Algebra 1 Nine Weeks Test Review
Unit 1 Review
Name: ________________________
Date: _________________________
Write an algebraic expression for each verbal expression.
1.
2.
3.
4.
56 increased by twice a number _________________________________
the product of x and 7 plus one half of y _____________________________
twice the difference of 4 and x __________________________________________
8 less than a number squared ________________________________________
Convert. Be sure to show all work in the solution process.
5. How many inches are in 568 centimeters? (1 inch = 2.54 cm)
6. How many minutes are in 3 days?
7. If you are traveling 65 miles per hour, how many feet per second are you traveling?
8. How many ounces are in 6 tons?
Simplify completely.
9. 3(4x –5) + 9x + 8
10.
4x – 2y+8x – 4y – 16x
For each problem below, select the best answer and place your answer in the space provided.
_______ 11. Erica wants to have an average of an 85 on her quizzes. If she took three quizzes and earned a
94, 75, and 82, what is the lowest score she has to earn on her fourth quiz?
A.
88
B. 84
C. 89
D. 98
_______ 12. If -2x + 9 = -11, then what is -6x?
A.
60
B. -60
C. -10
D. 10
_______ 13. What is the algebraic translation of: “four times the sum of eight and a number”?
A. 4(8 + x)
B. 4 + 8x
C. (4 + x)8
D. 4*8 + x
_______ 14. What is the algebraic translation of: “The square of the sum of a number and 11”?
A. x2 + 11
B. (x + 11)2
C. x + 112
D. x + 11
15. The sides of a rectangle have a length x + 4 and width x – 3. What is the equation that describes the area
of the rectangle in terms of x?
16. Find the perimeter of the triangle.
3x
2x
4x+ 6
17. a. Find the area of the rectangle.
b.
x+4
Find the perimeter of the rectangle.
5x – 2
Simplify.
18.
19.
20.
36 x 4 y 6
64
21.
2 3 57 3 2
72
22.
23.
3 27  7 3  12
5 6  3 24  150
Simplify.
24. (x2 – 3x + 7) + (2x2 – 5)
25. (4m3 – 6m2 + 11) – (2m2 + 4m -13)
26. 16p2 + 11p – (12p + 6 p2 - 5)
27. (33r2 + 12r ) + (16r – 18r2 + 7)
28. (-16m2n3 )(4mn5)
29. (3xy)(-8xy7)
30. (2m + 3) (3m – 1)
31. 2m3(3m2 + 5m -11)
32. (3x2 + 5x)(-2x + 11)
33. (4a – 1)2
34. How many term are in the expression 15x3 – 34x2 + 4x?
35. Denise wants to buy a new shirt that cost $45. She waited until the shirt was on sale for 25% off. How
much did Denise pay for the shirt at the sale price?
36. 2. In the segment below, XZ  9 x  7 and YZ  3x  1 . Write an expression to represent the length of XY .
Y
X
Z
36. XY =
37. In the segment below, AM  4 x  7 and MB  3x  5 . Write an expression to represent the length of AB .
A
M
37. AB
B
Unit 2 Review
Solving Equations
1.
2(x – 3) + 5 = 3(x – 1)
2.

1
x  8  2
2
3.
6x + 7 = 8x – 13
Solve for the given variable.
4. 2 x  3 y  15, solve for y
5. P = 2L + 2W, solve for w
6. Solve for x: y  3x  7
________7. If the slope of a line is -3 and the y-intercept is 8, which of the following equations could be used
to represent the line? A. y = 8x – 3
B. y = –3x + 8
C. –3x + 8y = 24
D. –3x + 8y = 0
8. Find the slope, x-intercept, and y-intercept of the following equations
a. -2x – 5y = 10
slope:__________
x-intercept: ____________
y-intercept:____________
b. y = ½ x + 7
slope:__________
x-intercept: ____________
y-intercept:____________
9. Find the slope of the line that passes through the given pair of points. Show all your work.
a. (4,5) and (5,5)
b. (7,8) and (5,8)
Write the equation of the line using the information in slope intercept form.
10. slope = -3, passes through (-4,6)
11. through (2,8) and (4,9)
12. Graph using the x-intercept and the y-intercept.
4x – 3y = -12
13. Graph using the slope and y-intercept
y=
1
x5
2
14. April goes shopping every weekend of the year. She starts out with $200 and spends $25 every shopping
trip. Identify the slope and the y-intercept. Then write an equation to model this situation.
15. John tutors students on the weekends to raise extra money. He charges an initial fee of $5 and an extra $2
per hour. Identify the slope and y-intercept.
A) Write an equation to model this situation. _________________________________
B) Which graph could be used to model this situation?
A
B
C
Write the first six terms of each sequence with the given criteria.
16. The first term of the arithmetic sequence is 5 and common difference is 3.5. Write the explicit and recursive
formula.
Recursive: __________________
____, ____, ____, ____, ____, ____
Explicit: ___________________
Using Point-Slope to get to Slope-Intercept Form:
Write the equation of the line using the following information in slope-intercept form.
17. through (0,5) and (4,0)
18. through (2, 4) with slope 4
Arithmetic Sequence:
Write the first six terms of each sequence with the given criteria.
19. The first term of the arithmetic sequence is -3 and common difference is 4. Write the explicit and recursive
formula.
Recursive: ___________________________
____, ____, ____, ____, ____, ____
Explicit: ______________________________
20. Find the 53rd term of the sequence: an = 3n - 11
Linear Equations Word Problems:
21. Meribeth likes to collect unusual rocks. She currently has 6 rocks in her collection but wants to add to it.
She decides she would like to collect 4 more rocks each week. The equation y = 4x + 6 can be used to model
the total amount of rocks she has collected.
a. How many unusual rocks should Meribeth have at the end of 7 weeks?
b. How many weeks would it take Meribeth to have 26 rocks?
22. Morgan’s grandma gave her $100 for Christmas. She decides that she will spend exactly 20 per week after
that. Write an equation to represent the total amount of money Morgan has left after x weeks. Don’t forget to
define your variables.
23. Madison wanted to rent a bike during her trip to the beach. She found out that the deposit was $7 and she
would be charged $3 per hour until it is returned. Write an equation to model this situation. Don’t forget to
define your variables.
Solving Inequalities:
24. 6x – 3 ≤ 3x + 12
25.
Graphing Inequalities
26. 2 x  y  5
7
2x
5
3
27. y  x  5
28. x  2
29. Given the inequality y < x – 5, which point is NOT a solution?
A. ( 5, 10) B. (10, 0)
C. (3, -3)
D. (6, 0)
Solve using Substitution and then find the sum of x and y :
 x  4y  1
 y  3x  8
30. 
31. 
2 x  3 y  9
x y 4
Solve using Elimination and then find the sum of x and y :
3 x  5 y  11
32. 
 x  3y  1
2 x  3 y  13
33. 
 x  3y  2
Write a System of Equations:
3x  2 y  19
35. 
5 x  4 y  17
 2x  y  5
34. 
3x  2 y  4
Write a system of equations for the information.
36. Jumping Jacks charges $8 to play on the inflatables and $5 for the climbing wall. Josh paid $68 for a total of
10 trips to Jumping Jacks. How many times did he play on the inflatables and the climbing wall?
37. Mrs. Mock wanted to buy 80 new rulers. Manip-u-view and FlexiRuler are two different types of rulers.
Manip-u-view cost $0.10 each and FlexiRuler cost $0.25 each. Mrs. Mock has $15.05 to spend. How many of
each can she buy?
Function Notation:
Identify the domain and range of the given relation. Then tell whether the relation is a function. If the relation is
a function, tell whether it is a one-to-one function.
38. (1, 1), (2, 2), (3, 3), (4, 4)
39.
Domain:__________________
Domain:_________________
Range:__________________
Range:___________________
Function: Yes or No
Function: Yes or No
One to One: Yes or No
One to One: Yes or No
Given the functions below find the value of each of the following.
f(x) = 2x3 – 3x2 + 4
h(x) = -3x + 9
41. f(-1) = _______
42. h(3) = _______
43. f(3) = _______
44. x when g(x) = 6
45. g(3) = _______
46. g(2) = _________
47. Fill in the properties used in solving the equation:
Equation
7 x  4 x  2  4
Properties
Given Equation
7 x  4x  2  4
3x  2  4
3x  6
x  2
Unit 3 Review
Solve by factoring:
48. x2 + 11x + 24 = 0
49. 3x2 – 13x = 10
Solve by using square roots:
50. x2 = 225
51. 3 + (x – 5)2 = 17
Solve by using the quadratic formula:
52. x2 + 2x = 9
53. 4x2 + x – 10 = 0
g(x)