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 if 2) Evaluate

Determine if a number is a solution of an equation or an inequality.

3) Is a solution of ?

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 8) Evaluate

Add, subtract, multiply or divide signed integers or fractions with or without a calculator.

9) 10)

Use the distributive property to multiply variable expressions.

11) Simplify

Identify like terms and properly add or subtract them.

12) Simplify

(over)Use the distributive property to divide variable expressions by an integer.

13) Simplify

Chapter 3: Solving Linear Equations

Solve equations.

14) Solve 15)

Recognize when a result is “no solution” or “all real numbers.”

16) Solve

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 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.

Apply formulas to real life application problems.

21) The formula for converting degrees Fahrenheit to Celsius is .

Convert to Celsius

22) The formula for simple interest is . 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 .

Given a linear equation, determine if a given point lies on the line.

25) Which of the following points lies on the line ? (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 and .

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 . graph .

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 .

(over)Graph a line using its slope and y-intercept.Rearrange equations to slope-intercept form, y = mx + b, then graph.

34) Graph 35) Write 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 , when , write the direct variation equation.

Understand and apply function notation.

38) If , find . 39) Graph

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, 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 .

(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 . 47) Graph

Solve and graph compound inequalities involving “and” and “or.”

48) Solve 49) Graph:

Solve and graph absolute value equations.

50) Solve (You should solve two cases!)

Solve and graph absolute value inequalities.

51) Solve (You should solve two cases!)

x

y

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 if 2) Evaluate

Determine if a number is a solution of an equation or an inequality.

3) Is a solution of ? Plug in 7 for x.

Yes, it’s a solution.

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 and twelve.”

Product means multiply. Sum means add. Is means equals.

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

Chapter 2: Properties of Real Numbers

Evaluate absolute value expressions. (No calc.)

7) Evaluate 8) Evaluate

Add, subtract, multiply or divide signed integers or fractions with or without a calculator.

9) 10) Multiply by reciprocal

Cancel & multiply

Use the distributive property to multiply variable expressions.

11) Simplify Distribute 3a Simplify & add like terms

Identify like terms and properly add or subtract them.

12) Simplify When you add like terms you get like terms. =

Use the distributive property to divide variable expressions by an integer.

13) Simplify

Chapter 3: Solving Linear Equations

Solve equations.

14) Solve 15)

Recognize when a result is “no solution” or “all real numbers.”

16) Solve

Left side identical to right side 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 Reduce

Cross multiplyDivide by 5

Solve percent problems by using proportions or changing words to symbols.

18) 27 is what percent of 48? 19) Find of 800.

so

Solve literal equations for one variable, in terms all of the other variables.20) Solve for L in terms of the other variables.

Apply formulas to real life application problems.

21) The formula for converting degrees Fahrenheit to Celsius is .

Convert to Celsius.

22) The formula for simple interest is . 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 .

The quadrants are labeled below. If , 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 ? (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): Yes. Plug in (0,3): No.

Plug in (-2, 1): 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 and .

Every point on must have an x-coordinate of 1.

Every point on must have an y-coordinate of -3.

12

3 4

x

y

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 . graph .

y-intercept: Find y when y-intercept:

Sub in 0 for x. x-intercept:

x-intercept: Find x when

Sub in 0 for y and solve for x.

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 = From the upper left point, count

down 2, then right 5 to get to the other

point. Slope =

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 and solve for the missing variable. , but y is missing.

Now multiply both sides by .

Subtract 3 from both sides to get .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 .

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 35) Write in slope- int.

form, then graph.Plot a point at the y-intercept (0, 1).Now use the slope to count down 2 andright 3 to another point on the line.

Start at -3 on the y-axis. Count up

2 and right 1 since the slope is .

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?

34

35

Write direct variation information as a linear equation.

37) y varies directly as x. If , when , write the direct variation equation.

Understand and apply function notation.

38) If , find . 39) Graph

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, 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 .

Determine whether a set of data has positive, negative or little correlation.

45) Does the plotted data have positive, negative or relatively little correlation?

x

y

Chapter 6: Solving and Graphing Linear Inequalities

Solve linear inequalities and graph the solution.

46) Solve . 47) Graph

Solve and graph compound inequalities involving “and” and “or.”

48) Solve 49) Graph:

Solve and graph absolute value equations and inequalities. (You should solve two cases!)

50) Solve 51) Solve