Algebra 1 Quarter 1 Common Test
Review
Directions:
Name ______________________________
November 2014
Complete each problem. Be sure to show all work to earn credit. You may NOT
use a calculator. Good Luck!
1. T
F
√2 is a rational number.
2. T
F
x = 4 is a solution to -3x = 12
3. T
F
The graph of y 
4. T
F
5. T
F
The opposite reciprocal of 1 is -1..
6. T
F
To determine the x-intercept of the graph of y = 2x + 5; let x = 0.
7. T
F
The equation of the line that passes through the point (7, 5) with an
undefined slope is y = 5.
8. T
F
A horizontal line that has a y-intercept at (0, -4) is defined by the
equation x = 0.
9. T
F
All lines have an x-intercept except a horizontal line.
10. T
F
The interval -2 ≤ x ≤ 11 is written [-2, 15) in interval notation.
1
x  2 is a curve.
4
3
3
Given the slope of  , as x increases by 1, y increases by .
2
2
Vocabulary. Give an example of each vocabulary term.
Associative Property of Multiplication
Real Numbers
Perfect square
Natural Numbers
Commutative Property of Addition
Whole Numbers
Commutative Property of Multiplication
Associative Property of Addition
Integers
Distributive Property
Rational Numbers
Additive Identity Property
Irrational Numbers
Multiplicative Identity Property
Terminating Decimal (Rational number)
Multiplicative Property of Zero
Nonterminating repeating decimal (Rational)
Opposite or Additive Inverse
Nonterminating Non-repeating decimal (Irrational)
Reciprocal or Multiplicative Inverse
11. Is 4 a solution to 5x-42= -3x-10 ? Explain why using the definition of solution.
12. Circle the perfect squares:
-1
0
81
44
256
900
B)
D)
integers
irrationals
111
8
-100
13. To what set of numbers does 2 5 belong?
A)
C)
whole numbers
rationals
14. Which of the following is an example of the distributive property?
A)
C)
2  3  5  2  (3  5)
2( x  5)  2 x  5
B)
D)
2( x  5)  2 x  10
(2  5) x  2(5 x)
15. Find the product of -1 and a number.
A.
C.
the opposite of the number
the number
B.
D.
0
-1
16. What is the multiplicative inverse (reciprocal) of 0?
A.
0
B.
1
C.
10
D.
undefined
3
17. What is the additive inverse (opposite) of  ?
8
A.

8
3
B.

3
8
C.
3
8
D.
8
3
C.
1
3
D.
3
C.
1
3
D.
3
D.
1
2
D.
1
2
18. What is the opposite reciprocal of 3?
A.
-3
B.

1
3
19. Which number is its own reciprocal?
A.
0
B.
1
20. Which of the following slopes has the lowest rate of increase?
A.
1
B.
5
C.
-5
21. Which of the following slopes has the most gradual rate of increase?
A.
1
B.
-5
C.
3
2
22. Which of the following pairs of coordinates are on a line with an undefined slope?
A.
C.
(-4, -6), (3, -6)
(-2, -2), (4, 4)
B.
D.
(3, -2), (3, 5)
(2, 1), (5, -2)
23. A horizontal line passes through the point ( 4,7). Which of the following points is also on
the line?
A.
(2, 4)
B.
(4, 2)
C.
(7, 0)
D.
(0, 7)
24. Which equation describes the line that contains the points (1, 1) and (3, -1)?
A.
y=x–2
B.
y=x+2
C.
y = -x – 2
D.
y = -x + 2
25. Which if the following tables represents y = 4x - 3
A.
x
-1
0
2
10
B.
y
x
-1
0
2
10
1
-3
-5
43
C.
x
-1
0
2
10
y
-7
-3
5
37
D.
x
-1
0
2
10
y
-7
-3
11
43
y
1
3
5
7
26. Use the table to find the rate of change in y with respect to x, if x is represented by the
number of items sold, and y is represented by the profit.
A.
1
2
B.

1
2
C.
2
D.
-2
C.
11
10
D.
0
27. Determine the slope of the line graphed below.
A.

10
11
B.
10
11
28. The table at the right shows a relationship between x and y.
Which of these equations represents this relationship?
B.
y  6x  7
C.
D.
y  7x  6
29. Write an equation for the line shown at the right.
y  7x  6
A.
y  6x  7
A.
y=x+1
B.
y=x+2
C.
y = 2x
D.
y = 2x + 2
1
30. Write an equation of a line that passes through (-3, 4) with slope  .
2
1
1
5
A.
B.
y  x
y  x 
2
2
2
1
23
1
11
C.
D.
y  x 
y  x 
2
6
2
2
31. Find the x- and y-intercepts of the graph of the equation y  50x  200.
A.
x-intercept is (200, 0)
y-intercept is (0, 4)
B.
x-intercept is (4, 0)
y-intercept is (0, 200)
C.
x-intercept is (2, 0)
y-intercept is (0, 100)
D.
x-intercept is (4, 0)
y-intercept is (0, 0)
32. Which is the equation of a line parallel to the line with the equation y = 3x - 4?
A.
C.
x - 3y = 1
3x - y = -2
33. Fill in the table to reflect a slope of
x
y
13
20
B.
D.
5
.
3
10
10
4
5
.
34. Find the slope from the graph shown.
x + 3y = 4
3x + y = 7
35. Write y  5 
4
(x  3) in standard form.
3
36. Write the equation of the line perpendicular to y 
3
x  4 that passes through the point
5
(3,-13).
37. Write an equation for a line that passes through (4, -2) and is parallel to the graph of 59
3
38. Write an equation in slope-intercept form for the line that passes through (4, -2) and is
perpendicular to the graph of y  1 x  7.
2
39. Graph the equations
2
a. y  4   ( x  5)
3
b.
2 x  y  1000
𝑥
Evaluate the following expressions given f(x) = 4x – 2, g(x) = -3x2 – 4, and h(x) = 3 . (2 pts.
each)
40. f(3)
41. g(-2)
42. h(0)
43. f( -2) + h( -15)
44. g(5) – f(0)
45. Find x if h(x) = -10
Solve each equation. All answers must be in simplest form.
46. 5 = 3 − 𝑥
48.
2
5
𝑥 = 30
47.
−3 + 4𝑎 = 17
49.
5(2𝑥 − 1) = 10𝑥 + 5
50.
3
𝑥+1
=
4
51. 4𝑥 = 9𝑥
7
Identifying Functions: Is each relation a function or not? If it is not a function, tell why.
52.
53.
Function? YES or NO
Function? YES or NO
If NO, explain:_________________________________ If NO, explain:____________________________________
Classify (Circle One): Continuous Discrete Neither
Classify (Circle One): Continuous Discrete Neither
State the domain and the range of the following relations.
54.
55. {(2, 3), (2, 5), (2, 7), (2, 9)}
56.
Domain: ___________________ Domain: ___________________
Domain: ___________________
Range: _____________________Range: _____________________
Range: _____________________
Classify: Continuous
Discrete
Neither
57. As the number of dogs are added
to a basket, the weight of the
basket increases.
Domain: ___________________
Classify: Continuous
Discrete
Neither
Classify: Continuous
Discrete
Neither
58.
Domain: ___________________
Range: _____________________
Range: _____________________
Classify: Continuous
Discrete
Neither
Classify: Continuous
Discrete
Neither
Use interval notation to state the intervals on which the function is increasing, decreasing, or constant.
59.
60.
Increasing: __________________________
Increasing: __________________________
Decreasing: __________________________
Decreasing: __________________________
Constant: __________________________
Constant: __________________________
61. g(x), f(x), and h(x) are defined below.
Order g(2), f(2), and h(2) from least to greatest. ______________________________________
62. Is the relationship a function or not a function?
63. What is the domain?
64. What is the range?
65. Is the relationship continuous, discrete, or neither? Explain.
Error analysis
66. There is one error in the following solution.
2
1
−5𝑥 + 8 + 2𝑥 = 5
2
1
10 (− 𝑥 + 8 + 𝑥) = 10(5)
5
2
−4 + 8 + 5𝑥 = 50
𝑥 + 8 = 50
𝑥 + 8 − 8 = 50 − 8
𝑥 = 42
a)Write the line with the error on the answer sheet and CIRCLE THE ERROR.
b)Explain the error and what should have been done.
c)What should the line read?