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

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download