FINAL REVIEW MATH 6 STUDENT NAME MATH TEACHER
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1 FINAL REVIEW MATH 6 STUDENT NAME MATH TEACHER ** As you go through this review packet, be sure to show all work as you have done throughout the school year. Remember- NO WORK NO CREDIT **
2 REAL NUMBERS, RATIONAL NUMBERS, OR IRRATIONAL NUMBERS? *All numbers we worked with this year are REAL NUMBERS *Every number, then, must be with RATIONAL or IRRATIONAL (a number can t be both!) *All rational numbers can be written as a fraction (see below) *Irrational numbers cannot be written as a fraction All RATIONAL numbers can be written as fractions: NATURAL NUMBERS numbers you count with WHOLE NUMBERS natural numbers and zero 1, 2, 3 also known as COUNTING NUMBERS 0, 1, 2, 3 INTEGERS whole numbers and their opposites -5,-4,-3,-2,-1, 0, 1, 2, 3 FRACTIONS 2 ALREADY A FRACTION!! 3 TERMINATING DECIMALS REPEATING DECIMALS = 1 3 All IRRATIONAL numbers cannot be written as fractions: PI NON-TERMINATING NON-REPEATING DECIMALS
3 Directions: Name ALL the sets of numbers to which each number belongs , Are integers always, sometimes, or neve rational numbers? 10. Are rational numbers always, sometimes, or never integers? 3
4 RATIOS, RATES, PROPORTIONS AND CONVERSIONS OH MY! Vocabulary Ratio- a comparison of 2 numbers Rate- a comparison of 2 numbers with different units of measure Unit rate- is a rate with a denominator of 1. Proportion- two equivalent ratios set equal to one another * Ratios must always be in simplest form * To find a unit rate for a given rate, DIVIDE *To find unit price- money is always in the numerator * We use proportions to solve for missing information, to solve word problems, conversion problems, and so much more. * When a fraction = a fraction, use cross-multiplication! Express each ratio as a fraction in simplest form: : to : to 54 Express each as a unit rate or unit price: 5. $12.00 for 2 kg bottles for $ L for $ km in 3hr Which is the better buy? 9. Oranges $2.25 for 3 lb. OR $2.00 for 4 lb. 10. Bananas $2.35 for 5 bananas OR $1.68 for 4 bananas 4
5 Solve each proportion: = x = 30 x Write a word ratio, set up a proportion and solve the following: 13. Four pounds of steak will serve 20 people. How many pounds are needed to serve 110 people? 14. In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1000? 15. A piece of cable 8.5 cm long weighs 52 grams. What will a 10-cm length of the same cable weigh? 16. A microscope slide shows 37 red blood cells out of 60 blood cells. How many red blood cells would be expected in a sample of the same blood that has 900 blood cells? 5
6 Complete the fraction-decimal-percent conversion table: WORK SPACE Fraction Decimal Percent % % Use a proportion to solve each problem (remember- part/whole/percent): is 60% of what number? 19. What is 0.6% of 59? is what percent of 425? 6
7 NUMBER THEORY HUH?? Vocabulary Number Theory- Study of WHOLE NUMBERS. Every number greater than 1 is either Prime or Composite. Zero and One are neither Prime nor Composite. Prime Number whole numbers with EXACTLY 2 factors (1 and itself) Example: 2 factors are 1 and 2 Example: 13 factors are 1 and 13 *FUN FACT: 2 is the only even prime number* Composite Number whole numbers greater than 1 that have MORE THAN 2 factors. Example: 6 factors are 1, 2, 3 and 6 Example: 12 factors are 1, 2, 3, 4, 6, and 12 7
8 Finding the Greatest Common Factor (GCF) 1. Find the prime factorization for each number (make a factor tree for each number) 2. Make your factor box (pair numbers accordingly) 3. Circle full columns 4. Take one number from every full column and multiply to get the GCF Finding the Least Common Multiple (LCM) 1. Find the prime factorization for each number (make a factor tree for each number) 2. Make your factor box (pair numbers accordingly) 3. Take one number from every column and multiply to get the LCM 8
9 Find the GCF and LCM of the following: and and and 70 Answer the following number theory questions: 4. Is the number 31 prime or composite? 5. Is the number 91 prime or composite? 6. Is the number 59 prime or composite? 7. Is the number 15 prime or composite? 8. What is the smallest prime number? 9. What numbers are neither prime nor composite? and 10. Write the prime factorization of Write the prime factorization of 80 in exponential notation. 12. What is the additive inverse of 45? 13. What is the absolute value of 45? 14. What is the largest negative integer? 15. What is the smallest positive integer? 16. Write an example of a number that is not an integer. 17. Order the following from least to greatest: {11, 3, -17, 0, -2, 1} 9
10 Evaluate each expression: (15 7) (3 2 4) Evaluate each expression if a=3, b=6, and c=5 21. ba (3b + a)c 23. a + c b Translate each verbal phrase or sentence into an algebraic expression or equation: more than a number n 25. A number, n, increased by seven 26. the product of 15 and x 27. Twice x is The difference between x and twelve is twenty. 29. y decreased by Seven more than the quotient of x and -2 is The difference of twice n and three 32. Three times the sum of 12 and x 33. Twice the difference of n and 9 is
11 Rectangle: A=lw Square: A=s 2 Parallelogram: A=bh 2-D and 3-D GEOMETRY AREA FORMULAS Note: These are all parallelograms. So A = bh will work for all of these. Triangle: A= bh 2 (b Trapezoid: A = 1 + b 2 2 )h **Note: A trapezoid has 2 bases. The bases are the 2 parallel sides. **Height Can never be slanted. Height must be PERPENDICULAR ( ) with the base. * Surface Area- the sum of the area of each face of a 3-D figure (find the area of each side and add them together); draw a net to help visualize each face * Volume- how many cubic units fit inside a 3-D figure Rectangular Prisms: A = lwh All other prisms: A = Bh (B = area of the base) NOTE: Area is always square units Volume is always cubic units 11
12 Find the area of each figure: Find the area of a rectangle 4.3cm by 2.7cm. 5. Find the area of a square with a side that measures 12in. 12
13 6. Find the surface area AND volume of the rectangular prism below. SA = 10m 15m 5m Volume = 7. Find the surface area of a rectangular prism 6ft by 3ft by 4ft. 13
14 Solve each of the following word problems on a separate sheet of paper. (Remember: some word problems might require you to write a proportion, use the percent proportion or define a variable ~ write a let statement) 1. Find 12% of 95? is 60% of what number? is what percent of 115? 4. 35% of what number is 52.5? 5. During the summer, Bob worked 35 hours a week for 8 weeks as a lifeguard. If he was paid $15.75 per hour, how much money did he earn for the summer? 6. Mary sold $192 worth of greeting cards. If she received 25% commission on her sales, how much commission did she earn? 7. If a train travels at a constant speed covering 416km in 4 hours, how far will it travel in 7 hours at the same speed? 8. If 6 liters of soda costs $4.50, how much will 14 liters cost? 9. There are 350 people at a luncheon. If 12% of the people will win a door prize, how many door people will win a door prize? 10. If Robert got 42 questions correct out of 52 questions on a test, what percent of the questions on the test did Robert get correct? (Round your answer to the nearest percent) 11. Anthony s mother asked him to go to the store and pick up ice cream pops for dessert. At the store, Anthony sees two different packages; 6- ice cream pops for $2.89 and 8- ice cream pops for $3.29. If Anthony wants the package of ice cream pops that is the better bargain, which package should he purchase? 12. If the length of a rectangle room is 19 feet and the width is 12 feet, find the area of the room. If the cost to carpet the floor of the room is $3.50 per square foot, find the cost of carpeting the room. 13. If Brandi s test scores in math are 85, 89, 90, 93 and 98, find her mean test score. 14
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