7th Grade Form B Summer Math Review Packet 2012 (For students entering 7th grade)Name _________________________6th Grade Math Teacher ________________
Objectives for the Math Summer Packet Grade 7 2011-2012I. Exponents (Problems 1 to 5) • Apply the definition of exponents. • Use expanded form to express exponents. • Evaluate exponential expressions.II. Order of Operations (Problems 6 to 10) • Review the correct order of operations. • Evaluate and simplify algebraic expressions using the correct order of operations.III. Rounding and Estimating (Problems 11 to 15) • Round whole numbers to specific place values. • Real world applications of estimating monetary values. • Estimating quotients.IV. Decimals (Problems 16 to 20) • Add, subtract, multiply, and divide decimals.V. Fractions and Decimals (Problems 21 to 25) • Understanding that a fraction and decimal represent the same value. • Convert a fraction to a decimal. • Convert a decimal to a fraction. • Real life application of converting a decimal to a fraction.VI. Triangles (Problem 26 to 30) • Identify the different types of triangles. • Sketch triangles. • Find the missing angle measures of triangles.
VII. Perimeter (Problems 31 to 35) • Find the perimeter of various polygons. • Apply algebraic applications to perimeter. • Find the dimensions of a polygon, given the perimeter.VIII. Area (Problems 36 to 40) • Find the area of various polygons using their formulas • Sketch a square and find its areaIX. Mean, Mode, and Median (Problems 41 to 45) • Analyze and interpret data • Find the mean, mode, and median of a given set of data.X. Sequences (Problems 46 to 50) • Discover the difference between an arithmetic and geometric sequence. • Find the missing terms of a given sequence. • Create a sequence.
Directions: Complete each problem showing all work. You must showwork in order to receive credit for the answer. EXPONENTS Question Hint1. Write 4●4●4●4●4 using exponents 3 4 = 3●3●3●32. Write 6 3 in expanded form. 8 2 = 8 ●83. Evaluate 22 + 61 Evaluate means to simplify the exponents4. Evaluate (3 2 ) 2 Add up the exponents then take 3 to that power5. Evaluate 7● 8 − 15 Follow PEMDAS
ORDER OF OPERATIONS Question Hint6. 4 + 8●2 Follow PEMDAS. Parenthesis, exponents, multiplication, division, addition, and subtraction7. 12 ÷3 + 9 Follow PEMDAS8. (3 + 1) + (2 + 10) Follow PEMDAS9. 2 ● 10 ÷ 5 Multiply and divide from left to right10. 18 + 2 – 8 + 1 – 7 Add and subtract from left to right
ROUNDING AND ESTIMATING Question Hint11. Round 213,789 to the nearest hundred. Underline the place value and then look at the digit to the right to decide if you round up or down.12. Round $45.275 to the nearest cent. Cent is the same as the hundredths place.13. Tom went shopping at the food store. First, round each itemIn his cart were the following items, a to the nearest dollar.2-liter bottle of soda for $2.97, one bag Then add.of chips for $1.29, and a hoagie for $4.89.Estimate the total amount of money thatTom will spend.14. Diego wanted to find the 7% sales tax Round to the nearest centon purchases that total $15.99. On hiscalculator the display showed $1.1193as the tax. How much sales tax willDiego pay?15. Estimate 41.79 divided by 7.23 Round first, then divide.
DECIMALS Question Hint16. 15.62 + 35.7 = Line up the decimal point.17. 7.3 + 18 + 0.49 = The decimal is behind a whole number.18. 18 – 6.89 = Add in a decimal point and zeroes.19. 0.45 X 0.003 = Multiply the numbers and then count decimal spaces.20. 0.462 ÷ 0.3 = The number after the ÷ is the divisor. The divisor must be a whole number.
FRACTION AND DECIMALS Question HintChange the following fractionto a decimal. 321. Numerator ÷ denominator 8 222. If it is a repeating decimal, 3 use the bar notation 0.4444… = 0.4Change the following decimalsto fractions:23. 0.3 The way you read it is the way you write it.24. 0.64 Simplify your fraction Divide out any common factors25. The tooth fairy left Emily $0.95under her pillow. Write Emily’smoney as a fraction, in simplest form.
TRIANGLES Question Hint26. Find a ruler and accurately An equilateral triangle draw an equilateral triangle. has 3 congruent sides. Label the lengths of each side.27. Name an object in your house A right Triangle has only that contains the shape of a one right angle Right triangle.28. Name and sketch a pattern in yourhouse that contains triangles.29. The measure of the angles of a The sum of three angles triangle are 52°, 37°, and x °. of a triangle equals 180°. Find the measure of “x”.30. Each angle in an equilateral All three angles in an equilateral triangle are triangle = ___________° congruent.
PERIMETER Question Hint31. Find the perimeter of a triangle Perimeter is thewith sides of 4.8 cm, 9.6 cm and distance around an5.3 cm. object.32. Find the perimeter of a regular Regular means allhexagon with sides of 0.75 m. sides congruent.33. Farmer Fred’s field is a rectangle Find the length first.32 yd wide. The length of the Opposite sides of afield is twice the width. How rectangle are congruent.much fencing does he need Sketch the rectangle.to go around it?34. The perimeter of a “STOP” sign A stop sign is anis 112 inches. What is the length octagon.of each side?35. The frame around a square poster A square has 4 congruentis 96 inches long. How long is sides.each side of the poster?
AREA Question HintFind the area of the shapes below.36. Rectangle A = lw 4cm 12cm37. Triangle A = ½ bh10ft. 15ft.38. 12 miles Square A = s2 s - side39. Circle A = π r2 Diameter = 10m radius = half of a diameter π ≈ 3.1440. Find something that is a Square square in your house. Measure A = s2 it and find its area.Item_________________ Length of side____________ Area___________
MEAN, MODE, AND MEDIAN Question Hint Use the data below to answer questions 41 to 43. 17, 14, 17, 11, 21, 20, 1941. Find the mean To find the mean, add up the numbers and divide by the number of items in your data set42. Find the mode Mode occurs most often43. Find the median Median is the middle number when the data is in numerical order44. If your grades for the quarter Mean = averageare 85, 93, 90, and 88, what isyour mean for the quarter?45. What is the median of the If there are 2 numbers infollowing data: 0, 3, 3, 5, 7, 9, 10, 11 the middle, then you have to find the average of those 2 numbers
SEQUENCES Question Hint46. Name the next 3 numbers in Arithmetic sequences- the arithmetic sequence below same number is added to and describe the pattern. find the pattern 25, 29, 33, 37, …47. Name the next 3 numbers in Geometric sequence - the geometric sequence below multiply by a common and describe the pattern. ratio to get the next term 2, 10, 50, …48. Create a sequence using the rule Multiply by .5 is the below. Provide 4 terms same as dividing by 2 start with 84; multiply by .549. Find the missing terms in the Find the pattern of sequence the numbers to find the missing terms 12, 15, _____, 21, 24, ______50. Name the next 3 numbers in the Find the pattern of sequence below and describe the the numbers given pattern. 4, 14, 12, 22, 20, 30,…