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ALGEBRA I PLACEMENT EXAM STUDY GUIDE
These are sample problems only. This review actually has more problems than are on the final.
The final is a multiple-choice test. A calculator is allowed for the final.
Topic I: Simplifying Expressions, Evaluating Expressions, Solving Equations/Inequalities
1.
2.
3.
4.
5.
6.
7.
8.
Evaluate: 22 + 23(8 - 2) ÷12
Simplify: 3( 2x – 8 ) – 5( 4x + 1 ) – ( x – 6 )
Solve: 2( x + 6 ) = 18
𝑥+1
2
Solve: 6 = 3
Solve and graph: 5( x + 6 ) = -3( x – 4 ) + 5
Solve and graph: 4( x – 3 ) ≤ 12
Solve and graph: -5x – 1 < 17
Solve and graph: -5 < 2x - 8 < x + 1
Topic II: Functions and Linear Equations
9. Find the missing value if the ordered pairs are in the same direct variation. (10, -3) (7, y)
10. Graph: y = 3x – 1
11. Graph: 2x + y = 8
12. Graph y – 1 = -2(x + 3)
13. Name the x and the y intercepts of 3x – 2y = 9
14. Find the slope of the line containing ( 3, 10 ) and ( -4, 3 )
15. Find the slope and y-intercept of 7x + y = 14
16. Write an equation of a line through ( 1, 3 ) with a slope of 2.
17. If f(x) = 3x -1 find f(-5) and f(10).
Topic III: Systems of Equations and Inequalities
𝑥+𝑦 =5
18. Solve: {
𝑥−𝑦 =1
19. Solve: {
2𝑥 + 𝑦 = −4
3𝑥 + 2𝑦 = −4
20. Graph: y = 2/3 x -1
1
21. Graph: {
𝑦 ≤ 2𝑥 + 5
𝑦 ≥ −2𝑥 − 1
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Topic IV: Exponents and Polynomials
22. Simplify each of the following:
a. (x4)(x5)
b. (x -3)(x-1)
23.
24.
25.
26.
c. x-5
d. x0
Simplify: (2x2y)3
Simplify: ( 3 x 2 ) ( 2 x3 )2
Simplify: (4x2 – 3x + 2 ) – ( x2 + 5x – 1 )
Find the perimeter:
5x -1
2x + 3
2x +1
2x +1
27. Simplify: 2x2( 3x2 – x + 10 )
Topic V: Quadratics
28. Multiply:
a. (2x – 1) (3x + 7)
b. ( x – 5 )2
29. Factor each of the following:
a. x2 – 64
b. 6x2 – 24
2
d. x – 25x - 24
e. 2x2 + 13 x + 21
30. Solve each of the following:
a. ( x – 1)( x + 5 ) = 0
b. 2(x + 6) = 0
d. x2 – 6x = -8
e. x2 – 6x + 9 = 0
c. 2x( x – 8 )
c. 3x3 - 6x2 + 9xy
f. 2x2 – 3x - 20
c. 2x2 – 5x = 7
f. x2 = 64
Topic VI: Radicals
31. Simplify each of the following:
a. √450
b.√4𝑎2 𝑏 6
2
c.√3
32. Simplify: 3√5 +7√5 - 12√5
33. Simplify: √18 + √8
34. Simplify: (3√5 ) ( 4√10 )
35. Simplify: (√3 + 2) (√3 -1)
36. Solve: √𝑥 − 8 = 4
1340 N. Acacia Avenue · Fullerton, CA · 92831· 714.879.6302 · www.rosaryacademy.org
Topic VII: Rational Numbers
37. Simplify each of the following:
a.
40 𝑥 2 𝑦 2
36𝑥𝑦 5
b.
𝑥2
38. Multiply each of the following:
a. (20xy ) • ( 14 x3 )
(7x2 )
( 40xy5 )
39. Divide:
𝑥 2 −4
𝑥+3
𝑥+5
7
43. Add:
2𝑥−3
𝑥−2
44. Subtract:
45. Solve:
b.
x2 + 4x + 3 • x2 + 2x -15
x –9
x2 + 6x + 5
2
𝑥−2
÷ 𝑥 2 +2𝑥−3
40. Find the LCM of 18, 15, and 24
41. Find the LCD of 1
,
1
,
9a2b
4a4b2
42. Add:
𝑥 2 −𝑥−6
c. 𝑥 2 +4𝑥+4
𝑥 2 −10𝑥+25
1
18ab4
2𝑥−10
7
+
𝑥−3
+ 𝑥−2
5
𝑥 2 −1
𝑥+3
𝑥
+
7
2𝑥
2
𝑥−1
=
5
𝑥
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1340 N. Acacia Avenue · Fullerton, CA · 92831· 714.879.6302 · www.rosaryacademy.org