UMHS PreCalculus - Summer Review
Summer Math assignments for current and incoming students
PreCalculus
All PreCalculus students are required to have a
TI 84-Plus Graphing Calculator for this course.
The calculator will be used throughout this course, and in future math courses.
Please keep your eyes open for sales and purchase one before school begins.
Show All Work
Finding the Equation of Parallel and Perpendicular Lines
PARALLEL LINES have the same slope.
PERPENDICULAR LINES have opposite and reciprocal slopes. (change the sign and flip the fraction)
WRITING THE EQUATION OF PARALLEL AND PERPENDICULAR LINES.
Write the equation of the line described. SHOW ALL WORK.
1. Write the equation of the line parallel to (See Picture) , passing 3 through (6, 5).
2. Write the equation of the line parallel to (See Picture) , passing through (10, 18).
3. Write the equation of the line perpendicular to (See Picture), passing through (6, -4).
4. Write the equation of the line perpendicular to (See Picture), passing through (−4, −5).
Identifying Domain and Range
Using Function Notation and Identifying Domain and Range
Domain: the set of possible inputs of a function, the “x” values Range: the set of possible outputs of a function, the “y” values.
We start by graphing the function, as shown at right. Since we can use any real number for x in this equation, the domain is all real numbers. The smallest possible result for y is –2, so the range is y ≥ −2.
IDENTIFYING DOMAIN AND RANGE. Identify the domain and range (when appropriate) of each function. SHOW ALL WORK.
Function Notation
The notation f(x) represents the output of a function, named f, when x is the input.
* g(2) represents the output of the function g when x = 2.
FUNCTION NOTATION. Evaluate each function. SHOW ALL WORK.
FInd f (5)
What is the value of x? x = ..... or .....
Find g(-2)
Multiplying Polynomials and Solving Quadratics
Multiplying Polynomials
In Algebra 1, you learned two methods for multiplying polynomials:
1) Distributive Property (used to multiply ONE term times a polynomial)
2) Generic Rectangle (used to multiply a polynomial times a polynomial)
Solving Quadratics
STEP 1: Make the quadratic equation = 0.
STEP 2: Factor the polynomial.
STEP 3: Use the Zero Product Property to solve for x. (Set each factor = 0)
In the example below "Factor using a generic rectangle. (Work is not shown.)
For problems #14-16, multiply each polynomial expression. For problems #17-19, solve each quadratic equation. SHOW ALL WORK.
Trigonometric Ratios and the Pythagorean Theorem
Three trigonometric ratios and the Pythagorean Theorem can used to solve for the missing side lengths and angle measurements in any right triangle.
In the triangle below, when the sides are described relative to the angle θ, the opposite leg is y and the adjacent leg is x. The hypotenuse is h regardless of which acute angle is used.
Pythagorean Theorem
To find the angle measurement in a right triangle, use the inverse trig. ratios.
tan = opposite leg/adjacent leg = y/x
sin = opposite leg/hypotenuse = y/h
cos = adjacent leg/hypotenuse = x/y
To find the angle measurement in a right triangle, use the inverse trig. ratios.
Use right triangle trig or the Pythagorean Theorem to solve for the variables. SHOW ALL WORK.
Multiplying and Dividing Rational Expressions
STEP 1: Change division problem→multiply by the reciprocal (flip the 2nd fraction). STEP 2: Factor the numerator and the denominator.
STEP 3: Multiply the numerators. Multiply the denominators.
STEP 4: Cancel the factors that are the same by making a GIANT 1.
Simplify each rational expression. SHOW ALL WORK.
Adding and Subtracting Rational Expressions
Addition and subtraction of rational expressions uses the same process as simple numerical fractions.
STEP 1: If necessary find a common denominator.
STEP 2: Convert the original fractions to equivalent ones with the common denominator.
STEP 3: Add or subtract the new numerators. Keep the common denominator.
STEP 4: Factor the numerator and denominator and simplify, if possible.
Add or subtract each expression. SHOW ALL WORK.
Laws of Exponents
Solve each equation. SHOW ALL WORK.
Laws of Exponents
Use the laws of exponents to simplify each expression. Your final answer should NOT have negative exponents in it. SHOW ALL WORK.