Math 7R Final Review. BRING: Calculator (collected) Sharpened Pencils

Transcription

1 Math 7R Final Review Name: BRING: Calculator (collected) Sharpened Pencils Grade 7 TOPICS: (the ones that will be tested are highlighted NUMBER SYSTEM - Adding/Subtracting - Multiplying/Dividing - Fractions - Decimals - Order of Operations - Properties - Combining Like Terms - Polynomials RATIOS AND PROPORTIONS - Ratios - Proportions/ Proportionality - Constant of Proportionality - Unit Rate/ Unit Price/ Better Buy - Scale Drawings - Rate of Change PERCENTS - Finding percent of a number - Finding a number given percent - Finding tips - Finding tax - Discounts - Percent Error - Percent Increase/ Decrease - Interest (I = prt) EXPRESSIONS, EQUATIONS & INEQUALITIES - Solving One-Step Equations - Solving Two-Step Equations - Word Problems - Solving Inequalities - Evaluate Expressions - Represent Expressions GEOMETRY - Area - Composite Shapes - Shaded Area - Perimeter - Volume - Cross Sections - Triangles - Types of Triangles - Correspondence/Congruence - Angle Sum Theorem - Inequality Theorem - Circles - Diameter/Radius - Circumference/Area - Angle Relationships - Supplementary - Complementary - Vertical Angles STATISTICS - Biased vs. Unbiased - Mean, Median, Mode, Range - Comparing Measures of Variability PROBABILITY - Tree Diagram - Probability of a single event - Compound events - Permutations Page 1

2 Page 2

3 NUMBER SYSTEM 1. Simplify A) B) C) D) none 2. Simplify -2(k + 3) + -3(-7k - 7) A) 19k + 15 B) 5k + 33 C) -32k + 33 D) 23k Simplify: 6(x + 5) + 2(x + 1) A) 6x + 5 B) 8x +31 C) 8x + 32 D) 2x Simplify: 4 + 3y 8 8y + 2 A) 11y + 14 B) 11y 2 C) -5y 2 D) -5y 6 5. Simplify the following expression. 3x 12x A) 0 B) 72x C) 212x D) 112x 6. Simplify the following expression. p+ 18p A) 98p B) 10p C) 2p D) 18p 7. A ball was thrown straight into the air. It went up 150 feet before it then returned toward the ground. After falling 100 feet from its top height, it landed on the roof of a 50 foot-tall building. Which expression describes the situation? A) B) C) D) A submarine started at the surface, then submerged 300 meters below the surface of the ocean. It then rose 125 meters to its final resting spot. Which expression describes this situation? A) B) C) D) (-125) 9. Name the number property shown in the statement: z + 6 = 6 + z A) Commutative Property C) Associative Property B) Multiplicative Identity D) Distributive Property 10. Name the number property shown in the statement: 1 + (x + 2) = (1 + x) + 2 A) Commutative Property C) Associative Property B) Multiplicative Identity D) Distributive Property Page 3

4 EXPRESSIONS, EQUATIONS & INEQUALITIES 11 Solve for x: -80 = -5(5x + 1) A) -3 B) 3 C) 6 D) No solution. 12 Solve for a: 6a 7a + 9 = 14 A) -5 B) -6 C) 4 D) 9 13 Solve for b: 4b + 4 = 8 A) -3 B) -1 C) 1 D) 3 14 Evaluate when c = 5 A) -79 B) -19 C) 71 D) Solve the following equation. 23n+323n=39 A) 13 B) 313 C) 133 D) 9 16 Solve the following equation: 48 = -4 4(-8 + x) A) -5 B) -1 C) 15 D) 3 17 Evaluate m(p + p) when m = 4 and p = 4 A) 37 B) 32 C) 28 D) Evaluate p 2 n when n =6 and p = 6 A) 28 B) 26 C) 30 D) Evaluate z + x + z when x = 2 and z = 4 A) 9 B) 10 C) 8 D) 5 20 Evaluate p 2 q when p = 5 and q = 2 A) 51 B) 55 C) 47 D) Solve the following inequality. -8 q > -7 A) q < -56 B) q < -8 C) q < 1 D. q < -1 Page 4

5 22 Solve the following inequality. A) v < 5 B) v > 5 C) v < 29 D) v > 4 23 Solve the following inequality. A) r > 9 B) r < 9 C) r < 3 D) r > 3 24 Solve the following inequality. A) x < 35 B) x < 36 C) x < 8 D) x < 4 25 Solve the following inequality. A) b < 8 B) b > 8 C) b < 32 D) b < 5 FOR QUESTIONS 36-40, GRAPH THE INEQUALITIES Which of the following is a solution of 3x - 2y = 0 A) (2,3) B) (3,2) C) (3,-2) D) (0,0) 32 What is the rule for the following function? Page 5

6 x y A) y = 4x C) y = 2x + 4 B) y = 4x + 4 D) y = 2x A monthly cell phone plan is represented by the equation y = x, where x is the number of hours a person talks on the phone and y is the total cost of the cell phone. If Nigel talks on the phone for 90 minutes, how much with the cell phone cost that month? A) $118 B) $112 C) $1180 D) $ Dustin weighed 225 pounds before going on a diet. His current weight is 187 pounds. Which equation represents how much weight, w, Dustin lost? A) w = 187 B) 225 w = 187 C) 187 w = 225 D) = w 35 If the following polygon has a perimeter of 74, what is the value of x? 2x x.5x.75x 2x + 9 A) 8 B) 9 C) 10 D) 11 Page 6

7 RATIOS & PROPORTIONS 36.) One car of a model train is 4 inches long. If the actual train car is 30 feet long, what is the scale of the model? A) 1 inch =.75 feet C) 1 inch = 30 feet B) 1 inch = 7 feet D) 1 inch = 7½ feet 37.) If Jacob spent $45 on dinner and wanted to tip the waitress 15%, which of the following would be a good estimate for the tip? A) $9.00 B) $7.00 C) $5.00 D) $ ) A scale drawing uses a scale of 1 inch = 5 feet. If the dimensions of the actual object are 40 feet by 50 feet, what are the dimensions of the scale drawing? A) 8 in. by 10 in. B) 16 in. by 20 in. C) 4 in. by 5 in. D) 10 in. by 12 in 39.) A 5-pound bag of bread flour is on sale this week for $2.05. What is the price per pound? A) $0. 32 C) $0.38 B) $0.41 D) $ ) Which statement is true about the table shown below? x y A) This is an example of a proportional relationship. B) This is not an example of a proportional relationship. C) This is an example of an exponential relationship. D) There is not enough information to determine. 41.) Store ABC sells 8 lbs. of oranges for $6.00. Store XYZ sells 14 lbs. or oranges for $ Which store is less expensive, and by how much per pound? A) ABC is less expensive by $.50 per pound B) XYZ is less expensive by $.50 per pound C) ABC is less expensive by $.05 per pound D) XYZ is less expensive by $.05 per pound 42.) Andy ran a 5-kilometer race in 40 minutes. If Andy maintains that same pace, how many kilometers can Andy run in 1 hour? A) 20 km B) 8 km C) 6 km D) 7.5 km Page 7

8 43.) 58 is 160% of what number? Round your answer to the nearest hundredth, if necessary. A) 92.8 B) C) 2.77 D) ) What is 145% of 50? Round your answer to the nearest tenth, if necessary. A) 7,250 B) 2.9 C) 95 D) ) Carol took a math test and answered 16 of the 20 questions correctly. What was Carol s percentage score on the test? A) 80% B) 85% C) 90% D) 95% 46.) Marcy is having a pool party and wants to make four gallons of punch. The punch consists of juice and soda pop. The recipe calls for three gallons of soda pop. What percent of the total punch will be made up of juice? A) 30% B) 75% C) 50% D) 25% 47.) A car travels a distance of 98 meters in 10 seconds. What is the average speed of the car during this interval? A. 9.6 meters per second B. 9.8 meters per second C meters per second D meters per second 48.) Sara drove 300 miles to her friend's house on 20 gallons of gas. How many miles per gallon did Sara get? A. 30 mpg B. 25 mpg C. 15 mpg D. 10 mpg 49.) Marie wants to buy an outfit that costs $ She has $100 and doesn t know if she has enough money after the sales tax is added on. If the sales tax is 8%, does Marie have enough money to buy the outfit? A. Yes B. No Page 8

9 50.) A scale drawing uses a scale of 1 inch = 5 feet. If the dimensions of the actual object are 40 feet by 50 feet, what are the dimensions of the scale drawing? A. 8 in. by 10 in. B. 16 in. by 20 in. C. 4 in. by 5 in. D. 10 in. by 12 in. 51.) Jackson enjoys going to the Monster Truck show with his dad each year on his birthday. To celebrate his birthday, his dad bought him a model of his favorite Monster Truck. Identify the scale factor. A. 1:5 B. 1:2 C. 1:3 D. 1:8 52.) The actual distance from Charlotte to High Point is 75 miles. If the map scale is 1.25 in. = 25 mi., what is the distance in inches between the two cities on the map? A in. B. 20 in. C. 3 in. D. 2.5 in. 53.) A model of a boat is 21 inches long. The actual boat measures 21 feet. What is the scale factor? A. B. C. D. Page 9

10 54.) A class project requires students to build models of important landmarks around the United States. Teresa and Scott created a 25 in. tall model of the Empire State Building. The actual Empire State Building is 1,250 ft. tall (base to roof). They want to maintain the same scale on their next landmark. How tall would their model of Mount Rushmore be if the actual height of Mount Rushmore is 500 ft.? A. 10 inches B. 20 inches C. 5 inches D. 50 inches 55.) The scale factor is the same for three of the four models below. Which of the following has a different scale factor? A. B. C. D. Page 10

11 PERCENTS 56.) The bill for a dinner was $ If you decide to leave a 15% tip, how much should you leave? A) $48.92 B) $4.25 C) $6.38 D) $ ) The manager of Runner s Stop shoe store compares her sales from 2012 to those of Last year, she sold 4235 pairs of sneakers and this year, her sales are 6122 pairs. What is the percent of increase in her sales, to the nearest percent? A) 1887 B) 45% C) 1.45% D) 145% 58.) A store raised the price of a shirt from $25 to $65. What was the percent of increase? A) 60% B) 100% C) 160% D) 260% 59.) Jim read 296 pages of a 400 page book. What percent of the book did he read? A) 74% B) 29.6% C) 148% D) 296% 60.) Best Buy has offered a laptop on sale. The computer costs $ and is discounted 20%. Which choice is not equivalent to the discount? A) 210(690) B) C).20(690) D) $ ) 225% of what number is 81? A) 36 B) 45 C) 108 D) ) A galaxy has about two billion stars. If 1% will turn into black holes, approximately what number of stars will turn into black holes? A) 200,000,000 B) 20,000,000 C) 2,000,000 D) 200,000 Page 11

12 62.) Boris gets paid an 8% commission on every car he sells. Last week, he made a commission of $1,240. What was the price of the car he sold? A) $15,500 B) $15,000 C) $12,500 D) $1, ) To find 10% of the number 5,246 Jimmy knew all he had to do was shift the decimal place. Which of the following represents the correct answer that Jimmy should have achieved? A) B) C) D) 5, ) Lauren brought a winter coat that was on sale for 40% off the regular price of $199. How much did Lauren pay for the coat? A) $ B) $ C) $ D) $ ) Mrs. Ronai estimated that 124 students would attend the school field trip, but 80 actually attended. What was her percent error? A) 155% B) 55% C) 35% D) 65% 66.) The ad said the television cost $240, but it was actually $200. What was the ad s percent error? A) 1.2% B) 120% C) 20% D) 16.67% 67.) A bank offers an interest rate of 2.5% per year on bank deposits. How much interest would $12,167 earn after 5 years? A) $ B) $1521 C) $ D) $ ) Sarah received $75 interest on her deposit of $450 over 3 years. What was the interest rate? A) 56% B) 5.6% C) 22% D) 11.2% Page 12

13 69.) Kathy invested $8200 at the rate of 4.5% per year. She earned $738 in interest. How long was her investment? A) 2 months B) 1 year C) 1 year 2 months D) 2 years 70.) John invested a sum of money, which earned $750 at the rate of 6% per year over 2 years. How much was his original investment? A) $88.80 B) $6250 C) $3125 D) $2125 Page 13

14 GEOMETRY 85. What is the value of x in the picture? 4x 80 A) 20 B) 40 C) 25 D) 320 Page 14

15 90) Which angles are adjacent to angle d? A) a and e C) e and c B) b and c D) b and e Page 15

16 103) The circumference of a circle is. What is the radius of the circle? A) 4 B) 8 C) 16 D) ) The length of a rectangle is 3 less than the width. The perimeter of the rectangle is 59 ft. Which of the following measurements is a possible length? A) ft. B) 59 ft. C) ft. D) 34 ft. Page 16

17 110) A) 300 cm 2 B) 27 cm 2 C) 90 cm 2 D) 48 cm 2 Page 17

18 Page 18

19 116) What is the volume a cube with a side of length 6 cm? A) 18 cm 3 B) 36 cm 3 C) 180 cm 3 D) 216 cm 3 117) Use the formula V=lwh to calculate the volume of a rectangular solid. What is the volume of the solid below? 8 cm 9 cm A) 27 cm 3 B) 270 cm 3 10 cm C) 72 cm 3 D) 720 cm 3 118) How much air is necessary to fill a (spherical) soccer ball with a diameter of 18 inches (to the nearest tenth of a cubic inch? A) in 2 B) 37.7 in 2 C) in 2 D) in 2 120) Find the volume of the following figure. Round your answer to the nearest tenth. A) 96 cm 3 B) 18 cm 3 C) 180 cm 3 D) 208 cm 3 122) Two containers in the shape of cones are equal in height. The radius of the larger container is 3 times the radius of the smaller container. The volume of the larger container is how many times the volume of the smaller container? A) 3 B) 6 C) 9 D) 27 Page 19

20 For questions , refer to the diagram at right, where EFD IHG. 124) Which method proves that EFD IHG? A) SAS B) ASA C) SSS D) SSA 125) Which statement identifies corresponding congruent parts? A) D G B) D I C) D H D) D E 126) Which statement identifies corresponding congruent parts? A) DF GH B) DF GI C) ED HG D) ED HI 127) To prove that the triangles below are congruent by ASA, what additional information is needed? B Z A) A Z B) C Y C) AC XZ D) B Y A C Y X 128) John has created a triangular sign for his t-shirt store. The measurements of two of the sides are 10 feet and 4 feet. What is a possible measure of the third side? A) 24 inches B) 15 feet C) 12 inches D) 10 feet 129) Can x = 5 in the diagram below? Why or why not? x+1 3x x+3 Page 20

21 130) Identify the following triangle by its angles. 35 A) Scalene B) Right C) Acute D) Obtuse ) Which choice best describes the triangle shown below? 50 A) acute isosceles B) acute scalene C) obtuse isosceles C) obtuse scalene ) Find the area of the shaded region in terms of pi. A) 4π cm 2 B) 10π cm 2 C) 8π cm 2 D) 40π cm 2 137) Find the area of the shaded region. 138) Find the area of the shape at right. A) 28.5 square inches B) 42.5 square inches C) 57.5 square inches C) 150 square inches Page 21

22 139) Which shape represents the cross-section of the cone sliced parallel to its base? 140) A) B) C) D) Page 22

23 STATISTICS 141.) Of the 100 students in the eighth grade, 50 are boys. What could be used to simulate whether the next student who shows up in the school is a boy? A) Rolling a number cube C) Spinning a spinner with 4 sections B) Tossing a coin D) Picking a card from a deck of 52 cards 142.) Mason is conducting a survey about favorite TV shows. Which of the following would most likely give Mason unbiased results? A) His 3 closest friends B) His sister and 3 brothers C) Twenty of the students in his math class D) 35 random customers who enter a large store during one afternoon 143.) If the weights of a group of children are 100 lbs, 71 lbs, 95 lbs, 80 lbs and 104 lbs, what is the mean weight for this group? A) 90 lbs B) 91 lbs C) 94 lbs D) 95 lbs 144.) Find the median for the following data set: 62, 73, 99, 16, 44, 11, 13, 50 A) 50 B) 47 C) 46 D) ) Mr. Ferrara recorded the following test scores on the Math test: 85, 64, 99, 80, 77, 80, 90, 72, 90, 80, 71, 74 Which data value will help Mr. Ferrara find the range of the scores? A) 90 B) 80 C) 77 D) 64 Page 23

24 146.) Box-and-whisker plots can sometimes compare two sets of data. What conclusion can be drawn from the box-and-whisker plot below? Cost to drive in the city per mile A) Cars generally cost more than cabs (about $6) B) Cabs generally cost more than cars (about $6) C) Cars and cabs cost the same. D) There is no conclusion that can be drawn from this data. 147.) Below is a frequency table that displays quiz scores. Construct a bar graph to display the data. 148.) Page 24

25 149.) 150.) 151.) 152.) 153.) 154.) Page 25

26 155.) 156.) 157.) For Questions , refer to the table at right. 158.) What is the mean of the data? 159.) What is the median of the data? 160.) State the lower quartile and upper quartile of the data. Page 26

27 PROBABILITY 161.) How many different outfits can be made using one shirt, one pair of pants, and one hat from 20 shirts, 10 pants, and 8 hats? A) 160 B) 1600 C) 1 D) ) A bag contains 6 red marbles, 4 blue marbles, and 3 green marbles. If a marble is randomly selected from the bag, what is the probability that it is green? A) B) C) D) For questions 158 through 160, refer to the spinner below ) What is the probability of spinning an odd number? A) B) C) D) 164.) What is P(1, then 5) when spinning the spinner shown twice? A) B) C) D) 165.) What is the probability of spinning a letter? A) 0 B) 1 C) D) 166.) If the probability of an event occurring is certain, what is its probability? A) 0 B) 1 C) D) 167.) Page 27

28 For questions 163 and 164, what would be the total number of outcomes in the sample space? 168.) 169.) 170.) Page 28