(P) Expressions
Name: _____________________________
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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