8th Grade Form A Summer Math Review Packet

2012

(For students entering 8th grade)

Name__________________________________ 7th Grade Math Teacher__________________

Objectives for the Math Summer Packet Grade 8

2011-2012

I. Order of operations (Problems 1 – 5) • Use PEMDAS to evaluate numerical expressions • Simplify numerical expressions • Evaluate numerical expressions with exponents and

parentheses

II. Ratios and Proportions (Problems 6 – 10) • Express ratios as fractions • Solve proportions • Write proportions to solve word problems

III. Solving Equations and Inequalities (Problems 11 – 15)

• Solve one step equations involving addition and subtraction

• Solve one step equations involving multiplication and division

• Use one step equations to solve word problems

IV. Integers • Compare and order integers (Problems 16 – 20) • Evaluate numerical expressions involving adding,

subtracting, multiplying and dividing integers.

V. Fractions, Decimals and Percents (Problems 21 – 25) • Convert fractions to decimals • Convert decimals to percents • Convert percents to decimals • Order numbers written in various formats • Find percent of a number in problem solving

VI. Geometry (Problems 26 – 30) • Classify types of angles • Classify polygons • Find the missing length in a pair of similar triangles • Classify quadrilaterals • Evaluate the sum of the measures of the interior angles

of a polygon

VII. Statistics: Analyze Data (Problems 31 – 34) • Create a stem and leaf plot given a set of data • Create a line plot given a set of a data. • Interpret a line plot • Interpret a box and whisker plot

VIII. Analyzing Data: Mean, Median and Mode (Problems 35 – 40) • Determine the mean, median, mode and range of a set of

data • Analyze data to find mode of a set of data • Interpret the effects of changing numbers in a set of data

IX. Coordinate System and Transformations (Problems 41 – 45)

• Identify quadrants in the coordinate system • Identify various transformations • Graph ordered pairs on a coordinate system

X. GCF/LCM (Problems 46 – 50)

• Find the prime factorization of a composite number • Find the greatest common factor of a pair of numbers • Find the least common multiple of a pair of numbers • Solve word problems involving GCF/LCM

Order of Operations

Directions: Simplify. SHOW ALL WORK. 1) 4 × 32 + 2 ÷ 2 - (5 + 3) Hint: Parentheses,

Exponents, Multiplication and Division, Addition and Subtraction

2) 12 ÷ 4 + 32 × 3 – 1 Hint: a2 = a x a 3) (3 + 6) × 10 – 8 Hint: Parentheses first! 4) 10 ÷ 5 + 52 × 3 – 2 Hint: work from left to right 5) 4 × 22 + 4 ÷ 4 - (6 + 1) Hint: PEMDAS

Ratios and Proportion

6. Solve for x: Hint: Use cross products to solve.

18

7 42

x =

7. The weather records for one month of 30 days show the following:

Sunny days - 16 Cloudy days - 10 Rainy days - 5 days

Write the following ratios. a. Sunny days to all days

b. Cloudy days to all days

c. Cloudy days to rainy days

8. A pancake recipe calls for 2.5

cups of pancake mix to make 10 servings. How many cups of mix are needed to make 14 servings?

9. Mrs. Wright wanted one daffodil plant for every 2 tulip plants in her garden. If she planted 20 daffodil bulbs, how many tulip bulbs did she plant?

Hint: Ratios must be written in the order specified and in simplest form. Hint: Set up a proportion. Hint: Keep similar units in the same location in both sides of the proportion.

10. The scale on a map is 0.25 inches Hint: Keep similar units in the same equals 8 miles. The measured distance location in both sides of the proportion. Between 2 cities is 5 inches. What is the actual distance in miles?

Solving Equations and Inequalities

11. Solve by adding or subtracting. Hint: use the inverse operation to a. 7 + t = 12 isolate the variable. b. h – 21 = 52

c. 15 = m + 9

12. Solve by multiplying or dividing. Hint: 8z mean 8 times z.

a. 8z = 160 3

v mean v divided by 13.

b. 523

v =

c. -12q = -24

13. Solve each inequality. Hint: Inequalities are solved the a. t – 11 < 22 same as equations. b. 15 < y + 12

c. 16k ≥ 64

14. Two sisters, Jenny and Penny, play on Hint: Write an addition equation. the same basketball team. Last season they scored a combined total of 458 points. Jenny scored 192 of the points. Write and solve an equation to find the number of points, p, Penny scored.

15. Gary needs to buy a suit to go to a formal dance. Hint: Write a division equation.

Using a coupon, he can save $60, which is 1

2 of

the cost of the suit. Write and solve an equation to determine the cost, c, of the suit.

Integers

16. After the first round of the 2005 Masters golf Hint: Negative numbers are Tournament, scores relative to par were Tiger Woods 2, less than zero. Vijay Singh -4, Phil Mickelson -2, and Justin Leonard 5. List the golfers in order from the lowest score to the Highest. 17. Compare using <, >, or =. Hint: Make a number line

a. −9 ____ 15 if necessary. b. 13 ____ −17 c. −14 ____ 0 d. 5 ____ −5

18. Evaluate each expression: Hint: If the signs are the a. −6 + (−12) = same, add the numbers. If b. −15 + 8 = the signs are different, find c. 7 + (−10) = the difference of the

numbers and use larger sign 19. Evaluate each expression: Hint: Subtracting a negative

a. −8 − (−11) = is the same as adding b. 24 − (−27) = c. −43 – 13 =

20. Evaluate each expression: Hint: Same signs stay a. −3 x −7 = positive. Different signs b. −144 ÷ 12 = are negative. c. −42 ÷ −6 =

Fractions, Decimals, and Percents

21. Write the following fractions as decimals: Hint: Divide numerator by denominator.

a. 5

7

b. 7

20

c. 10

3

22. Write the following decimals as percents: Hint: Move the decimal two places a. 0.65 to the right or multiply by 100. b. 2.43 c. 0.08

23. Write the following percents as decimals: Hint: Move two decimal two places a. 43% to the right or divide by 100. b. 120% c. 5%

24. Write 0.25%, 13

5

13

5, 0.57, and 300% Hint: Change all to decimals first.

in order from least to greatest.

25. Bags of trail mix are made from 3 Hint: The mix is made up of a total parts peanuts to 2 parts dried fruit. of five parts. Make a fraction of the What percent of the mix is peanuts? parts of peanuts to the whole, then convert to a decimal then a percent.

Geometry

26. Classify each angle below as acute, obtuse, Hint: Look up definition of right, or straight: each type of angle. a. b. c.

27. Classify each polygon by the number of sides: Hint: Look up definition (i.e. pentagon, hexagon..) a. b. c. 28. The triangles below are similar. Find the missing side Hint: Set up a proportion.

labeled x. x 8 5 10 29. Name each quadrilateral below: Hint: Use definition (i.e. trapezoid, square...) a. b. c. 30. The sum of the measures of a polygon can be Hint: In the formula, n found using the formula (n -2)180. Find the sum represents the number of of the measures of the angles of a decagon. sides a decagon has.

Statistics: Analyzing Data 31. Write the stems that would be used Hint: In the plot the leaves are in a stem-and-leaf plot for each set the last digit and the stems are of data. Then make a stem and leaf plot. digits in front of it. 28, 32, 38, 30, 31, 13, 18, 26, 24, 15, 32 32. Make a line plot for the data below: Hint: Draw a number line and use an X for each time the 45, 35, 50, 40, 40, 55, 30, 35, 45, 35 number appears. 33. The line plot below shows how far in kilometers Hint: Count the number of some students live from school. How many students X’s. are represented in the plot? X X X X X X X X X 0 1 2 3 4 5 6 7 8 9

34. This box-and-whisker plot indicates the scores on last week's science test. Which

grade represents the lower quartile? Hint: Find the median of the lower half of the data.

Analyzing Data – Mean, Median, Mode Use the following Data for questions 35, 36,37, and 38: 17, 13,18, 20, 17,15,12 35.Find the mean of the above data Hint: It is the average 36. Find the median of the above data Hint: Put the numbers in order and find the middle number. 37. Find the mode of the above data Hint: It is the number that occurs the most. 38. Find the range of the above data. Hint: It is the difference between the highest and lowest number. 39. Rachel is curious about the number of pets that people own. She surveyed her 20 classmates, asking them exactly how many pets they own. Rachel's data is shown below:

Number of Pets 0 Pets 1 Pet 2 Pets 3 Pets

Number of Classmates 7 7 2 4

What is the mode number of pets owned by Rachel's classmates? Hint: Same as #37

40. A set of data set contains 50, 100, 75, 60, 75, Hint: Think about the what 1,000, 90, 100, 125 and 75. Without calculating, each one represents and would the mean, median or mode be most affected how each one is found. by eliminating 1,000 from the list? Explain.

Coordinate System and Transformations 41. In which quadrant is the ordered pair (3,−2)? Hint: The 1st Quadrant is at the top right and then follow counter clockwise. 42. What type of transformation is shown in the figure below? Hint: Is it a reflection (flip),

translation (slide), or rotation (turn)?

⊳

43. What type of transformation is shown in the figure below? Hint: Refer to #42

44. Graph and label the following ordered pairs below:

A(3,4) , B(−1,2) and C(−2, −3) Hint: (x, y) , go across then

up or down.

45. When playing chess, you can move the game Hint: Refer to #42 pieces up or down, left or right, or diagonally. What type of transformation is used in this game? Give reasoning for your answer.

GCF/LCM

46. Find the prime factorization of 18. Hint: Use a factor tree to find primes.

47. Find the GCF of 12 and 36. Hint: Think of which is the greatest factor (a number that divides evenly) of both numbers.

48. Find the LCM of 12 and 15. Hint: The multiples are like counting by that number. For example, multiples of 6 would be 6, 12, 18, etc.

49. Mary has piano lessons every two weeks. Hint: Find the LCM of the weeks. Her brother has soccer tournaments every three weeks. Her sister has an orthodontist appointment every four weeks. If they all happen to fall on this Saturday, how long until it would happen again? 50. What would be the greatest number Hint: Find the GCF of the rows. of crayons in each row of a 6, a 10, and a 12-crayon box if all rows have the same number of crayons in them?