Algebra 1: EOC Review Packet
Solving Linear
Equations
Solve the following equations for n.
1. 2(2n + 3) + n = -5n + 1
2.
Solving Literal
Equations
Exponent
Properties
n
4
−3= 7−n
3. Solve for E.
F+V=E+2
4. Solve for r.
A = πr 2
5. Solve for x.
ax2 + bx + c = 0
6. Simplify.
9x4y · 3x5y-8
7. Fill in the blanks to make a true statement.
x y ·
Linear Functions
x y =
120𝑦
𝑥3
8. Find the rate of change between the points (5, -4) and (-10, -20)
9. Write an equation for the line represented by the points in the table below:
x
y
-16
-22
-12
-19
-8
-16
-4
-13
10. Choose all of the following options below that represent a line which is parallel to the
line that contain the points:
{ (-10, 4); (-15, 2); (5, 10); (20, 16)}
2
y − 4 = 5 (x − 8)
2x – 5y = 10
5x + 2y = 7
2
y = 5x− 4
-5x = 2y – 7
5
x = 2 y + 15
Systems of
Equations
11. Solve the systems:
a.
3x + 2y = −2
y = −3x + 5
b.
3𝑥 + 2𝑦 = −1
5𝑥 + 6𝑦 = −15
Inverse Functions
12. Find the inverse of the function f(x) = 2x – 10
13. Match each function to its inverse.
Function
1
𝑦=
5
𝑥
Inverse
A
y = 5x
2
y = x3
B
y = 5x
3
y = (x + 5)2
C
y=± 𝑥−5
4
y = x2 + 5
D
y=± 𝑥−5
5
𝑦=
6
7
1
𝑥
5
𝑦=
y = log5x
F
y=x–5
y=x+5
G
y = x5
Factoring
Quadratics
14. Factor each of the following trinomials:
A) x2 – 2x – 15
B) 6x2 – 13x – 5
C) 8x2 – 52x + 24
D) 9x3 + 54x2 + 45x
15. Factor each of the following binomials:
A) 3x2 + 15x
B) 9x4 – 12x3
C) 16x2 – 9
D) 12x4 – 75x2
Solving Quadratic
Equations
16. Solve the following equations:
A) x2 = 100
B) 4x2 – 9 = 0
C) 2x2 = 35x – 3x
D) 15x2 + 35x = 0
17. Solve the following quadratic equation:
2x2 + 26 = 12x
Graphing
Quadratics
3
E
𝑥
18. Graph each of the following parabolas and list the following:
a. The Axis of Symmetry
b. The Vertex
c. The x- and y-intercepts
d. The Domain and Range
A) y = x2 – 4x – 12
1
B) y = 2 x 2 - 4x + 16
Quadratic System
of Equations
19. The product of two numbers is -144. The sum of the numbers is -7. Find the two
numbers.
20. The product of two numbers is 198. The sum of the numbers equals 29. Find the two
numbers.
System of
Equations Word
Problems
Classifying
Polynomials
21. A concert hall sells half price tickets to members of the armed forces. For a concert
last week, the hall sold 300 tickets altogether and 50 of them were to members of the
armed forces. Altogether, they made $6050. What is the normal ticket price (without
the military discount?
22. The sum of two numbers is 24. Twice the smaller number is 3 less than the larger
number. What are the two numbers?
23. You have thirteen coins in your wallet, some are nickels and some are dimes.
Altogether you have $0.85. How many nickels do you have?
24. You buy 9 packs of colored paper and 4 packs of plain white paper for $99.50. The
next month you buy 3 packs of colored paper and 10 packs of white paper for $51.00.
How much is one pack of colored paper?
25. Classify the following polynomials by degree and number of terms.
A) 3x2 + 9x – 6
B) -9x5 + 7x2
C) 14x3
D) x4 – π
26. List all of the reasons why this is not a polynomial.
1
8
-9x4 + 18x 2 − x + 9x π − 2
Operations on
Polynomials
27. Perform each of the following operations on polynomials and then classify your
result by degree and number of terms.
A) (x3 + 9x – 8) + (2x3 – 9x + 16)
B) 3x(x3 – 2x) – (9x4 – x3 – 6x2 + 2)
C) (x – 3)(x + 5)(x – 6)
D) (x2 + 2x – 1)(3x2 – 4x – 6)
E) (x – 2)4
Composition of
Functions
28. Consider the following functions:
f(x) = x + 4 and g(x) = x2 – 2x + 1
Find each of the following
A) 2f(x)
B) f(2x)
C) g(2x)
D) f(x) + g(x)
E) f(x) + g(2x)
F) f(x) – 3g(x)
G) g(x) – f(2x)
H) g(x) ÷ f(x)
I) f ∘ g x
J) g ∘ f(x)
Exponent
Properties
1 2
3
29. 2x 2 y 3 ∙ 3x 4 y
30. Choose numbers from the box below to create a true statement:
1
3
−
1
3
1
2
3
a ∙ a
−
2
3
= 𝑎1
1
4
−
1
4
3
4
−
3
4
-2
Square Roots
Box and Whisker
Plots
31. Simplify the following square roots:
a. 200
b.
50x 2
c.
−125x 4
d.
9x 4 y 2
32. Plot the following data on a box and whisker plot and then answer the questions that
follow:
4
4
5.5
6
6.5
6.5
7
a. What is the Inter Quartile Range of the data?
b. What percent of the data is greater than or equal to 8?
c. What percent of the data is between 5.5 and 8?
8
9.5
12