(P) Expressions



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HONORS ALGEBRA FINAL STUDY GUIDE - SEMESTER 1

I. Number Properties

• Arithmetic rules, order of operations, factors, multiples, fractions

II. Algebraic Expressions

• Evaluating expressions

• Distributive property

• Combining like terms

III. Fractions, decimals and percentages

• Scientific notation

• Tax and discount

• Ratios and proportions

IV. Equations

• Solving one step, multi-step and equations with no solutions or infinite solutions

• Literal equations

• Translating from words to equations

V. Functions

• Plotting and locating points on the (x, y) coordinate plane

• Evaluating functions, domain and range, vertical line test

• Determining whether relations are functions

• Graphing absolute value functions

• Writing algebraic rules given graphs, tables or drawings

x- and y-Intercepts

• How to find and graph lines using the x and y intercepts, Zero-zero method

• Interpreting the x- and y-intercepts

• How to find the slope using [pic]

VI. Slope

• How to find using the formula [pic]

• How to find from a table, graph, equation

• Slope as rate of change; interpreting slope through equations, tables or graphs

VII. Slope – Intercept Form: y = mx + b

• y = mx + b (m represents slope and b represents y-intercept)

• How to write equation in slope-intercept form

• How to graph lines using slope-intercept form

VIII. Standard Form: Ax + By = C

• How to find and graph lines in standard form (x- and y-intercepts)

Point-Slope form: y – y1 = m(x – x1 )

• How to find and graph lines in point-slope form

Parallel Lines and Perpendicular Lines

• Parallel lines have the same slope

• Perpendicular lines have slopes that are opposite reciprocals. In other words, the product of their slopes equals -1.

• Using parallel and perpendicular lines to write the equation of a line.

Number Properties

1. Which of the following numbers is the least in value?

A. 1.5 x 10-8

B. 0.15 x 108

C. 15,000

D. 0.0015 x 109

2. 54 – 6 ÷ 2 + 6 =

A. 30

B. 24

C. 27

D. 57

3. Which of the following lists all the positive factors of 16?

A. 1, 8

B. 2, 4, 6, 8, 16

C. 8, 4, 16

D. 1, 2, 4, 8, 16

Algebraic expressions

4. The expression (3x2 + 5x – 12) – 2(x2 + 4x +9) is equivalent to which of the following:

A. x2 – 3x – 30

B. x2 + 13x + 6

C. 5x2 + x – 18

D. x2 + 3x – 21

5. What is the product of x3 − 3y2 + 6xy − 52 and -3xy?

A. -3x3 + 9y2 − 18xy + 156

B. -3x4y + 9xy3 − 18x2y2 + 156xy

C. 3x4y − 9xy3 + 18x2y2 − 156xy

D. 3x4y + 9xy3 − 18x2y2 + 52

6. Which expression is equivalent to 2x + 3y − 5x2 − 10y + 7x2 ?

A. 4x2 − 7y

B. 2x2 + 2x − 7y

C. 2x2 − 5xy

D. 2x + 13y + 12x2

Fractions, Decimals, Percents

7. What is the value of the expression 3p + 5 when p =[pic]?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

Equations

8. Katerine spent $10.95 at the store. She bought a box of cereal that cost $3.45 and 3 gallons of milk for g dollars each. Which algebraic rule represents this situation?

A. 3.45 + 10.95 = g

B. 10.95 – 3.45 = g

C. 3.45g + 3 = 10.95

D. 3.45 + 3g = 10.95

9. The table shows the cost C of rent a boat for h hours.

|Hours |1 |2 |3 |

|Cost ($) |7.25 |14.5 |21.75 |

Which equation best represents the data?

A. C = 7.25h

B. C = h + 7.25

C. C = 21.75 – 7.25h

D. C = 7.25h + 21.75

10. When a student subtracts 18 from a number, the result is [pic]of the number. What is the number?

A. 06

B. 18

C. 24

D. 36

Functions

11. Evaluate the function f(x) = x2 – 13x + 40 when x = 7

A. (7, -2)

B. (0, -2)

C. (-2, 7)

D. (7, 2)

12. For the function f(x) = 3x + 12, what is the value of x when f(x) is –6?

A. 3

B. -3

C. 9

D. -6

13. Given the function f(x) = 3x – 4, for what value of x does the function f(x) = 5?

A. 3

B. -3

C. 4

D. -4

14. Water leaked from a tank at a constant rate, m. Which equation models the amount of water, a, that has leaked out of the tank in time t?

A. a = m + t

B. a = m − t

C. a = mt

D. a = [pic]

15. What are the domain and range for the relation [pic]

A. Domain = {all real numbers}, Range = {all real numbers}

B. Domain = {all real numbers ≠ 5}, Range = {all real numbers}

C. Domain = {all real numbers ≠ −5}, Range = {all real numbers}

D. Domain = {all real numbers}, Range = {all real numbers ≠ 5}

16. What is the range of f(x) = -3(2x − 1)? ______

A. {all real numbers ≥ 0}

B. {all real numbers ≤ 15}

C. {all real numbers ≥ 15}

D. {all real numbers}

17. Daniela plotted the coordinates of the 2 largest toy shops in the city. The coordinates of Shop A are (2, 6). The coordinates of Shop B are in Quadrant II with the same y-coordinate as Shop A. What are the coordinates of Shop B?

A. (2, 0)

B. (3, 6)

C. (4, -6)

D. (-5, 6)

x- and y-intercepts

18. What are the x- and y-intercepts of the function below?

A. (-3, 0) and (0, 2)

B. (-3, 0) and (2, 0)

C. (0, -3) and (0, 2)

D. (0, -3) and (2, 0)

19. Find the x and y intercepts of 4x – 5y = 7

A. ( 0, 5) (4, 0)

B. ([pic], 0) (0, -[pic])

C. (0, -5) (4, 0)

D. (0, [pic]) (-[pic], 0)

Slope

20. Find the value of r so the line through (6, 2) and (9, r) has a slope of -1.

A. -3

B. -1

C. 0

D. 4

21. If the graph of a line has a positive slope and a negative y-intercept, what happens to the x-intercept if the slope and the y-intercept are doubled?

A. The x-intercept becomes four times larger.

B. The x-intercept becomes twice as large.

C. The x-intercept becomes one-fourth as large.

D. The x-intercept remains the same.

|t |0 |1 |2 |

|v |120 |152 |184 |

22. Which of the following equations represents the linear relationship between time, t, and velocity, v, shown in the table below?

A. v = 32t

B. v = 32t + 120

C. v = 120t

D. v = 120t + 32

23.

Slope-Intercept Form

24. What is an equation of the line that passes through (0, 1) and has a slope of 3?

A. y = 3x – 1

B. y = 3x – 2

C. y = 3x + 4

D. y = 3x + 1

25. Which of the following is the equation of the line that has the same slope as y = -4x + 2 and the same y-intercept as y = 3x + 2?

A. y – 2 = -4x

B. -4x = y + 2

C. y + 2 = -4

D. -4x = y + 3

26. Which statement best describes the graph of x = 5?

A. It is parallel to the x-axis.

B. It is parallel to the y-axis.

C. It passes through the point (2, 5).

D. It has a y-intercept of 5.

Slope-Intercept Form

27. What is the equation, in standard form, of the line that passes through (-3, -5) and has a slope of 2?

A. -2x + y = 1

B. -2x + y = -2

C. y = 2x + 7

D. y = 2x + 1

28. Kelly drew a sketch of a square garden, on a coordinate grid. Three corners of the garden are the points P(-6, 2), Q(-2, -2), and R(-2, 6), and point S is the 4th corner. What is the equation, in slope-intercept form, of the line containing R and S?

A. y = -3x + 6

B. y = x + 8

C. y = 2x + 6

D. y = -x + 4

29.

[pic]

Standard Form

30. Write the following equation in standard form: y = 3x + 4.

A. y = 3x + 4

B. y – 3x = 4

C. 3x + y = -4

D. 3x – y = -4

31. Write the following equation in standard form: y = [pic].

A. y = 5x + 6

B. y – 5x = 6

C. 5x + 2y = 6

D. 5x – 2y = -6

Point-Slope Form

32. Write an equation in point-slope form for the line that passes through (2, -8) with a slope of -5.

A. y + 8 = -5(x – 2)

B. y + 8 = -5(x + 2)

C. y – 8 = -5(x – 2)

D. y – 8 = -5(x + 2)

Parallel Lines and Perpendicular Lines

33. Which equation best represents the graph that is parallel to the graph below?

A. y = -2x + 4

B. y = 2x + 3

C. y = [pic]x+ 2

D. y = [pic]x+ 2

34. What is the slope of a line that is parallel to the line determined by the equation 2x + 3y = 7?

A. [pic] B. [pic]

C. [pic] D. [pic]

35. Which equation of a line is perpendicular to[pic]?

A. [pic]

B. [pic]

C. [pic]

D. [pic]

Short Response Question

[pic]

Extended Response Question (Complete on a separate sheet)

1. Given a linear function that passes through the points (-1, 4) and (2, -2):

a. Plot the two points.

b. Find the slope using the slope formula.

c. Write the equation of the line in slope-intercept form.

d. Graph the equation using the slope-intercept form.

e. Write the equation of the line in standard form.

f. Find the slope using the standard form slope equation.

g. Using the point (-1, 4), write the equation of the line in point-slope form.

h. Find the x-intercept and write as an ordered pair.

i. Find the y-intercept and write as an ordered pair.

j. Graph the line using the x- and y-intercepts.

k. Is the line y = 2x – 4 parallel or perpendicular to the line? Explain.

l. Is the line y = 1/2x + 5 parallel or perpendicular to the line? Explain.

m. Is the line y = -2x + 5 parallel or perpendicular to the line? Explain.

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