CST Review
Alg 1H
Please work on graph paper, number your problems neatly and circle final
answers for easy correcting.
1. Evaluate the expression 72x + 15 – x3 when x = -2.
2. A grocer has raisins selling for $1.50/lb. and peanuts selling for $1.25/lb. He mixed how
many pounds of each to make a mixture of 10 pounds at $1.30/lb.? Write an equation,
and solve to find your answer.
3. You have $75.35. You wish to buy a calculator which costs $18.95 and a CD player priced
at $51.99. There is a 6% sales tax. Prove whether or not you have enough money to pay
for both?
4. Simplify: 30 – 21x
3
5. Two cars, traveling toward each other at 60 and 70 mph, respectively leave from points
260 miles apart. How long will it be before they meet? Write an equation, and solve to
find your answer.
6. Solve the equation for a:
12ab + 7b = 5a
7. Answer the following questions:
a. What type of lines have zero slope?
b. What type of lines have an undefined slope?
c. Write the equation of the horizontal line that passes through the point (5, -4).
d. Write the equation of the vertical line that passes through the point (2, 7).
e. Find the slope and equation of the line passing through (3, 7), (-1, 7).
8. Write the equation of the line that is parallel to the line 4x – 7y = 14 and passes
through the point (7,7). Write your equation in slope intercept form.
9. Find the slope of the line containing the points (-3, 8) and (5, 2).
10. Sketch the graph and label the intercepts of the equation: 5x – 3y = 30.
11. Write the equation of the line that is perpendicular to the line 2x – 3y = 15 and
passes through the point (2, 1).
12. Find the rate of change between the two points (4, 36) and (8, 108) and give the unit
of measure.
x is measured in square yards
y is measured in dollars
13. Rewrite in slope-intercept form, then graph the equation.
3x – 2y = 12
14. Find the coordinates of the vertex of the graph y  x  2  4 , then graph it.
15.
Complete the table and sketch the graph of the equation.
y 3 x2
x
y
0
1
2
3
4
y
10
16. Write the equation of the line shown in the
graph.
9
8
7
6
5
4
3
2
1
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6
7
8
-2
-3
-4
-5
-6
-7
-8
-9
-10
17. Write in slope-intercept form the equation of the line passing through the points
points (4, -1) and (0, 3).
18. A salesman receives a salary of $400 per week plus a commission of 5% of all sales.
Write a linear model (equation) for the weekly income y in terms of sales x.
19. Rewrite the equation y = 
20. Solve the inequality:
6
3
x 
in standard form with integer coefficients.
5
2
5 – 7x < 12x + 40.
21. Write the inequality for the graph shown here.
22. Solve the absolute value inequality:
1
2
x 

2
3
-6 -4
-2
0
2
23. Rewrite in slope-intercept form, then graph the inequality: x – 2y < 2.
4
9 10
24. Write an inequality to fit the graph at the right:
y
10
9
8
7
6
5
4
3
2
1
x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6
7
8
9 10
-2
-3
-4
-5
-6
-7
-8
-9
-10
25. State whether the system represents parallel lines, intersecting lines, or a single line.
Also state whether there is one, none, or many solutions.
3x + 4y = 5
6x + 8y = 5
26. Solve the linear system.
2x - 5y = 6
-6x + 15y = -18
27. A total of $20,000 is invested in two funds paying 6% and 7% annual interest. The
combined interest is $1325. How much of the $20,000 is invested in each fund?
Write a system of equations and solve for your answer.
28.
F1 I
Simplify: c
3x hG J
H27x K
4 c
y h
Simplify
use positive exponents.
2 4
0
29.
2
3
2 4
x 5
30. Simplify the expression:
8a3b2 8a 4 b3

22 b 4 32a 5b2
31. A principal of $800 is deposited in an account that pays 5.4% annual interest
A  p(1  r) t
compounded yearly. Find the balance after 6 years.
32. Solve: x2 = 0.81
33. Sketch the graph of the equation. What is the vertex of this graph? Use graph paper.
y = x2 + 2x – 2
34. Use the quadratic formula to solve the equation.
x2 + 2x – 5 = 0
35. Find the product: -x2(-2x2 + x – 3).
36. Find the greatest common factor of all three terms: 30a5b3
75a3b6
45a4b2
37. Factor the expression 4y2 – 49.
38. Factor the expression 2x2 – 16xy + 32y2.
39. Solve the proportion:
7
4

x 3
x
40. 48 is 30% of what number?
41. x and y vary inversely. If x = 2.4 when y = 130, find an equation relating x and y.
42. A jar contains 9 marbles numbered 1 through 9. If one marble is removed at random,
what is the probability it will carry an odd number?
x2  4
x2  4 x
43. Find the domain of the rational expression:
44. Simplify:
b g
3x3 y  3
5y 2 x 2
45. For this collection of the
mode.
27 32 14 28
28 15 21 41
20 10 30 32
15y 3
4 y  12
b
g
weights of a group of dogs, find the mean, median, and
35
32
40
46. Working alone, Sylvia can complete a project in 7 hours. It would take Valerie 3 hours
to complete the same project. If they work together, how long will it take them to
complete the project? Write an equation and solve for your answer.
47. How many liters of water must be added to 50 L of a 30% acid solution in order to
produce a 20% acid solution? Write an equation(s) and solve for your answer.
48. An old boat took three hours to go 48 miles downstream, and six hours to return
upstream all 48 miles. What was the rate of the boat in still water and the rate of the
current? Write a system of equations, and solve for your answer.
49. Write the product in simplest form. (x  2) 
50. Solve the equation:
x
6
1


5
x
5
x 6
x2 4