1 - Alg I Review
Name: ___________________________________________ Period: ____ Teacher: ______________ Date: ___________
DHS Algebra I Fall Semester Exam Review
Check whether the given number is a solution of the equation or inequality. (yes or no)
6 f  7  29; 5
1.
_______________
2.
3.
Use the table below to answer the following questions.
_______________
Input
0
3
8
15
19
a) ________________________ Is the pairing a function or a relation?
b) ________________________ Identify the domain.
c) ________________________ Identify the range.
4.
5.
x5
 5.9; 23
3
Output
0
0.55
4.5
6.25
8.0
Draw a mapping of the pairing in the boxes to the right.
x
y
3
-6
7
8
7
12
11
17
15
20
Make an input-output table to represent the function y  8x  6 .
1 3
2 4
Use 6, 4,  , , and 3 for your domain values.
Write a function rule for each of the following.
6.
23.
Input
2
3
4
9
10
Output
4
6
8
18
20
Function Rule: ____________________
Input
0
1
5
12
16
Output
12
12.75
15.75
21
24
Function Rule: ____________________
2 - Alg I Review
Does each graph represent a function? Why or why not?
7.
8.
_____________________
9.
_____________________
_____________________
Simplify each expression.
11.
15t  (t  4)
_____________
5(n  7)  4(3  n)  3 _____________
13.
3
 (12m  8)
4
_____________
14.
m
 6  22
2
15.
12 
16.
8s  4s  168
17.
42  18b  4b  7b
18.
27  3c  3(6  2c)
19.
3
(n  3)  9
4
20.
11y  4  6y  1 _____________
21. 5(1  4m)  2(3  10m)
22.
5.4t 14.6 10.1t  12.8  3.5t  0.6
23. 2(3g  2) 
24.
v 8

20 4
26.
m3
 40 _______________
8
10.
7(w  5)  3w
12.
_____________
Solve.
_____________
_______________
4
a8
7
_____________
1
(12g  8)
2
_____________
_____________
4.5
1.8

x
5
_______________
3
5h

11 h  1.4
_______________
25.

27.

3 - Alg I Review
Write an equation for the function described. Then find the input.
28.
The output of a function is fourteen less than six times the input. Find the input when the output is twenty-two.
Equation: _________________
Input: __________
Determine the value of x for the triangle or rectangle.
29.
Perimeter = 23 ft
30.
Perimeter = 24 m
(x + 3) ft.
x ft.
(x +3) m
2x ft.
2x m
31. Abel has to save 15% of his monthly income. If his monthly income is $2450, how much will he save? If he saved
$380 last month, what was his monthly income?
32. _____________
34.
V  lwh
Solve for w .
_____________ 6 x  3 y  9 ; solve for y.
33. _____________
1
A  bh
2
Solve for b .
35. _____________ 8x  2 y  10 ; solve for y.
Solve each inequality and graph each solution.
36.
9.4  t  3.5
36. _______________
37.
g
 20
6
37. _______________
38.
90  4t
38. _______________
39.
5  3 p  2 p  p  7
39. _______________
40.
2(a  4)  16
40. _______________
41.
3(2v  4)  2(3v  6)
41. _______________
4 - Alg I Review
42. Find the next three terms in each of the arithmetic sequence, find the common difference, write the explicit rule
and find the 100th term of each sequence.
Sequence
a)
Common
Difference
Rule
100th Term
2, 8, 14, 20, ____, ____, ____
b) 90, 80, 70, 60, ____, ____, ____
c)
-1, -5, -9, -13, ____, ____, ____
d) 1, 6, 11, 16, ____, ____, _____
e)
43.
1 1 3
, , , 1, ... ____, ____, _____
4 2 4
Graph both equations on the same graph.
6 x  y  11
44. Find the x and y intercepts and graph.
x  8
3x  9 y  18
Slope formula: _____________________
Determine the slope for each of the following.
45.
________________ (2, 1) and (8, 4)
46.
Find the slope and write an equation for each line.
47.
Line A: _______________
___________________
Line B: _______________
___________________
Line C: _______________
___________________
Line D: _______________
___________________
________________ (3, 14) and (3, 5)
5 - Alg I Review
Find the rate of change for the data graphed on the line.
48.
________________
Graph Using Slope & y-intercept
Re-write each equation in slope-intercept form. Then, identify the slope and the y-intercept of the line and graph the
equation.
49. y  4  8x
Slope: _________
50.
y -intercept: _________
8x  2 y  14
Slope: ________
y -intercept: ________
Direct Variation
51.
Tell whether the table represents a direct variation. If so, write the direct variation equation.
Direct variation:
y = ___________
Yes / No
x
y
3
6
9
12
15
2
4
6
8
10
52. Given that y varies directly with x and y =15 when x=7. Find the value of y when x = –5.
6 - Alg I Review
53. Graph the each transformation, g(x), of the function, f ( x)  2 x  1 in a different color. State the
transformation(s) for each.
a) g ( x)  f ( x)  3 ________________________________
b) g ( x)  f ( x  5) ________________________________
c) g ( x)   f ( x)  3 ________________________________
d) g ( x)  f (3x) ________________________________
Slope-Intercept form of a linear equation: ______________________________
Point-Slope form of a linear equation: __________________________________
Standard Form of a linear equation: __________________________
Write the equation of the line in slope-intercept form with the given slope and y -intercept.
54.
______________ slope: 7; y -intercept: 4
55._______________ slope: -3; y -intercept: 5
Write the equation of the line shown.
56.
57.
_________________
_________________
Write an equation of the line that passes through the given points.
58.
________________ (6, 0), (0, 24)
59.
________________ (1, 9), (6, 5)
7 - Alg I Review
Write an equation of the line that passes through the given point and has the given slope m .
60.
________________ (5, 1), m  2
________________ (10, 3), m  2
61.
Write an equation in point-slope form of the line that passes through the given point and has the given slope m .
62.
________________ (8, 2), m  5
63.
Which equation represents the line that passes through the point (6, 2) and has a slope of 1 .
A)
y  2  ( x  6)
B)
y  2  ( x  6)
C)
y  2  ( x  6)
D)
y  1  2( x  6)
Which equation in standard form ( Ax  By  C ) represents line that passes through the two given points
(3, 9), (1, 1) .
64.
65.
Two lines are parallel if the slopes of the lines are the _______________, while two lines are
considered __________________ if the slopes are _______________ ________________.
Tell whether the equations of the two lines below are parallel.
66.
_____________ y  8x  3 ;
8x  y  3
67.
_____________ 2 x  y  5; 6 y  12 x  30
Determine which lines, if any are parallel or perpendicular.
68.
a)
y  4x  2
b)
1
y x
4
c)
y  4 x  1
__________________________________________________________________
69.
a)
y
3
x 1
5
b)
5 y  3x  2
c)
10 x  6 y  4
__________________________________________________________________
70. Write the equation of the line that is parallel to y  
4
x  7 and passes through the point (10, 2) .
5
71. Write the equation of the line that is perpendicular to y  
4
x  7 and passes through the point ( 2,10) .
5
8 - Alg I Review
72.
A)
Which scatter diagram shows the strongest positive correlation?
B)
C)
D)
73.
The following chart gives information on 10 high school students. The data shows how many hours per week each
student watched and what their GPA is. Use the chart to answer questions a - e below.
Student
1
2
3
4
5
6
7
8
9
10
Hours per week
watching tv
41
22
32
35
16
26
39
24
11
5
GPA
2.5
3.5
3.0
2.8
3.7
3.4
2.9
3.6
3.8
3.9
a) Create a scatter plot using the data in the chart above, and then draw the line of best fit.
b). Estimate the correlation coefficient, and use words to describe the direction and the strength.
c) We used technology to find the equation of the line to be
expect someone to have if they watched TV for 40 hours?
. Using the equation what GPA would you
d) In the equation what does the -.05 value for slope mean? What does the 4 value for y-intercept mean?
e) Describe the relationship (if any) between number of hours watching TV and GPA.
Review Systems of Equations
a) What does it mean to be a solution to a system of equations? How can you verify a solution to a system?
b) What does it mean when a system of equations has no solution? What does that look like graphically? algebraically?
c) Be prepared to solve a system of equations by graphing, substitution or elimination. See your systems review.