Summer Practice for Geometry Students June 018 Name This booklet is a review of basic Algebra & Geometry concepts. The work has been chosen to help keep basic Algebra skills that will be needed in geometry fresh in your mind and to allow you to practice the geometry standards that you missed by skipping 7 th & 8 th grade math. You should complete each page showing all work. If your work is on a separate page, then attach. Pages through 1 have the answers at the bottom. Please place the number of each problem in the space that matches the answer. For page 14, please place the formulas in the spaces provided. Turn this booklet in the first Day back to school. Please be sure to not use the calculator when you see this symbol. Best wishes for a wonderful summer break! See you in August, Mrs. DiGioia Michelle.digioia@polk-fl.net
Geometry Students Summer Skills Work Page Simplify the following by combining like terms. Like terms have the same variable and eponent. These terms should be combined with addition and subtraction without changing the eponent of each term. 1) 5 ) 4y 7y ) y 6y y y 4) 5 y + 7 5) 7y 1 y 6) 4 + + 8 7) 5y + z y + 6 + 8 8) 4( ) ( + 7) 9) 4 ( 5) + 10) 8 4 11) 7 8 4 y y y y y 1) y y 5 y 4 y 4y 1) 5( y + ) (y + + 7) 14) 9 7 4 y y y y y Place the number to the correct answer for questions 1 through 14 in the bo below. 9 + y - z + 8 5 + 4 - + 19 5y y - 9 7 8 9 8 7 y y y -y 4y -1 5y y y 5 y 7y - 14y + 1 4 - y + 7
Geometry Students Summer Skills Work Page Use order of operations (PEMDAS) to simplify the following. 1) 8 + 6 ) 15 (7 ) ) 5(4) 10 4) 4 1 5) 18 1 4 6) 1 (4 + 7) 7) 7( + 4) 8) 1 4 9) (11 + 4) 5 10) (1 4) ( ) 11) 0 6 1 1) 4 (5 + ) Place the number to the correct answer for questions 1 through 1 in the bo below. Some will remain blank. 11 16-10 7-7 10 1 17-15 1 18 4 0 49 19
Geometry Students Summer Skills Work Page 4 Simplify the following: 1) 1 5 ) 4 1 ) 5 5 1 1 5 4) 4 5) 7 9 5.56 5 6) 5 10 7) 8) 5 9 1 5 1 9) 5 6 1 4 5 10) 11) 1 1) 4 5 4 4 1 1 1 7 4 Place the number to the correct answer for questions 1 through 1 in the bo below. 46 14 4 11 1 957 88 9 6 15 5 10 15 15 5 0 5 4 1 5
Geometry Students Summer Skills Work Page 5 Solve the following multi-step equations: 1) + 4 = 8-6 ) 9 = + 8 ) - 1 = 5 4) 7 9 = 4 5) 8 = + 1 6) 4 + 8 = + 7 7) 4( ) = -1 8) 5( + 7) = -15 9) 4( + 6) = ( 4) 10) ( 7) = 6 + ( ) 11) 1 4 5 1) 5 Place the number to the correct answer for questions 1 through 1 in the bo below. -0.5 10 0-5 -16 5 17-8 5.5
Geometry Students Summer Skills Work Page 6 The slope m of a line describes how steep it is. The slope is calculated by finding the quotient of the vertical change (change in y) and the y y m 1 horizontal change (change in ). Formula: 1 Find the slope of the line that contains each pair of points. 1) (, 4), (4, 6) ) (, ), (-, -8) ) (-1, ), (-, 5) 4) (8, -), (10, 0) 5) (0, 0), (6, -) Place the number to the correct answer for questions 1 through 5 in the bo below. No - 1 0 1 7 8 - slope 4
Geometry Students Summer Skills Work Page 7 The number 18 is not a perfect square, but it does have a perfect square factor. 18 9 should be further simplified to. Simplify the following radicals. Think of the largest perfect square that can be simplified. 1) 8 ) - 18 ) 8 4) 75 5) 6 6) 500 7) 4 8) 50 9) 700 10) 98 11) 0 1) 45 1) 4 14) 1 15) 48 Place the number to the correct answer for questions 1 through 15 in the bo below. 4 5 7 10 7 11 5 7 6 5 5 10 5 7
Geometry Students Summer Skills Work Page 8 Multiply the following either using the Distributive Property, Area Model or FOIL: 1) 4 ( 8) ) 4 ( 7) ) 5 ( 8) 4) 9 ( 8) 5) ( 6) 6) 7 ( 8) 7) 10 ( 8) 8) 11 ( ) 9) 1 ( 4) 10) 15 ( ) 11) ( + 4)( + 5) 1) ( 5)( + 4) Place the number to the correct answer for questions 1 through 1 in the bo below. 8 6 7 0 1 7 15 1 40 18 80 7 18 1 45 9 7 56 6 0 8 48
Geometry Students Summer Skills Work Page 9 Factor the following trinomials. 1) 5 6 ) 9 8 ) 1 4) 15 6 5) 7 1 6) 7 6 7) 7 10 8) 9 0 9) 9 18 10) 9 14 11) 9 8 1) 10 4 1) 10 11 14) 10 9 15) 8 0 Place the number to the correct answer for questions 1 through 15 in the bo below. 1 11 5 1 4 5 1 8 6 7 1 4 6 10 6 10 4 8 4 1 6 7 1 8 7 4 15 1 10
Geometry Students Summer Skills Work Page 10 Simplify the following using the rules for eponents: 1) 5 4 5 4 ) ) 4 4 4) 4 5) y( )( y ) 6) 4 4 y yz y z 7) 4 8) y 5 4 9) y 10) 1 4 4 5 11) 1) y y 1) 4 5 14) 4y y 7 Place the number to the correct answer for questions 1 through 14 in the bo below. 5 1 9 15 5 8 5 5 7 7 y y y 8 y y 6 y 7 y 10 8 1 y14 y 5 y 184 y 8 6 4 y z 4 1 9 6 1.15 5 11
Geometry Students Summer Skills Work Page 11 Identify the following formulas for the circle: Circumference (C) = or Area = If π is used in the original information, leave your answer in terms of π, otherwise use π.14. Given the missing part of the following: 1) C = 4 π cm diameter = radius = Area = π cm ) C = 10 π cm diameter = radius = Area = π cm ) C 7.68 cm diameter = radius = Area = cm 4) C 15.7 cm diameter = radius = Area = cm 5) A = 49πcm diameter = radius = C = π cm 6) A = 100πcm diameter = radius = C = π cm 7) A 8.6 cm diameter = radius = C = cm 8) A 50.4 cm diameter = radius = C = cm Place the number to the correct answer for questions 1 through 8 in the bo below. 8 cm, 4 cm, 5.1 cm 14 cm, 7 cm, 14 π cm 4 cm, 1 cm, 144 π cm 1 cm, 6 cm, 11.04 cm 0 cm, 10 cm, 0 π cm 6 cm, cm, 18.84 cm 7 cm,.5 cm, 1.5 π cm 10 cm, 5 cm, 5 π cm 8 cm, 14 cm, 615.44 cm 5 cm,.5 cm, 19.65 cm
Geometry Students Summer Skills Work Page 1 Leaving your answers in terms of π, find the Circumference and the Area of the following: 1) 4) 1 cm 4 cm C = A = C = A = ) 5) 10 cm cm C = A = C = A = ) 6) 9 cm 7 cm C = A = C = A = Place the number to the correct answer for questions 1 through 6 in the bo below. 9 π cm, 0.5 π cm 1 π cm, 6 π cm 6 π cm, 9 π cm 10 π cm, 5 π cm 8 π cm, 16 π cm 14 π cm, 49 π cm
Geometry Students Summer Skills Work Page 1 The Pythagorean Theorem is a b c where a and b are the legs of a right triangle and c is the length of the hypotenuse. 1) Find the length of the hypotenuse of a right triangle whose legs are 5 cm and 1 cm. ) Find the length of the hypotenuse of a right triangle whose legs are 7 cm and 4 cm. ) Find the length of the hypotenuse of a right triangle whose legs are 15 cm and 8 cm. 4) If the hypotenuse of a right triangle is 0 cm and the length of one leg is 1 cm, what is the length of the other leg? 5) If the hypotenuse of a right triangle is 10 cm and the length of one leg is 8 cm, what is the length of the other leg? 6) If the hypotenuse of a right triangle is 5 cm and the length of one leg is cm, what is the length of the other leg? 7) If the hypotenuse of a right triangle is 65 cm and the length of one leg is 16 cm, what is the length of the other leg? Place the number to the correct answer for questions 1 through 7 in the bo below. 4 cm 16 cm 5 cm 6 cm 6 cm 1 cm 17 cm
Geometry Students Summer Skills Work Page 14 A geometry student should be adept at remembering and incorporating formulas into the Geometry curriculum. Complete the following Formulas using the variables indicated Perimeter Area Rectangle L W Square S S Parallelogram A H B Trapezoid A B H C Triangle D A H B C