Sussex Academy. Summer Math Practice. Entering 8 TH GRADE

Transcription

1 NAME (Please print your first and last name) Sussex Academy Summer Math Practice Entering 8 TH GRADE May, 2014 Dear Students and Parents, Purpose: To help students retain prior knowledge and be better prepared for 8 th grade, all Sussex Academy students are required to complete this practice/review packet over the summer. The packet and completed work is due on the first day of school. It is also very important that students have quick recall or fluency with basic facts. This includes all four operations (addition, subtraction, multiplication and division) for the numbers Options to improve quick recall and fluency with math facts: 1. Play games online, there are a multitude of apps available that students will enjoy practicing as well as websites such as These websites also offer help or lessons on a variety of topics that may help students complete the work included here. You can also do a search for any of the topics in a search engine and many more sites will be available to you. 2. Use flash cards, play games with hexahedron (dice) and regular playing cards, as well as board games that challenge students to handle and count money are also good options. 3. Use real-life situations that encourage students to use math. Figuring out tips in restaurants, estimating totals when purchasing items, or figuring out discounts for sale items without the use of a calculator or calculator app on their phone reinforces number sense problem solving. SHOW YOUR WORK and do not use a calculator! Many answers can be neatly written within the worksheet pages, however, if additional space is needed, you may use loose-leaf paper. If you use loose-leaf paper, label it with page number, section title and problem number. Attach any loose-leaf you use to the back of the packet. Have a great summer and keep those math skills sharp! Sussex Academy Math Department

2 INTEGERS 1 Add. 1. (-34) + (-77) = 2. (-32) + 19 = (-45) = 4. (-55) + (-7) = _ (-6) + 12 = 6. (-9) + (-6) + (-15) = Subtract (-3) = 2. (-7) 1 = 3. (-4) (-6) = (-41) = 5. (-1) 6 (-9) = (-12) 12 = Multiply or divide. 1. (-4) (-10) = _ (-6) = 3. (-52) 13 = (-4) = 5. (-5) (-13) (-4) = (-3) (-7) = Find each absolute value. 1. = 2. = 3. 5,187 = 4. ( 43) ( 8) = Challenge Problem! Evaluate. 1. [2 + ( 4)]+ 5 [( 11) ( 2)] ( 7) =

3 EQUATIONS & INEQUALITIES 2 Solve. 1. x 7 = y = b + 7b = f 1.2 = (w 9) + 7w = x 1.2 = 1.8x = -x y + 20 = y = y Solve and graph y < x x < m 3m 4

4 3 FRACTIONS/DECIMALS/PERCENTS Use >, <, or = to compare each pair of numbers Write each percent as a decimal and as a fraction/mixed number in lowest terms. Decimal Fraction/Mixed Number 1. 82% 2. 60% 3. 8% % Order each group of numbers from least to greatest. Write your answer on the line ,0.7, 3, , 2 2, 2.1, Challenge Problem! Complete the statement using >, <, or = % of % of 12

5 FRACTION OPERATIONS 4 Add, subtract, multiply, or divide. All answers must be in fraction/mixed number form

6 DECIMAL OPERATIONS 5 Add, subtract, multiply, or divide. All answers must be in decimal form = = (-0.04) = 4. (-4.844) (-0.56) = = (-1.564) = 7. (-9.767) (-4.089) = (-4.3) =

7 6 DATA, STATISTICS, & PROBABILITY Find the mean, median, mode, and range for each set of data. Then display the data in a stem-and-leaf plot AND a box-and-whisker plot , 38, 42, 38, 17 Mean Median Mode Range , 581, 508, 588, 580 Mean Median Mode Range Find the probability. 1. A bag contains 5 red, 6 blue, 7 yellow, and 8 purple marbles. What is the probability that you randomly choose a marble that is not purple? 2. The spinner at the right is divided into equal parts. What is the probability that the pointer lands on: A prime number? An even number? The number 3?

8 7 GEOMETRY In the following diagram, lines a & b are parallel and line t is a transversal line. The measure of angle 8 is 117. Use this information to answer the questions. 1. Name both pairs of alternate interior angles. 2. m 2 = 3. Name a pair of corresponding angles. 4. m 5 = 5. Name a pair of vertical angles. 6. Name both pairs of alternate exterior angles. 7. What kind of angles are 1 & 2? In the following diagram, quadrilateral KLMN quadrilateral SPQR. Use this information to answer the questions. 1. m S = 2. Find the length of NK = 3. m LMN = In the following diagram, CDFG ~ HJLK. Use this information to find the value of x. 1. x =

9 Name the quadrant or place in which each point lies (-4, -2) 2. (0, -7) 3. (0,0) 4. (6, -9) 5. (3, 5) 6. (8, 0) Graph and label (with letters) these figures on the same plane. 1. PQRS: P(-2,4), Q(-5,4), R(-8,0), S(-2,0) TUVW: T(4,8), U(8,8), V(8,0), W(4,0) ABC: A(0,-3), B(0,-7), C(-6,-7) DEFG: D(3,-1), E(5,-3), F(3,-5), G(0,-5)

10 EXPRESSIONS & EXPONENTS 9 Evaluate for the given value. Write your answer on the line. 1. 4x 5, for x = 7 2. (a b) 2 + (a b), for a = 77 & b = x, for x = 5 & y = (b c) + 8(b + c), for b = 3 & c = -3 y + 3 Evaluate each expression. 1. (2 + 1) = 2. (5 3) 2 (63 7) 3 = = 4 4. [(9 7) ] 1 = 7

11 RATIOS, PROPORTIONS, & PERCENTS 10 Find the unit rate. 1. $56 = 8lbs 2. 7 phone calls in 2 hours = Write the ratio as a fraction in simplest form to 130 = = 63 Solve each proportion by cross-multiplying y b = 2. = 3. = x Find each value % of 25 is what number? is 45% of what number? 3. What percent of 600 is 180? 4. The cost of a meal is $35.27 and you leave an 18% tip. What is the total cost of the meal? Round to the nearest cent. 5. You spend $ shopping, but the store is offering a 30% discount. What is the total cost after the discount? Round to the nearest cent.

12 11 MEASUREMENT, AREA, & VOLUME Find the area of each figure Use the Pythagorean Theorem (Formula) to find the missing side length. 1. a =?, b = 9 ft, & c = 15 ft 2. a = 0.9 cm, b = 1.2 cm, & c =? Find the volume of each figure. Use 3.14 for π In this cylinder, the diameter is 10m.