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) = ___
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