Algebra 1 Semester 1 Review - Magoffin County Schools
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).
1) Evaluate [pic] if [pic] 2) Evaluate [pic]
Determine if a number is a solution of an equation or an inequality.
3) Is [pic] a solution of [pic]?
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 [pic] 8) Evaluate [pic]
Add, subtract, multiply or divide signed integers or fractions with or without a calculator.
9) [pic] 10) [pic]
Use the distributive property to multiply variable expressions.
11) Simplify [pic]
Identify like terms and properly add or subtract them.
12) Simplify [pic]
(over)
Use the distributive property to divide variable expressions by an integer.
13) Simplify [pic]
Chapter 3: Solving Linear Equations
Solve equations.
14) Solve [pic] 15) [pic]
Recognize when a result is “no solution” or “all real numbers.”
16) Solve [pic]
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) Find [pic] of 800.
Solve literal equations for one variable, in terms all of the other variables.
20) Solve for L in terms of the other variables. [pic]
Apply formulas to real life application problems.
21) The formula for converting degrees Fahrenheit to Celsius is [pic].
Convert [pic] to Celsius
22) The formula for simple interest is [pic]. 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 [pic].
Given a linear equation, determine if a given point lies on the line.
25) Which of the following points lies on the line[pic]? (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 [pic] and [pic].
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
of [pic]. graph [pic].
Calculate slope given two ordered pairs.
Find slope by counting from point to point on a linear graph.
29) Find slope between 30) What is the slope of the line
(-1, 5) and (-7, 9). 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? 33) What is the slope of [pic].
(over)
Graph a line using its slope and y-intercept.
Rearrange equations to slope-intercept form, y = mx + b, then graph.
34) Graph [pic] 35) Write [pic] 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 [pic], when [pic], write the direct variation equation.
Understand and apply function notation.
38) If [pic], find [pic]. 39) Graph [pic]
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
for the line containing (2, 7) of the line with slope, [pic] and
and (4, 12). containing (-3, 5).
Write equations of horizontal or vertical lines.
42) Write an equation of the line 43) Write an equation of the vertical line
containing (-2, 5) and (3, 5). 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 [pic].
(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?
Chapter 6: Solving and Graphing Linear Inequalities
Solve linear inequalities and graph the solution.
46) Solve [pic]. 47) Graph [pic]
Solve and graph compound inequalities involving “and” and “or.”
48) Solve [pic] 49) Graph: [pic]
Solve and graph absolute value equations.
50) Solve [pic] (You should solve two cases!)
Solve and graph absolute value inequalities.
51) Solve [pic] (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 [pic] if [pic] 2) Evaluate [pic]
[pic] [pic]
Determine if a number is a solution of an equation or an inequality.
3) Is [pic] a solution of [pic]? Plug in 7 for x.
[pic]
[pic]
[pic] Yes, it’s a solution.
Convert words to equations and inequalities.
4) “Six less than a number is greater than twice the number.” [pic]
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. [pic]
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
[pic]
Chapter 2: Properties of Real Numbers
Evaluate absolute value expressions. (No calc.)
7) Evaluate [pic] 8) Evaluate [pic]
[pic] [pic]
[pic]
Add, subtract, multiply or divide signed integers or fractions with or without a calculator.
9)[pic] [pic] 10) [pic] Multiply by reciprocal
[pic] [pic] Cancel & multiply
Use the distributive property to multiply variable expressions.
11) Simplify [pic] Distribute 3a [pic]
Simplify & add like terms [pic]
Identify like terms and properly add or subtract them.
12) Simplify [pic] [pic]
When you add like terms you get like terms. =[pic]
Use the distributive property to divide variable expressions by an integer.
13) Simplify [pic] [pic]
[pic]
Chapter 3: Solving Linear Equations
Solve equations.
14) Solve [pic] 15) [pic]
[pic] [pic]
[pic] [pic]
[pic] [pic]
[pic]
Recognize when a result is “no solution” or “all real numbers.”
16) Solve [pic] [pic]
[pic]
Left side identical to right side [pic]
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.
Let x = number of democrats [pic] [pic] Reduce
[pic] Cross multiply
[pic] Divide by 5
Solve percent problems by using proportions or changing words to symbols.
18) 27 is what percent of 48? 19) Find [pic] of 800.
[pic] so [pic] [pic]
[pic] [pic]
Solve literal equations for one variable, in terms all of the other variables.
20) Solve for L in terms of the other variables. [pic] [pic]
[pic]
[pic]
[pic]
Apply formulas to real life application problems.
21) The formula for converting degrees Fahrenheit to Celsius is [pic].
Convert [pic] to Celsius. [pic]
22) The formula for simple interest is [pic]. How much interest will be earned if $15000 is invested at 3.5% annual interest for 4 years?
[pic]
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 [pic].
The quadrants are labeled below. If [pic], a point lies below the
Moving left three, then up 5 puts x-axis in quadrants 3 & 4.
a point in quadrant 2.
Given a linear equation, determine if a given point lies on the line.
25) Which of the following points lies on the line[pic]? (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): [pic] Yes. Plug in (0,3): [pic] No.
Plug in (-2, 1): [pic] Yes. (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 [pic] and [pic].
Every point on [pic] must have an x-coordinate of 1.
Every point on [pic] must have an y-coordinate of -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
of [pic]. graph [pic].
y-intercept: Find y when [pic] y-intercept: [pic]
Sub in 0 for x. [pic] x-intercept: [pic]
x-intercept: Find x when [pic]
Sub in 0 for y and solve for x.
[pic]
Calculate slope given two ordered pairs.
Find slope by counting from point to point on a linear graph.
29) Find slope between 30) What is the slope of the line
(-1, 5) and (-7, 9). sketched below?
Slope = [pic] From the upper left point, count
[pic] down 2, then right 5 to get to the other
point. Slope = [pic]
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.
Fill in [pic] and solve for the missing variable. [pic], but y is missing.
[pic] Now multiply both sides by [pic].
[pic] Subtract 3 from both sides to get [pic].
Know special cases of slope for horizontal and vertical lines.
32) What is the slope of a vertical line? 33) What is the slope of [pic].
Memorize: The slope of a vertical The slope of a horizontal line is 0.
line is undefined.
Graph a line using its slope and y-intercept.
Rearrange equations to slope-intercept form, y = mx + b, then graph.
34) Graph [pic] 35) Write [pic] in slope- int.
form, then graph.
Plot a point at the y-intercept (0, 1).
Now use the slope to count down 2 and [pic]
right 3 to another point on the line. [pic] [pic]
[pic]
[pic] [pic] [pic]
[pic]
Start at -3 on the y-axis. Count up
2 and right 1 since the slope is [pic].
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 [pic], when [pic], write the direct variation equation.
Understand and apply function notation.
38) If [pic], find [pic]. 39) Graph [pic]
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
for the line containing (2, 7) of the line with slope, [pic] and
and (4, 12). containing (-3, 5).
Write equations of horizontal or vertical lines.
42) Write an equation of the line 43) Write an equation of the vertical line
containing (-2, 5) and (3, 5). 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 [pic].
Determine whether a set of data has positive, negative or little correlation.
45) Does the plotted data have positive, negative or relatively little correlation?
Chapter 6: Solving and Graphing Linear Inequalities
Solve linear inequalities and graph the solution.
46) Solve [pic]. 47) Graph [pic]
Solve and graph compound inequalities involving “and” and “or.”
48) Solve [pic] 49) Graph: [pic]
Solve and graph absolute value equations and inequalities. (You should solve two cases!)
50) Solve [pic] 51) Solve [pic]
-----------------------
x
y
1
2
3
4
x
y
[pic]
[pic]
34
35
x
y
................
................
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