Download Algebra I Review Sheet: Name 1. Translate into an equation: 5 less

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Algebra I Review Sheet:
Name ________________________
1. Translate into an equation: 5 less than a number is the quotient of the number and 16
2.
What operation should you use to solve the equations:
a. x – 6 = 19
b. -14x = 28
3.
What is the correct order in completely solving the equation 5 – x = 23 ?
4.
Solve the equations:
a. 3x + 18 = 24
d.
𝑥
6
− 8 = 10
g. 14 – 5x + 5 = -6x + 8 + 4x
b. -6(x + 5) = 66
c. 5x – 15 = 10(x – 6)
e. -3x + 18 – 6x = 20
f. 3(6x – 2) = -(-20x – 3)
h.
4
7
𝑥
= 21
5.
When the sum of a number and 8 is multiplied by -3 the result is -36. What is the original number?
6.
Write an equation for the scenario: A child signs up for an online video game service for which there is
a $5 sign-up fee and the cost to download each game is $2. How many games can the child download if
they have $35?
7.
Solve and graph:
a. x + 8 < 0
c. 3x + 8 > 42
8.
9.
b. -3x + 9 > -36
d. -4x + 8 > 5x – 9x
e. 2x + 5 < -4x + 6x
Write an inequality representing all real numbers greater than 19 and less than or equal to 43
List the domain. Then determine whether or not it is a function:
a. {(9, 4), (5, 6), (9, -10)}
b. {(8, 7), (5, 4), (3, 7)}
10. Describe Kenny’s motion in the graphs below:
a.
b.
11. Sketch a reasonable graph for the data:
Time (minutes)
30
45
60
70
Number of pages a student still
needs to read for HW
18
14
13
10
12. a. Let f(x) = 4x + 6 ; Evaluate f(12)
b. Let g(x) = 3x2 – x ; Evaluate g(-3)
13. Determine whether or not the following are functions:
a.
b.
14. Solve for y: 4x – 3y = -24
c.
15. Sketch and label the points
A(-2, 5)
B(6, 0)
C (0, -3)
16. Which ordered pair is a solution to the equation y = 3x – 15?
a. (0, 15)
b. (2, 9)
c. (2, -9)
d. (5, 30)
17. What is the slope of the line passing through (15, 9) and (16, -8)?
18. Determine the slope and a point the line passes through: y + 5 = 6(x – 3)
19. Write the equation of the line passing through (4, -6) that is:
a. Horizontal
b. Vertical
20. Which equation is represented by the points in the table?
x
-3
0
3
a.
y
10
4
-2
y=x–7
b. y = -2x + 4
b. y = -3x + 1
d. y = -x + 7
21. a. Determine the equation of the line:
b. Sketch the graph: -3x + 6y = 24
22. What it the slope of the line? 9x + 3y = 54
23. Write the equation of the line passing through (8, -4) with a slope of
3
4
in slope intercept form
24. Write the equation of the line passing through (3, 7) and (-9, 11) in slope-intercept form.
25. What is the slope of the line parallel to the line passing through the points (9, 6) and (-3, 2)
26. Write the equation of the line passing through (10, 3) that is:
1
5
a. Parallel to 𝑦 = 𝑥 + 6
1
5
b. Perpendicular to 𝑦 = 𝑥 + 6
27. Determine the x- and y-intercepts of 6x – 8y = -36
28. Write the equivalent equation in slope-intercept form: y – 8 = -3(x – 6)
29. Solve {
2𝑥 + 4𝑦 = 46
𝑥 =5+𝑦
−4𝑥 + 7𝑦 = −11
30. Solve. {
𝑥 + 3𝑦 = −2
31. What is the best method to solve the system of equations, and why?
{
−10𝑥 + 7𝑦 = −11
5𝑥 + 6𝑦 = −2
32. Determine the solution to the system of equations:
33. What is the result after the first step in solving the system by linear combination/elimination:
4𝑥 − 12𝑦 = −12
{
−3𝑥 + 12𝑦 = 15
34. How many solutions does each system have?
2𝑥 − 𝑦 = 8
a. {
6𝑥 − 3𝑦 = 16
𝑥 + 4𝑦 = 7
b. {
3𝑥 + 12𝑦 = 21
35. Sketch the solution to the system of inequalities:
3
{
𝑦 ≥ −4𝑥 + 6
1
𝑦 < 2𝑥 + 2