Warm-up for Geometry

Transcription

1 Summer Work Packet Warm-up for Geometry Who should complete this packet? Students who will be taking Geometry in the fall of 018. Due Date: The first day of school How many of the problems should I do? ALL OF THEM How should I organize my work? You should show all work in a separate sheets of loose-leaf paper. If a problem requires a graph, then you should use graph paper. Keep your materials in a standard -Ring binder. You will continue to use this ring binder in your math class next fall.) How will my teacher know that I ve done the work? Your teacher will collect your notebook on the first day of school. Your teacher may choose to QUIZ or TEST you on this material if he or she feels it is necessary BE PREPARED! How well should I know this material when I return? You should recognize that you ve seen this material before, and you should also be able to answer questions like the ones in this packet. If the material is revisited in your next class, it will only be for a brief amount of time your teacher will assume that all you need is a quick refresher. Note from your teachers: We feel that this summer work will truly help you succeed this year. We understand that summer is a time for relaxation and fun, but it is imperative that you spend some time before you return reviewing your materials. This packet is mandatory, and you must treat it as you would any other extremely important homework assignment. You will be held accountable for this material. We also highly suggest that you do a bit of it at a time in the weeks leading up to school don t leave it for the last day!!!

2 What if I get stuck? - You should check out other additional study materials. Consult a standard algebra textbook. Find a study buddy or a classmate to help you remember the material. Consult the following websites for hints and examples:

3 Warm-up for Geometry Instructions: Complete the problems on loose-leaf paper in pencil. If a problem requires a graph, please use graph paper and a ruler. Complete all the problems carefully. Show enough work to indicate your method of solution. Make sure your work justifies your answer. Keep the packet and your work in a -prong report folder or report cover. Remember, your teacher will collect your work on the first day of school! Late work will NOT be accepted..

4 Warmup for Geometry Page 1 1. Simplify the expression. a. ( 9)( 8) 5 6 b. ( ) ( ) 1 1 e. 5 d. ( )( ) f Evaluate the expression for the given value of x: a 1 x ; x = b. 4 x ; x = 1 + = 4x 8x 9; x 5. Solve the equation. a. 18y = b p = x e. 5r 6 4r r d. ( x ) 5 9 = 10 9 = ( w) + = + f. ( ) 4y 5y+ 6 = 7y+ 4. The length a rectangle is 5 meters less than twice the width. The perimeter of the rectangle is 5 meters. Find the dimensions of the rectangle. 5. Translate each sentence into an equation and then solve. a. Seven more than three times a number is equal to thirty-four. b. One-fourth of the sum of a number and five is equal to eight. 6. Compute the slope between the given points. a. (, ) & (5,9) b. (, 4) & ( 6,5) 5 1, &, 5

5 Warmup for Geometry Page 7. Graph the line described by each equation. Show your method. a. y = x+ b. x 5y = 15 y = 8. Describe each set of lines as parallel, perpendicular, or neither. a. y = 5x+ 1 y = x 5 b. 6y = 5 8x 4x+ y = 1 y = x = 5 9. Find the equation of the line shown in the graph: 10. Solve the system of equations graphically, that is, carefully graph each line and give the coordinates of the point of intersections. y = x+ 8 y = x

6 Warmup for Geometry Page 11. Use the substitution method to solve the system of equations. 5x y = 7 x + y = 1. Use the method of elimination to solve the system of equations. 8x+ y = 9x y = 1. Simplify each radical expression. a. 81 b d. 48 e f. ( 6) 14. Find the length of a side of a square whose area is 00 cm. Give your answers in simplified form. 15. Multiply and simplify each expression. a. (9x 1)(7x+ 4) b. ( w 6)(4w w 7) + ( 7x + ) f. ( 8x+ )( 8x ) 16. Factor each expression completely. a. y 9y+ 14 b. x x 0 9k The area of a rectangular garden is 81 ft. Its length is three times the width. Find the perimeter.

7 Warmup for Geometry Page The ratio of boys to girls in a summer camp is 4:5. If there are 15 girls, what is the total number of students in this camp? 19. Simplify using properties of exponents: a. 5 4 n n m m 4 6 b. 6( a ) + ( a ) an an d. 4 ( )( ) 4 5 x y 5 4 ( xy) 0. Solve each inequality. Graph your solution on the number line. a. 0 6c < 44 b. r 18 5r+ 5m 1 > m +