MAT30S Grade 10 Review Mr. Morris

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1 GRADE 11 PRECALCULUS REVIEW OF GRADE 10 The following Grade 10 concepts should be reviewed for Grade 11 Precal: 1. Slopes of the Graphs of Linear Functions 2. Powers and Roots 3. Simplifying Radicals 4. Multiplying Binomials 5. Factoring (We will do this we the start of our first unit) 6. Graphing Linear Functions 7. Solving Systems of Linear Equations 8. Trigonometry 9. Operations on Rational Numbers 10. Solving Linear Equations 1

2 1. SLOPES OF THE GRAPHS OF LINEAR FUNCTIONS The steepness of a line is called its slope. To determine the slope of the line from a graph we use: slope = rise run or m = y 2 y 1 x 2 x 1 2

3 The equation of a linear function can be written in the form y = mx + bwhere m is the slope and b is the y-intercept (where the graph crosses the y-axis) The equation of the below linear function is: 3

4 2. POWERS AND ROOTS Exponents represent repeated multiplication. 3 5 is a power in exponential form = is the base and 5 is the exponent. Example) Evaluate ( 1 2 )5 The root of a number can be represented by a n radical symbol x, where n represents the index of the root. 5 Example) Evaluate 32 4

5 3. SIMPLIFYING RADICALS When given an entire radical we can simplify it to write it as a mixed radical: Example) Simplify Example) 120 5

6 4. MULTIPLYING BINOMIALS We use FOIL to expand the binomial and then collect the like terms to simplify your answer. Example) Expand and Simplify (3x + 2y)(4x + 5y) 6. GRAPHING LINEAR FUNCTIONS We can graph linear functions using a table of values OR using the slope and y-intercept from the form y = mx + b, OR determine the intercepts. NOTE: If the linear function is not given to us in y = mx + b form it is often easier to rearrange it into this form before we start working with it. 6

7 Example) Graph the linear function y = 2x 1in the following ways: TABLE OF VALUES SLOPE AND Y-INTERCEPT INTERCEPTS X AND Y-INTERCEPTS 7

7. SOLVING SYSTEMS OF LINEAR EQUATIONS A system of linear equations means two or more equations. The solution is the values that hold true for all the equations.

8 7. SOLVING SYSTEMS OF LINEAR EQUATIONS A system of linear equations means two or more equations. The solution is the values that hold true for all the equations. We can solve a system using the graphing method, substitution method or elimination method. Example) Solve the system GRAPHING y = 2x 5 y = 3x + 5 Substitution 8

9 8. TRIGONOMETRY Recall: SOH CAH TOA We have three scenarios: 1. Finding a missing angle remember to use inverse on your calculator 2. Finding a missing side when the unknown is on the top multiply 3. Finding a missing side when the unknown is on the bottom flip and divide Example) 9

10 Example) 10

11 9. OPERATIONS ON RATIONALS Rational numbers are any numbers that are written as a fraction or CAN BE written as a fraction. We will be building on operations (adding, subtracting, multiplying and dividing) of fractions by adding polynomials into our fractions. Example) Example)

12 10. SOLVING LINEAR EQUATIONS To solve a linear equation containing rational numbers (fractions) multiply both sides of the equation by a common multiple of the denominators. If this is done correctly, the fractions should disappear allowing you to isolate the variable. When solving equations we can verify our answers by plugging the solution back into the original question and show the equation is equal. Example) 2x =

Algebra II Summer Packet. Summer Name:

Algebra II Summer Packet. Summer Name: Algebra II Summer Packet Summer 2017 Name: NAME ALGEBRA II & TRIGONOMETRY SUMMER REVIEW PACKET To maintain a high quality program, students entering Algebra II are expected to remember the basics of the