pg. 1

Northwood High School Pre-Calculus/Honors Pre-Calculus

Summer Review Packet

This assignment should serve as a review of the Algebra 2 skills necessary for success. Our hope is that this review will keep your mind mathematically active during the

summer months and help to identify your strengths and weaknesses coming into Pre-Calculus. Try to enjoy your summer, while staying sharp mentally. We look forward to

working with you in the fall.

NOTE: This assignment will be collected on the first day of school and you will have a quiz directly from the packet during the first week of school. Name_______________________________________ Date______________

pg. 2

Families of Functions Match the following equations to its function family.

___ 1. 𝒇(𝒙) = |𝟐𝒙 − 𝟕| A. Linear Function

___ 2. 𝒇(𝒙) = √𝟑𝒙 + 𝟓𝟑

B. Quadratic Function

___ 3. 𝒇(𝒙) =𝟐𝒙−𝟔

𝒙𝟑+𝟓 C. Absolute Value Function

___ 4. 𝒇(𝒙) = 𝟐𝒙𝟒 − 𝟑𝒙𝟑 + 𝟒𝒙𝟐 D. Cubic Function ___ 5. 𝒇(𝒙) = 𝟑𝒙𝟑 − 𝒙𝟐 + 𝟐𝒙 − 𝟑 E. Cube Root Function

___ 6. 𝒇(𝒙) = 𝟏𝟐𝒙 − 𝟏𝟕 F. Square Root Function ___ 7. 𝒇(𝒙) = 𝒙𝟐 − 𝟒𝒙 + 𝟒 G. Rational Function

___ 8. 𝒇(𝒙) = √𝟐𝒙 − 𝟔 H. Polynomial Function

Inverses Ex: Given 𝑓(𝑥) = 3𝑥 + 5, find its inverse 𝑓−1(𝑥).

Write out the steps in order. Reverse the steps. Make your equation.

𝑓(𝑥) = 3𝑥 + 5 𝑓−1(𝑥) =𝑥−5

3

A. You multiply by 3 B’. You subtract 5 B. Then add 5 A’. Then divide by 3

1. Given 𝑓(𝑥) = 2𝑥 − 1, find its inverse 𝑓−1(𝑥).

2. Given 𝑓(𝑥) = √3𝑥 + 4, find its inverse 𝑓−1(𝑥).

pg. 3

Odd/Even Functions

1) A function is even if the graph is symmetric across the y-axis. Give an example of an even function.

𝑓(𝑥) = ___________________________

2) A function is odd if the graph is symmetric around the origin. Give an example of an odd function.

𝑓(𝑥) = ____________________________

Complex Numbers

Simplify. 𝟏. √−49 𝟐. √−12 𝟑. (6𝑖) 2

𝟒. (3 − 4𝑖) 2 𝟓. (6 − 4i)(6 + 4i) 𝟔. −6(2 − 8𝑖) + 3(5 + 7𝑖)

pg. 4

Right Triangle Trigonometry

cos(47) = 𝑥

3 Ex:

3 ∗ cos(47) = 𝑥 𝑥 = 2

Solve for the missing side, x. You should use a scientific calculator in DEGREE mode. (Your phone may be able to act as a calculator) 1. 2.

3. 4.

hypotenuse

adjacent

opposite

pg. 5

Exponents

Express each of the following in simplest form. Answers should not have any negative exponents.

𝟏) 5𝑎0 𝟐) 3𝑥5

𝑥2 𝟑)

2𝑓4

𝑓6 𝟒) 𝑥3𝑥5

𝟓) 3𝑚2 ∗ 2𝑚 𝟔) (4𝑝2)3 𝟕) (2𝑏2𝑎3)4 𝟖) (3𝑛)4

𝟗) 𝑥2

5𝑥2 𝟏𝟎)

3𝑐

𝑐−3 𝟏𝟏) (4𝑎2𝑏−8)0 𝟏𝟐)

𝑎−2

𝑏−5

pg. 6

Multiplying Binomials

Multiply.

𝟏. (3𝑎 + 1)(𝑎 − 2) 𝟐. (𝑥 + 3)(𝑥 − 3)

𝟑. (𝑐 − 5) 2 𝟒. (5𝑥 + 7𝑦)(5𝑥 − 7𝑦)

𝟓. (2𝑥 − 7)(4𝑥 + 2) 𝟔. (2𝑥 − 1)(𝑥 − 3)

pg. 7

Quadratic Equations

Ex: 𝑥2 − 5𝑥 − 8 = 0 Cannot factor, so use Quadratic Formula.

a = 1, b = – 5, c = –8 Find a, b, and c.

𝑥 =5±√(−5)2−4(1)(−8)

2(1) Substitute.

𝑥 =5±√25+32

2 Simplify.

𝑥 =5±√57

2

Solve for x. 𝟏. 𝑥2 − 4𝑥 − 12 = 0 𝟐. 𝑥2 + 25 = 10𝑥

𝟑. 𝑥2 − 14𝑥 = −40 𝟒. 𝑥2 + 2𝑥 − 5 = 0

Think: What two numbers

multiply to make –21, but combine to make –4?

(3)(–7) = 21 and 3 – 7 = – 4

Quadratic Formula

𝑥 =−𝑏 ± √𝑏2 − 4𝑎𝑐

2𝑎

pg. 8

Evaluating Logarithms Definition of logarithm: Example: 𝑙𝑜𝑔𝑏(𝑥) = 𝑦 𝑙𝑜𝑔2(8) = 3 𝑏𝑦 = 𝑥 23 = 8

Evaluate the expression.

1. log6 (36) = ___ 2. log9 (81) = ___ 3. log7 (710) = ___

pg. 9

Graphs of Trig Functions

1. 2.

3. 4.