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ALGEBRA I Review
Name: _____________________________
Substitution/Linear Equations
Evaluate each if x = 3, y = -8, z = 2
1. xy2
2. z – y
4. 6(xy)2
3. 1/5x
5. x3
6. z + y2
Use the formula d = rt to answer the following
7. How fast did you drive if you traveled 80 miles in 4 hours?
8. How far did you travel if you drove at a speed of 80 mph for 3 hours?
Write each expression in exponential form:
9. 7p 7p 7p
10. 7 ppppp
11. 4 squared
Expand each expression
12. 8p3
13. (4t)3
Fill in the input/output table for each equation. Identify the domain, range, and determine if the relation
is a function
14. y = 3x + 8
4
6
8
10
12
D:
R:
15. y = 1/2x2 + 4
1
2
3
D:
R:
function: yes or no
4
5
function: yes or no
Order of Operations
Evaluate the following:
1. 4(3 – 4)2 + 2
Write the numbers in increasing order:
2. 3.5, -1/2, -31/2, -0.6, 0.5
3. -2, 3.4, 0, 3, 1.3, -0.25, -1/2
Simplify the following expressions:
4. 3x + 4(x – 2)
5. 5 – 3(2a + 2)
Solving Equations
Solve the following. Show all your work.
1. -5x = -20
2. 5x - 10 = 5
3. 6(x - 4) = 1
4. 3/4(4x + 16) = 36
6. 19 + (-3) = x + 3
5. 4x - (-3) = 18
Solve the following for y.
7. 3x + 2y = 10z
8. xyz = w
Solve the following. Round to the nearest tenth.
9. 3.4(3x + 2.1) = 3x
10. 5x + 4 = -3x + (-2)
11. What is the unit rate if you earn $650 in 10 hours
Solve each equation.
12. 7(2x + 4) + 7x = 14x + 14
13. 4x + 10 = x – 5
14. -4(x – 5) = -2x
15. 8y - 7 = 3y +4
Graphing Terminology
Find the x and y-intercepts for the following equations.
1. 2x + 4y = 12
2. -x + 4y = -8
Find the slope of the line that passes through the points.
3. (4, 3), (11, 5)
4. (1, -3), (4, -5)
Find the slope and y-intercept of the equation.
5. y = -3x – 4
6. y = 2/3x + 6
Rewrite the equations in slope-intercept form.
7.
5x + y = -12
8.
3x + 4y = 16
Graphing
1. Write an equation of the line in slope-intercept form given the slope is 4 and the y-intercept is -3.
2. Write the equation in slope-intercept form of each line shown in the graphs below.
3. Write an equation of the line that passes through the point and has the given slope. Write the equation in
slope-intercept form. (2, -1), m = -2.
4. Write the equation in slope-intercept form of each line shown in the graphs below.
5. Write an equation of the line in slope-intercept form that is parallel to the given line and passes through the
given point. y  3x  1 ; (-2, 1).
Inequalities
Graph each on the provided number line:
1. All real numbers less than or equal to seven
_______________________
2. All real numbers less than -2 or greater than 5
_______________________
3. All real numbers greater than or equal to six
_______________________
4. 5 < x < 9
_______________________
5. x < -5 or x > 1
_______________________
Solve each for x. Show all steps but do NOT graph
6. -4x > 16
7. x + 3 > 12
8. ½ x > 6
9. 15 < 3x + 3
Systems of Equations
Solve each systems of equations using any method.
1. x + y = 10, 2x – y = 14
2. 3x + 1 = 2y , x + y = 3
3. 7x + y = 10 , x – y = -10
4. 2x + 3y = 50, x – y = 0
Exponents
Simplify each expression.
1. (4x).(-7x5)
2. 6x11(2x2)
3. (53).(52)
Simplify by writing each expression using positive exponents.
6. 4x-3
7. 5p-2
8. (5p7)0
4. (-5x).(3x).(2x)
5. (2x6)3
Radicals
Evaluate each
1.
36
2.
196
3.
-25
Solve each equation or write no solution
4. 7x2 = 28
5. x2 + 9 = -91
6. 1/2x2 - 7 = 43
Simplify each radical expression
7.
24
9. 7 8  2
8. 5 40
Polynomials
Simplify each by finding the sum or difference.
1. (3x2 + 2x – 5) + (2x2 – 5x + 8)
2. (4x3 – 5x2 + 2x + 1) – (x3 + 3x2 + 8)
Find the product.
3. (4x + 3)(2x – 5)
4. (7x + 3)(2x – 3)
5. (3x2 + 2x – 1)(x + 3)
6. (2x + 3)2
Solve each for x.
7. (5x – 3)(x + 4) = 0
8. (3x + 8)2 = 0
9. x2 + 13x + 36 = 0
Factor the following polynomials completely.
10. x2 + 3x + 2
11. 2x2 – 15x + 7
12. 4x2 - 25