Algebra 1: EOC Review PacketSolving Linear

EquationsSolve the following equations for n.

1. 2(2n + 3) + n = -5n + 1

2.n

4− 3 = 7 − n

Solving Literal Equations

3. Solve for E.

F + V = E + 2

4. Solve for r.

A = πr2

5. Solve for x.

ax2 + bx + c = 0

Exponent Properties

6. Simplify.

9x4y · 3x5y-8

7. Fill in the blanks to make a true statement.

x y · x y = 120𝑦

𝑥3

Linear Functions 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:

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)}

y − 4 =2

5(x − 8)

2x – 5y = 10

5x + 2y = 7

y =2

5x − 4

-5x = 2y – 7

x =5

2y + 15

Systems of Equations

11. Solve the systems:

a. 3x + 2y = −2y = −3x + 5

b. 3𝑥 + 2𝑦 = −15𝑥 + 6𝑦 = −15

x y

-16 -22

-12 -19

-8 -16

-4 -13

Inverse Functions 12. Find the inverse of the function f(x) = 2x – 10

13. Match each function to its inverse.

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

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

B) y = 1

2x2 - 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.

Function Inverse

1 𝑦 = 5 𝑥 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 =1

5𝑥 E 𝑦 = 3 𝑥

6 y = log5x F y = x – 5

7 y = x + 5 G y = x5

System of Equations Word

Problems

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?

ClassifyingPolynomials

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.

-9x4 + 18x1

2 −8

x+ 9xπ − 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

29. 2x1

2y2

3 ∙ 3x3

4y

30. Choose numbers from the box below to create a true statement:

a ∙ a = 𝑎1

1

3−1

31

2

3−2

3

1

4−1

4

3

4−3

4-2

Square Roots 31. Simplify the following square roots:

a. 200

b. 50x2

c. −125x4

d. 9x4y2

Box and Whisker Plots

32. Plot the following data on a box and whisker plot and then answer the questions that

follow:

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?

4 4 5.5 6 6.5 6.5 7 8 9.5 12