• Basically, anyone who needs a solid foundation in algebra needs this algebra practice test
  
  

Teachers!!! Use this algebra practice as a pre-test, as a test, or as a final exam!

This algebra practice test should take about 3 hours or 4 hours to complete