College Prep Algebra II Summer Packet

Transcription

1 Name: College Prep Algebra II Summer Packet This packet is an optional review which is highly recommended before entering CP Algebra II. It provides practice for necessary Algebra I topics. Remember: When simplifying fractions the numerator and denominator should not have any common factors Simplify and leave in fraction form (no decimals) Remember: When multiplying fractions you multiply the numerators and then the denominators. 5 0 (Always Simplify!) When adding or subtracting fractions you must have a common denominator. Multiply one or both of the fractions by an equivalent to one that is also the least common multiple of the denominators. 6 Once you have a common denominator add or subtract the numerators only Perform the indicated operation. Leave all fractions in simplified terms (no decimals)

2 Evaluate each expression Remember: 5( x 6) 8 ( x ) 7 Step : Multiply by using the distributive property 5x 0 8 x 6 7 Step : Add like terms on each side of the equal sign 5x 8 x Step : Combine like terms by adding or subtracting x 5 Step 4: Divide both sides by x 7 Solve for the variable.. 7 (4 x). m 4m. 7( x ) 8 ( x 4) 4. 6 k

3 Solve for the variable. 5. y ( 0) x r y 9. 4m v r x 7 5. x x g 5 4

4 Remember: The rules of exponents are: Rule name Rule Example Product Rules a n a m = a n+m 4 = +4 = 8 Quotient Rules a a n m = a n-m Power Simplify. Rules (b n ) m = b n m ( ) = = 64 5 = 5- = 4 Negative Exponents b -n = n b - = = a b ab 6. 60xy xy x x 8. xy xy x

5 Remember: Be sure to READ the problem and perform the indicated operation. For example, multiplying two binomials: ( x 6)( x ) Step : Multiply by using the distributive property (FOIL) Step : Combine like terms x x x 6 8 F O I L x x 8 Simplify.. 5x x x x 8. x 6x 7 x x 4. a 8a 0 4. g 4 8g k 5. x x 4 6. x x 7. 4x 7 x 8. x 4 5

6 Remember: The Greatest Common Factor (GCF) is the largest term that can be divided into each of the terms. For example: 7x y x y 4xy Step : Find the GCF of the integers and the variables 7 xy( ) Step : Divide the GCF into each term and write its quotient Step : To check your work, distribute the GCF over the polynomial. You should always get the original polynomial. 7 xy( x y x y ) Factor out the Greatest Common Factor. 9. 0x x xy x y Remember: When factoring polynomials you are looking for the pair of factors of the third term that add up to the second term. Don t forget always look for a GCF first! For example, to factor trinomials with a squared term: Step : Find the factor pairs of Step : Chose the pair that add up to Factor into two binomials x 5x 4 4. x 6x 5 x x 8. Watch your signs! x 4 x 7 Step : To check your work, multiply the terms using the FOIL method. You should always get the original polynomial. 4. x 4x x x 0 6

7 Remember: When graphing linear equations written in y mx b form, m represents the slope and b represents the y- intercept. For example, a linear equation that is solved for y: y x 4 Step : Plot the y-intercept by identifying b b 4 so plot the point 0, 4 Step : Identify your slope m m Step : From the y-intercept plot points using the slope. Don t forget slope is rise so, from run go up two and then to the right three plotting a second point of the line at,. Plot at least three points when graphing a line. 45. Graph the line. y x Graph the line. y x 7

8 Remember: When finding the slope and y-intercept form from an equation, the equation first must be in y mx b form, with m being the slope and b the y-intercept. 47. Find the slope of the line y x Find the slope of the line y 5 x. 49. Find the slope of the line x y Find the y-intercept of the line x y Find the y-intercept of the line 5x 4y. 5. In slope-intercept form, the y-intercept is represented by: a) m b) b c) x d) y e) y 5. Which of these points is on the line x y 7? a), b), c), d) 4,5 e) 0,0 8

9 Remember: When finding the equation of a line, first you need a slope. If you are given two points, use the y y slope formula, m, to find the slope. Then use the point-slope formula, x x y y m x x to find the equation of the line. Substitute the slope in for m and one of the points into x and y 54. Write the equation of the line with a slope of - and passing through the point 0,. 55. Write the equation of the line with a slope of and passing through the point,5. Remember: Parallel lines have the same slope. Perpendicular lines have opposite sign and reciprocal slopes, for example and What is the slope of a line parallel to y x? 57. What is the slope of a line perpendicular to y x 6? 5 9

10 58. Which pair of equations represents perpendicular lines? a. y x and y x b. y x and y x c. y x and y x d. y 7x 4 and y 7x 6 0