Algebra 1 Semester 1 Final Review HW
Chapter 1: Expressions, Equations & Functions
Understand and use variables to take the place of a number.
Evaluate expressions containing exponents using the order of operations (PEMDAS).
2) Evaluate 12  2(32  2  5)  3
1) Evaluate 40  3x2  x if x  2
Determine if a number is a solution of an equation or an inequality.
3) Is x  7 a solution of 3  2 x  x  26 ?
Convert words to equations and inequalities.
4) “Six less than a number is greater than twice the number.”
5) “The product of four and a number is the sum of the number an twelve.”
Write equations to solve word problems.
6) Write an equation but do not solve.
A plumber’s bill is $350 dollars for 3 hours of works. If the bill includes $110 for
parts, write an equation to find his hourly rate.
Chapter 2: Properties of Real Numbers
Evaluate absolute value expressions. (No calc.)
7) Evaluate 12  18  2
8) Evaluate  (2)3  15  3
Add, subtract, multiply or divide signed integers or fractions with or without a
calculator.
9)
1 3

2 13
10)
4 8

15 25
Use the distributive property to multiply variable expressions.
11)
Simplify 3a(2a  5)  11a
Identify like terms and properly add or subtract them.
12)
Simplify 2a2  3a  a2  5a  7
(over)
Use the distributive property to divide variable expressions by an integer.
13)
Simplify
12 x  27
 11x
3
Chapter 3: Solving Linear Equations
Solve equations.
14)
11 

Solve 2  x    8(3  x)
2

15)
1 3
1
 x 2 x
2 7
2
Recognize when a result is “no solution” or “all real numbers.”
16)
Solve
2
(6 x  12)  x  2  3( x  2)
3
Use ratios and proportions to solve word problems.
Solve proportions by cross-multiplying.
17)
In a sample of 55 voters in one county, 22 said they would vote democratic. If
6000 people voted in the county, how many would be expected to vote
democratic? Set up a proportion and solve.
Solve percent problems by using proportions or changing words to symbols.
18)
27 is what percent of 48?
19)
1
Find 16 % of 800.
2
Solve literal equations for one variable, in terms all of the other variables.
20)
Solve for L in terms of the other variables.
S   rL   r 2
Apply formulas to real life application problems.
21)
22)
5
The formula for converting degrees Fahrenheit to Celsius is C  ( F  32) .
9
Convert 68 F to Celsius
The formula for simple interest is I  P  r  t . How much interest will be earned if
$15000 is invested at 3.5% annual interest for 4 years?
Algebra 1 Semester 1 Final Review HW (Day 2)
Chapter 4: Graphing Linear Equations and Functions
Know the quadrant numbers in the coordinate plane.
23) In which quadrant number is (-3, 5)?
24) In which two quadrants is y  0 .
Given a linear equation, determine if a given point lies on the line.
25) Which of the following points lies on the line y  2 x  3 ? (2, -7), (0, 3), (-2, 1)
Plot horizontal and vertical lines given their equations.
26) Graph on the same set of axes, the two lines x  1 and y  3 .
Find the x-intercept and the y-intercept of a line from its linear equation.
Graph a line by finding and connecting its x and y-intercepts.
27)
Find the x and y-intercepts
28) Find the x and y-intercepts and
2
of y  x  12 .
graph 3x  4 y  8 .
5
Calculate slope given two ordered pairs.
Find slope by counting from point to point on a linear graph.
29)
Find slope between
(-1, 5) and (-7, 9).
30)
What is the slope of the line
sketched below?
Solve for x or y given slope and two ordered pairs with one x or y missing.
31)
Find y such that the slope between (2, y) and (5, -3) is 7.
Know special cases of slope for horizontal and vertical lines.
32)
What is the slope of a vertical line?
(over)
33)
What is the slope of y  4 .
Graph a line using its slope and y-intercept.
Rearrange equations to slope-intercept form, y = mx + b, then graph.
34) Graph y 
2
x 1
3
35) Write 12 x  6 y  18 in slope-int. form, then graph.
Solve word problems using linear equations.
36)
To rent a bike there is a set fee, plus an hourly rate. Renting a bike for 4 hours
costs $24. Renting it for 7 hours costs $37.50. How much to rent it for 3 hours?
Write direct variation information as a linear equation.
37) y varies directly as x. If y  15 , when x  6 , write the direct variation equation.
Understand and apply function notation.
39) Graph g ( x) 
38) If f ( x)  5x  3 , find f (8) .
1
x3
2
Chapter 5: Writing Linear Equations
Write a linear equation in slope-intercept, point-slope or standard form.
40) Write a slope intercept equation
41) Write a standard form equation
2
of the line with slope, m  and
5
containing (-3, 5).
for the line containing (2, 7)
and (4, 12).
Write equations of horizontal or vertical lines.
42) Write an equation of the line
containing (-2, 5) and (3, 5).
43) Write an equation of the vertical line
through the point (9, -8).
Apply information about parallel or perpendicular lines to write equations.
44) Write a slope-intercept equation of a line containing (-6, 11) and parallel to the line
y  3x  1.
(over)
Determine whether a set of data has positive, negative or little correlation.
45) Does the plotted data have positive, negative or relatively little correlation?
y
x
Chapter 6: Solving and Graphing Linear Inequalities
Solve linear inequalities and graph the solution.
46)
Solve 2 x  12  5( x  6) .
47) Graph 2  x  3
Solve and graph compound inequalities involving “and” and “or.”
48)
1
Solve 5  6  x  8
2
49) Graph: x  1 or x  3
Solve and graph absolute value equations.
50)
Solve 2 x  9  21 (You should solve two cases!)
Solve and graph absolute value inequalities.
51)
Solve 3  x  4  17 (You should solve two cases!)
Algebra 1 Semester 1 Final Review HW Solutions
Chapter 1: Expressions, Equations & Functions
Understand and use variables to take the place of a number.
Evaluate expressions containing exponents using the order of operations (PEMDAS).
1) Evaluate 40  3x2  x if x  2
40  3(2)2  (2)
40  3  4  2
40  12  2  28  2  26
2) Evaluate 12  2(32  2  5)  3
12  2(32  2  5)  3
12  2(9  10)  3
12  2(1)  3
12  2  3  17
Determine if a number is a solution of an equation or an inequality.
3) Is x  7 a solution of 3  2 x  x  26 ?
Plug in 7 for x.
3  2(7)  7  26
3  14  19
11  19 Yes, it’s a solution.
Convert words to equations and inequalities.
4) “Six less than a number is greater than twice the number.” x  6  2 x
5) “The product of four and a number is the sum of the number and twelve.”
Product means multiply. Sum means add. Is means equals. 4 x  x  12
Write equations to solve word problems.
6) Write an equation but do not solve.
A plumber’s bill is $350 dollars for 3 hours of work. If the bill includes $110 for
parts, write an equation to find his hourly rate. Let h = hourly rate
350  3h  110
Chapter 2: Properties of Real Numbers
Evaluate absolute value expressions. (No calc.)
7) Evaluate 12  18  2
6  2  4  4
8) Evaluate  (2)3  15  3
  8  15  3    8  5
  8  5   3  3
Add, subtract, multiply or divide signed integers or fractions with or without a calculator.
1 3
9) 
2 13
1 13 3 2
  
2 13 13 2
13 6 19


26 26 26
10)
4 8
4 25
Multiply by reciprocal

 
15 25 15 8
1 5 5
  Cancel & multiply
3 2 6
Use the distributive property to multiply variable expressions.
11)
Simplify 3a(2a  5)  11a
3a  2a  3a  5  11a
Distribute 3a
6a2  15a  11a  6a2  4a
Simplify & add like terms
Identify like terms and properly add or subtract them.
12)
Simplify 2a2  3a  a2  5a  7
2a2  3a  a2  5a  7  2a2  a2  3a  5a  7
When you add like terms you get like terms.
= 3a2  8a  7
Use the distributive property to divide variable expressions by an integer.
13)
Simplify
12 x  27
 11x
3
12 x  27
12 x 27
 11x 

 11x
3
3
3
12 x 27

 11x  4 x  9  11x  7 x  9
3
3
Chapter 3: Solving Linear Equations
Solve equations.
14)
11 

Solve 2  x    8(3  x)
2

2 x  11  24  8 x
8 x
 8x
10 x  11  24
 11  11
10 x 35

10 10
x  3.5
15)
1 3
1
 x 2 x
2 7
2
1 
1 3 

14   x   14  2  x 
2 
2 7 

7  6 x  28  7 x
 7x
 7x
7  13x  28
7
7
13x 21
=
13 13
Þ
x=
21
13
Recognize when a result is “no solution” or “all real numbers.”
2
2
16) Solve (6 x  12)  x  2  3( x  2)
(6 x  12)  x  2  3( x  2)
3
3
4 x  8  x  2  3x  6
Left side identical to right side
4x  8  4x  8
All Real Numbers
Use ratios and proportions to solve word problems. Solve proportions by cross-multiplying.
17)
In a sample of 55 voters in one county, 22 said they would vote democratic. If
6000 people voted in the county, how many would be expected to vote
democratic? Set up a proportion and solve.
22
x
2
x
Let x = number of democrats
Reduce


55 6000
5 6000
12000  5x Cross multiply
Divide by 5
2400  x
Solve percent problems by using proportions or changing words to symbols.
1
18) 27 is what percent of 48?
19) Find 16 % of 800.
2
1
27
27  48 p so p 
 0.5625
16 %  16.5%  0.165
48
2
p  56.25%
0.165  800  132
Solve literal equations for one variable, in terms all of the other variables.
20) Solve for L in terms of the other variables. S   rL   r 2
S   rL   r 2
 r 2
  r2
S   r 2  rL

r
r
2
S r
L
r
Apply formulas to real life application problems.
21)
22)
5
The formula for converting degrees Fahrenheit to Celsius is C  ( F  32) .
9
5
5
5
C  ( F  32)  (68  32)  (36)  20
Convert 68 F to Celsius.
9
9
9
The formula for simple interest is I  P  r  t . How much interest will be earned if
$15000 is invested at 3.5% annual interest for 4 years?
I  (15000)(0.035)(4)  $2100
Algebra 1 Semester 1 Final Review HW (Day 2)
Chapter 4: Graphing Linear Equations and Functions
Know the quadrant numbers in the coordinate plane.
23) In which quadrant number is (-3, 5)?
24) In which two quadrants is y  0 .
The quadrants are labeled below.
Moving left three, then up 5 puts
a point in quadrant 2.
If y  0 , a point lies below the
x-axis in quadrants 3 & 4.
y
2
1
x
3
4
Given a linear equation, determine if a given point lies on the line.
25) Which of the following points lies on the line y  2 x  3 ? (2, -7), (0, 3), (-2, 1)
A point lies on a line if it makes the equation true when substituted into the equation.
Plug in (2, -7):
7  2  2  3
Yes.
7  7
Plug in (0,3):
3  2  0  3
No.
3  3
Plug in (-2, 1):
1  2  2  3
Yes.
1 43
(2, -7) and (-2, 1) lie on the line.
Plot horizontal and vertical lines given their equations.
26) Graph on the same set of axes, the two lines x  1 and y  3 .
Every point on x  1 must have an x-coordinate of 1.
Every point on y  3 must have an y-coordinate of -3.
y  3
x 1
Find the x-intercept and the y-intercept of a line from its linear equation.
Graph a line by finding and connecting its x and y-intercepts.
27)
Find the x and y-intercepts
2
of y  x  12 .
5
y-intercept: Find y when x  0
2
Sub in 0 for x. y  (0)  12  12
5
x-intercept: Find x when y  0
28)
Find the x and y-intercepts and
graph 3x  4 y  8 .
y-intercept: 4 y  8  y  2
8
x-intercept: 3x  8  x 
3
Sub in 0 for y and solve for x.
2
0  x  12
5
12
 12
5
2 5
 12  x 
2
5 2
30  x
Calculate slope given two ordered pairs.
Find slope by counting from point to point on a linear graph.
29)
Find slope between
(-1, 5) and (-7, 9).
difference of y values
difference of x values
9-5
4
2
m=
=
=-7 - (-1) -6
3
Slope =
30)
What is the slope of the line
sketched below?
From the upper left point, count
down 2, then right 5 to get to the other
point. Slope =
2
5
Solve for x or y given slope and two ordered pairs with one x or y missing.
31)
Find y such that the slope between (2, y) and (5, -3) is 7.
y2  y1
and solve for the missing variable. m  7 , but y is missing.
x2  x1
y  (3)
y3
7
 7
Now multiply both sides by 3 .
25
3
Fill in m 
21  y  3 Subtract 3 from both sides to get 24  y .
Know special cases of slope for horizontal and vertical lines.
32)
What is the slope of a vertical line?
33)
Memorize: The slope of a vertical
line is undefined.
What is the slope of y  4 .
The slope of a horizontal line is 0.
Graph a line using its slope and y-intercept.
Rearrange equations to slope-intercept form, y = mx + b, then graph.
34) Graph y 
2
x 1
3
35)
Write 12 x  6 y  18 in slope- int.
form, then graph.
Plot a point at the y-intercept (0, 1).
Now use the slope to count down 2 and
right 3 to another point on the line.
35
12 x  6 y  18
12x
12x
6 y  12 x  18
6
6
6
y  2x  3
Start at -3 on the y-axis. Count up
2
2 and right 1 since the slope is .
1
34
Solve word problems using linear equations.
36)
To rent a bike there is a set fee, plus an hourly rate. Renting a bike for 4 hours
costs $24. Renting it for 7 hours costs $37.50. How much to rent it for 3 hours?
Write direct variation information as a linear equation.
37) y varies directly as x. If y  15 , when x  6 , write the direct variation equation.
Understand and apply function notation.
38) If f ( x)  5x  3 , find f (8) .
39) Graph g ( x) 
1
x3
2
Chapter 5: Writing Linear Equations
Write a linear equation in slope-intercept, point-slope or standard form.
40) Write a slope intercept equation
for the line containing (2, 7)
and (4, 12).
41) Write a standard form equation
2
of the line with slope, m  and
5
containing (-3, 5).
Write equations of horizontal or vertical lines.
42) Write an equation of the line
containing (-2, 5) and (3, 5).
43) Write an equation of the vertical line
through the point (9, -8).
Apply information about parallel or perpendicular lines to write equations.
44) Write a slope-intercept equation of a line containing (-6, 11) and parallel to the line
y  3x  1.
Determine whether a set of data has positive, negative or little correlation.
45) Does the plotted data have positive, negative or relatively little correlation?
y
x
Chapter 6: Solving and Graphing Linear Inequalities
Solve linear inequalities and graph the solution.
46)
Solve 2 x  12  5( x  6) .
47) Graph 2  x  3
Solve and graph compound inequalities involving “and” and “or.”
1
48) Solve 5  6  x  8
49) Graph: x  1 or x  3
2
Solve and graph absolute value equations and inequalities. (You should solve two cases!)
50)
Solve 2 x  9  21
51)
Solve 3  x  4  17