1) This document contains a review of various algebra 2 concepts across 9 standards, including solving linear equations, quadratic equations, systems of equations, exponents, functions, and probability. 2) Several problems provide examples of solving systems of equations, factoring quadratic expressions, graphing quadratic and exponential functions, simplifying expressions with exponents, and calculating probabilities of independent and dependent events. 3) The review covers a wide range of algebra 2 topics to help students prepare for an upcoming benchmark exam.

1. Algebra 2
Benchmark Review
Ms. Cheung

2. Standard
1.0
1)
The absolute value of any number will always
be positive, thus the equation |5 – 6m| > - 7
will always be true!!

3. Standard
1.0
2)
10 5x 7 62 10 5x 55
10 5x 55 10 5x 55
5x 45 5x 65
x 9 x 13

4. Standard 2.0
3. Which order pair is the solution to the system of equations below?
x 7 y 20 Solve for x x 7 y 20
4 7 y 20 4 y 16 Substitute for x x 7(2) 20
28 y 80 4 y 16 Distribute x 14 20
32y 80 16 Combine Like Term x 6
32y 64 Combine Like term
y 2 Solve for y

5. Standard 2.0
4. Which order pair is the solution to the system of equations below?
8 x 2 y 20 4x y 2
2 4 x y 2 Multiply 2 to equation 2 4x 6 2
8 x 2 y 20 4x 4
Add the two equations
8x 2 y 4 x 1
4y 24 y 6

6. Standard 2.0
5) Ms. Cheung’s current phone plan is about to
be expired. She has been offered two
promotions from two different phone
providers. AT&T provides a 500 minute plan at
$30 with 40 cents per text message. T-Mobile
provides a 500 minute plan at $40 with 30
cents per text message. If x represents the
number of text sent and y is the total amount
charge for both plans, how do you write a
system of equations that model this situation?
y 30 0.4 x
y 40 0 .3 x

7. Standard 2.0
6) Gerardo wrote a matrix equation.
4 3 x 20
1 2 y 6
What is the solution to Gerardo’s equation?
4 3 x 20 4x 3 y 20
1 2 y 6 x 2y 6
4x 3y 20
2, 4
x 2y 6

8. Standard 2.0
7) Jackie wrote a matrix equation.
2 1 x 3
3 2 y 6
What is the solution to Gerardo’s equation?
2 1 x 3 2x y 3
3 2 y 6 3x 2 y 6
2x y 3
0, 3
3x 2 y 6

9. Standard 3.0
8)
5n 4 3n3 8n 2
3n 4 2n3 7n 2
2n 4 n3 15n 2

10. Standard 3.0
6a 2 6a
14a 14
6a 2 20a 14

11. Standard 3.0
6k 2 12 k
5k 10
6k 2 17k 10

12. Standard 3.0
11)
6x 4 8x 3 4 2x 4 4x 3 3
4 3
8x 12x 1

13. Standard 3.0
12)
Given a polynomial expression x 4 10x 3 35x 2 50x 24
such that it has two factors of ( x 1) and ( x 4).
A) (x 1) and ( x 2).
1 4 4
B) (x 1) and ( x 3).
C) (x 2) and ( x 3). 2 3 6 24 4 6
D) (x 3) and ( x 4).

14. Standard 5.0
13) Which of the following represent the graph
of 3 2i ?
A C
B D

15. Standard 5.0
14. Kevin knows that 1 i . What will he get if
he simplifies 16 ?
A) 4 and 4
B) 4
C) 4i
D) 4i and 4i

16. Standard 5.0
15. Jocelyn knows that 1 i . What will he get
if he simplifies 64 ?
A) 8 and 8
B) 8
C) 8i and 8i
D) 8i

17. Standard 6.0
16. Jocelyn knows that 1 i . What will she
get if he simplifies 2 25 ?
A) 5i
B) 10i
C) 10i
D) 5i

18. Standard 6.0
17)
(3 i )(3 i )
9 3i 3i i 2
9 ( 1)
10

19. Standard 6.0
18)
3 2i 5 i
2 3i

20. Standard 6.0
19)
12 5i ( 3 4i)
12 5i 3 4i
9 i

21. 20)
2
p 4 0 a 1, b 0, c 4
0 0 2 4 (1)( 4 ) 16 4
x 2 (1) 2 2 x 2 or x 2

22. 21)
6x 2
5x 25 0 a 6, b 5, c 25
5 52 4 ( 6 )( 25) 5 25 600 5 625 5 25
x 2(6) 12 12 12
5 25 5 25
x 12 or x 12 x 5
3 or x 3
5

23. Standard 9.0
22. Given the graph f(x)=ax2+bx+c. If a is
negative, what would my graph look like?
f(x)=ax2+bx+c is a Quadratic
Equation since it has a
A) A linear graph going up power of 2.
B) A linear graph going up Since a is
C) A quadratic graph going up negative, the graph
will be going
D) A quadratic graph going down downward.

24. Standard 9.0
23)
Vertex
(-3, -2)
Vertex From (-3, -2) to (2, 2)
(2, 2) We get ( 2, 2)
( 3, 2)
(2 3, 2 2)
(5, 4)
Positive 5, so it’s 5 unit to Positive 4,
the right. 4 units UP!!

25. Standard 9.0
24)
Vertex
(5, 1)
Vertex
(-5, 1)
Both functions are
positive, so their vertices
are minimums.
Both functions
have the same
coefficient: 3, both
have the same
shape.
Both functions are
positive, so both
vertices are minimum.

26. Standard 10.0
25) What is the minimum value of the function
f(x)=x2 – 9?
Minimum  The lowest Point!
A) –9 Find the vertex!
B) –3 X= - b/2a
X = 0/2 = 0
C) 0
y = 0 – 9= -9
D) 9
The lowest Point!

27. Standard 10.0
26)
X= - b/2a
X = -6/2 = - 3
y=(-3)2+6(-3)+5
= 9 – 18 + 5 = - 4
Vertex: ( - 3, - 4)

28. Standard 24.0
27)

29. Standard 24.0
28)

30. Standard 24.0
29) Which of the following functions is the
inverse of f(x) = 3x – 2?
A) 1 3
f ( x) x 2
B) f 1 ( x) 3
x 2
1 x 2
C) f ( x) 3
D) f 1 ( x) x 2
3

31. Standard 7.0
30) Rewrite the following exponents to positive
exponents.
x 2
A) f ( x) 3
y
2 5
x y
B) f ( x) 4 2
x y

32. Standard 7.0
31)

33. Standard 7.0
32)

34. Standard 7.0
33)

35. Standard 7.0
34)
-1

36. Standard 22.0
35)
Strategy: Convert to decimal
=0.5 + 0.25+ 0.125 + 0.625 + …
=0.5 + 0.25+ 0.125 + 0.0625 + …
=0.9375
Closest to 1

37. Standard 22.0
36)
Strategy:
1st term 2nd term term 4th term5th term Substitute n=1, 2, 3, 4, 5
3rd
into the answer choice to
n=1 n=2 n=3 n=4 n=5 see if the term generated is
= 4(1) = 4 (first term) same as the question
the
= 3+4(1) = 7 (first term)
= 2(1)+1 = 3 (first term)
= 2(2)+1 = 5 (second term)
= 4(1)-1 = 3 (first term) = 4(2)-1 = 7 (second term)
= 4(3)-1 = 11 (third term) = 4(4)-1 = 15 (fourth term)
= 4(5)-1 = 19 (fifth term)

38. Standard PS 1.0
Strategy: Identify Keywords
37)
P(cm label & no labels)
Multiply
No. of rulers
No. of rulers
with cm labels
without labels
One less ruler
Total No. of
Rulers

39. Standard PS 1.0
38)
Strategy:
Identify Keywords
Not raining in San Francisco
Multiply
and not raining in Sydney
P(not raining in SF & not raining in Sydney)

40. Standard PS 1.0
Strategy:
39) Identify Keywords
Green and green Multiply
P(green & green)
No. of green
marble in 1st No. of green marbles
bag in 2nd bag
Total No. of
Total No. of
marbles in 2nd
Marbles in
bag
1st bag

41. Standard PS 2.0
40)

42. 41) Standard PS 2.0