4) Simplify 5( 6) Simplify. 8) Solve 1 x 2 4
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1 Algebra Summer Assignment 1) Simplify x 4y 10 x ) Simplify 4y 6x 3( x y) 3) Simplify 1 3 ( x 3) 4) Simplify 5( x 9x) (3x 4) 7 5) Simplify ( x 3)( x ) 6) Simplify ( x 4) 3 7) Simplify ( 5x 8)(4x 1) 8) Solve 1 x 4 4 9) Solve 5x ) Solve x x 5 x ) Solve 4( 3x 1) 10( x 4) 14x 1) Solve x x 13) The formula for the volume of a cylinder is V r h. Solve the equation for h. How tall is a 3 cylindrical can with a radius 3 cm. and volume 00 cm? 1
2 Algebra Summer Assignment 14) Find the value of f (4) for f ( x) x ) Find the value of f () for f ( x) x 7 16) Find the value of f (9) for f ( x) n 5 17) Find the value of f () for f ( x) x x 3 18) Find the value of f () for f ( x) x 6x 5 Solve the equation for y. 1 19) 5x 3y 7 0) x y 1 4 Identify the domain and range of the function. 1) ) x y Domain: Range: Domain: Range:
3 Algebra Summer Assignment 3) Graph y x 4) Graph y 3 3 x-intercept = y intercept = slope = x-intercept = y intercept = slope = 5) Graph 5x y 10 6) Graph x 4 x-intercept = y intercept = slope = x-intercept = y intercept = slope = 3
4 Algebra Summer Assignment Solve the linear system by graphing. x y 5 x y 7) 8) x 3y 9 3x 4y 36 Solution: Solution: Solve the system by substitution or combination/elimination. x 3y 7 x y 5 9) 30) 4x 5y 13 x 3y 9 31) Graph y x 4x 7 3) Graph y ( x )( x 1) Vertex: Domain: Range: Vertex: Domain: Range: 4
5 Algebra Summer Assignment 33) Factor x 11 34) Factor 18x 35) Factor 49 x ) Factor 16x 9 37) Factor x 7x 3 38) Factor 3x 3x 11 39) Factor 6x 18x 4 40) Factor 5x 3 45x ) Factor 3x 1x 8x 3 4) Factor 1x x 30x 5 Solve the following equations. 43) 5x 7x 0 44) 3x 1x 45) 4 x ) x 4x 8 x x 47) x 9x ) x 3x 8 5
6 Algebra Summer Assignment Simplify each expression completely. 4x 49) 18x 50) 0 1x 51) 4 0 3x y 5) 1xy 7x 4 5 7x y 4y 53) 3 8m 3 54) 7g 3 5 h ( h k 0 ) ) a b b 56) 3x y ( x y) ) Tickets for the school play are $3 for students and $5 for non-students. On opening night 937 tickets are sold and $3943 is collected. How many tickets were sold to students? To non-students? 58) In 1990 a 4-function calculator cost $45. In 1995 a 4-function calculator cost $5. Find the average rate of change in the cost of calculators in dollars per year. 6
7 Algebra Summer Assignment 59) a. Find the slope from the graph. b. Explain its meaning in a sentence. c. Find an equation for the line. 60) Your school biology club is organizing a pancake breakfast to raise $400 for a trip to an aquarium. You decide to charge $ for each child and $5 for each adult. a) Write an equation to show the relationship between the number of people and the amount of money raised. b) How many adult tickets would you have to sell in order to sell only adult tickets to raise the money for the trip? c) How many child tickets would you have to sell in order to sell only child tickets to raise the money for the trip? d) Graph the equation you came up with in part a. e) How many adult tickets do you need to sell if you sold 45 child tickets? 7
8 Algebra Summer Assignment 61) Find the area of the triangle formed by the x-axis, the y-axis, and the line described by 3x + y = 18. 6) The height of a ball in meters is modeled by f(x) = 5x + 50x, where x is the time in seconds after it is hit. a) Graph the function. b) How long is the ball in the air? c) What was the maximum height of the ball? d) How long did it take to reach the maximum height? 8
9 Algebra Summer Assignment Find the dimensions of the following figures. 63) Area of rectangle = 51 square feet 64) Area of triangle = 36 square feet For 65-67, a dart is thrown. For each figure, find the probability that it will hit the unshaded region. 65) 66) In the following diagram AB=10, AC=6 and is the diameter of the circle. Triangle ABC is a right Inscribed in the circle. 67) In the following diagram MATH is a rectangle with an inscribed circle. The circle has a diameter of 8 centimeters and the rectangle has a height of 1 centimeters (as shown). Be sure you can simplify the following expressions without a calculator ) Simplify 69) Simplify ) Simplify ) Simplify
10 Algebra Summer Assignment 10
QUESTIONS 1 10 MAY BE DONE WITH A CALCULATOR QUESTIONS ARE TO BE DONE WITHOUT A CALCULATOR. Name
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