For students entering Algebra 1 during the School Year Math 6-8 th Grade Math Overview

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1 Name: For students entering Algebra 1 during the School Year Math 6-8 th Grade Math Overview Please be prepared to turn this in during the first week of school. Completing this review shows math teachers that you have reviewed material over the summer and are ready to take an advanced course. Please understand that after a few days of basic Pre-Algebra review you will be taking a test on basic Pre-Algebra Skills. Completing this review is very helpful on this test. Pre-requisite skills needed for success in Algebra 1 1. Integer Rules 2. Order of Operations 3. Math Properties 4. Completing the table 5. 2-Step Equations 6. Practical Problems that use multistep equations These items are taught and reviewed in 8 th grade. Students skipping 8 th grade math and going directly into Algebra will need to know the following items to be successful in future math classes. 1. The Real Number System 2. Positive and Negative Square Roots and Estimating and Computing the two consecutive integers in which a square root lies 3. The relationships between pairs of angles and determining missing angles values 4. Area and Perimeter of Irregular Shapes 5. Pythagorean Theorem In addition, We strongly suggest that you also attempt a released 8 th grade math practice SOL over the summer to ensure that you understand the content. Released 8 th Grade Math SOL:

2 Integer Rules Review Evaluate. These problems should be completed WITHOUT the use of a calculator! 1) -4 + (-2) 2) 4 (-9) 3) ) ) - 7 (-2) 6) 4 - (-8) 7) 12 (-3) 8) ) ) 24 (-8) 11) ) (-3) 13) ) 66 (-2) 15) 6 (-8) 16) 12 - (-12) 17) (-12) 18) - 5 (-10) 19) ) (-14) Order of Operations Review Evaluate. These problems should be completed WITHOUT the use of a calculator! 21) ) ) (1) 24) 36 25) ) 27) 28) ) ) ) )

3 Properties Review 33) Determine the property being used in each statement. Commutative Property of Addition/Multiplication Multiplicative Identity Additive Identity Associative Property of Addition/Multiplication Multiplicative Inverse Additive Inverse Multiplicative Property of Zero Distributive Property 6(0) = 0 7(2 + 3) = 7(2) + 7(3) = (-4) = = (2 + 9) = (1 + 2) + 9 (8e 3) + 0 = (8e 3) 9c + 0 = 9c -7q + 7q = = = 2 6 6h = 1 r 0 = 0 6(11 9) = 6(11) 6(9) -3 + (3 + 5) -4 + (2 + 4) a) Which math property was used in Step 1 to rewrite the problem? a) Which math property was used in Step 1 to rewrite the problem? a) Which property was used to get to Step 1? b) Which math property was used to go from Step 1 to Step 2? b) Which math property was used to go from Step 1 to Step 2? b) Which math property was used to go from Step 1 to Step 2?

4 Completing the Table Review Complete each table using the given domain values. Calculators may be used in this section. 34) 35) x y = x x y = 2x ) 37) x y = x x y = x ) 39) x y = 12x ) y = 7x 4 41) y = x ) y = x + 3

5 Graph each function using a table of values. Use -1, 0, 1, and 2 as the domain values. 43) y = 2x ) y = -x + 1 Inequality and Equation Review Solve each equation. Show all work! Calculators may be used in this section. 45) n + 4 = 19 46) x 2 = 5 47) 5m + 3 = ) ) ) ) Translate and solve: The quotient of x and five is the same as fifteen. 52) Translate and solve: Two more than the product of three and x is fourteen. 53) Translate and solve: The difference of eight times a number x and eight is equal to the sum of five times a number x and thirteen.

6 Using Equations to Solve Practical Problems 54) Anna is the neighborhood dog walker. She charges $8 a session plus $3 per dog (d). How much does Anna earn (e) per session? How much would Anna charge you to walk 2 dogs? 55) The phone bill is $25 a month plus $0.10 per call made (x). How much is the phone bill (b) per month? How much was the monthly phone bill if you made 200 phone calls? 56) Karl s Rental Cars charges $30 per day plus $0.20 for each mile (m) driven to rent a car. What would the cost (c) be to rent a car? How much does it cost to rent a car for one day and driving the rental car 90 miles? These items are taught and reviewed in 8 th grade. Students skipping 8 th grade math and going directly into Algebra will need to know the following items to be successful in Algebra and later in Geometry. Real Number System State the set(s) of numbers to which each number belongs. List all that apply! You may use the symbols for each word. Rational (Q), Irrational ( ), Integer ( ), Whole ( ), Natural ( ) 57) -5 58) 59) ) 25 61) 62) ) 9 64) 45 65) ) ) 0 68) 114 Square Roots and Perfect Squares Evaluate each square root, if possible. Calculators may be used in this section. 69) 9 70) ) ) 289 Find each square root to the nearest tenth. 73) 26 74) ) 52 76) 904

7 Naming and Measuring Angles Angle Type Definition Picture Acute An angle whose measure is less than 90. Right An angle whose measure is exactly 90. Obtuse An angle whose measure is bigger than 90 and less than 180. Straight An angle whose measure is exactly 180. Use the protractor to find the measure of each angle. Then classify it as an acute, obtuse, right, or straight angle. 77) 78) 79) 80) 81) 82)

8 Angle Relationship Vertical Angles Adjacent Angles Complementary Angles Supplementary Angles Angle Relationships Definition Vertical angles have a common vertex. Vertical Angles are Congruent (=). Adjacent angles have a common side. Two angles are complementary if their measures add to 90 degrees. Two angles are supplementary if their measures add to 180 degrees. Picture For each pair of angles a. Identify the pair as complementary, supplementary or vertical b. Find measure of the missing angle. 83) 84) x x 85) 86) x x 87) What is the relationship between angles 5 and 7? If the measure of angle 5 is 130, find the measure of angle 7.

9 Perimeter and Area of Irregular Shapes (Note: Figures are NOT drawn to scale!) Find the perimeter of the irregular shape. A calculator may be used. be found on the last page of the packet. 88) 89) 90) A formula sheet can 91) 92) 93) Find the AREA of each shape! Show the formulas used! A calculator may be used. Strategy: Break the complex figure into smaller shapes and find the area. Depending on the shape, add or subtract to find the final area. 94) 95) 96) 97) Find only the shaded area: 98) Find only the shaded area: 99)

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