REVIEW: HSPA Skills 2 Final Exam June a) y = x + 4 b) y = 2x + 5 c) y = 3x +2 d) y = 2x + 3

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Phebe Beverly Dickerson
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1 Part I- Multiple Choice: 2 points each: Select the best possible answer. 1) The nutrition label of cookies states that there are 20 servings in a box and that one serving contains 1.5 grams of fat. Kyle ate about one- half of the cookies in the box. Which is the best estimate of the number of grams of fat that Kyle ate? 2) Almac Finance company randomly selected 500 mortgage statements being sent out at the end of the year and found errors on 4 statements. Based on this information, how many of the 16,000 mortgage statements sent out may be expected to be incorrect? a) 4 b) 128 c) 1,280 d) 4,000 3) Which of the following equations gives the rule for finding the value of y for the table below? x y a) y = x + 4 b) y = 2x + 5 c) y = 3x +2 d) y = 2x + 3 4) A number cube has sides numbered 1 to 6. If the cube is rolled once, what is the probability that the number rolled is: I) a factor of 4? II) Even number? III) Factor of 3? 5) Jim works 34 hours per week and earns $7.50 per hour. What is the best estimate of his gross pay per year? 6) Which list shows elevations above and below sea level in order from the highest elevation to the lowest? a) ft., - 20 ft., 350 ft., 1,200 ft. b) - 20 ft., ft., 350 ft., 1,200 ft. c) 1,200 ft., 350 ft., - 20 ft., ft. d) 1,200 ft., 350 ft., ft., - 20 ft. 7) The chance of snow on Sunday is 50%. The chance of snow on Monday is 40%. What is the probability that it will NOT snow both days? 8) A wooden box with 8 video cassettes weighs 6.8 kilograms. The box weighs 0.9kg when it is empty. Using x to represent the weight of one video cassette, which of the following describes the situation? a) 8x = 6.8 b) 8x 0.8 = 6.8 c) 8(x + 0.9) = 6.8 d) 8x + 9 = 68 1

2 9) The figure below is a rectangular prism. Which of the following is perpendicular to face AEHD? a) AB b) AE c) CG d) BF B C G A D H E 10) Which of the following is NOT equivalent to the others? a) 30 divided by 0.5 b) 6% of 1,000 c) 1/3 of 60 d) 6 times the square root of ) Shane gets $5.50 a week for his allowance. He also earns $4.00 for each hour of chores that he completes. The following chart shows last week s chores: Mowing the lawn 1.25 hours Cleaning the garage 3.0 hours Emptying the trash 0.5 hours Painting the garage 6.5 hours How much did he receive that week? 12) Which of these symbols would produce a true statement when written in the blank? a) < b) > c) = d) > 2

3 13) A group of students were studying weather facts. They kept records of the increase or decrease in temperature for one week in December. A rise was indicated with a + sign and a drop was indicated with a sign. If the temperature on January 2 was 6 and the daily temperature changes were recorded as below, what was the temperature on January 9 th? 1/3 1/4 1/5 1/6 1/7 1/8 1/ ) Footlocker has Air Forces on sale for 1/3 off their regular price of $ Finish Line has the same sneakers on sale for 45% off their regular price of $ Which store is cheaper and by how much? a) Footlocker by $11.50 b) Finish Line by $11.50 c) Footlocker by $6.50 d) Finish Line by $ ) The Cycle Shop has a 10-speed racer on sale. They are offering 30% off the normal $ price. The Bicycle-Built-for-You Store lists the same bicycle for $ and offers a 38% discount. Which store has the better buy? 16) A bicycle is on sale for $ If you include 6% sales tax, what would the bicycle cost? 17) Which of the following is NOT equal to the others? a) 0.5(80) b) 2(2 + 6 x 3) c) 40% of 100 d) x 5 18) A house originally cost $75,000. The owner wants to make a profit of 35% on the sale. For how much should he sell it? 19) A house is worth $104,000 today. If the price of the house has increased 30%, what was the original cost of the house? a) $70,000 b) $75,000 c) $80,000 d) $85,000 3

4 20) If the dimensions of the rectangle shown below were increased by 30%, what would be the area of the new rectangle? (Round your answer to the nearest tenth.) OLD NEW 21) Kira s bicycle tires have a diameter of 65 cm. If her tires make one complete revolution, how far did the bicycle move? (Use =3.14) 22) A right triangle has legs of 5 inches and 12 inches. Find the length of the hypotenuse. 23) A tree casts a 10.2 foot shadow. Kayla who is 5.5 feet tall, casts a 2.4 foot shadow. How tall is the tree? 24) A photo with dimensions 8 inches by 10 inches is placed in a copy machine that enlarges the dimensions by 22%. What will the new dimensions be? 25) A classroom is 35 feet long, 26 feet wide, and 12 feet high. If 30 students are assigned to the room, how many cubic feet of air and space does this allow for each student? 26) How many different three-letter words can be made out of the word LEARN (not all of the words have to make sense)? a) 6 b) 60 c) 90 d) ) Mr. Jimenez s math class got the following scores on one exam: 89, 97, 67, 73, 90, 93, 77, 86, 59, 88 89, 76, 57, 98, 93, 95, 93, 79, 91, 84 What was the class mean? 28) Alex bowled 24 games to date and has a bowling average of 110. His goal is to bring his average up to 114 at the conclusion of next week s 3 games. What must his minimum average be on his next 3 games in order to reach a total average of 120? 4

5 29) Shannon recorded the following measurements for a physics experiment: 1.0 cm 1.1 cm 1.05 cm 1.23 cm 1.4 cm 1.36 cm What was the mean measurement? a) 1.15 cm b) cm c) 1.19 cm d) cm 30) Simplify: (7x 2 + 3) + (5x 2 + 8)? 31) Simplify (a 3 5a + b 2) (3a 3 + 5a b + 2) 32) Simplify (5x 3 + 2x 2-7x +9) (-4x 3 + 3x 2 + 2x +1 )? 33) Simplify: -2y 3 (2y 2 5y + 6)? 34) Use the FOIL method to simplify: (x 6)(x + 3)? 35) Solve the equation: (4x 5) 2 = 0 (Leave answers as fractions.) 36) Choose the solutions of the equation (3x -1)(x + 6)(2x + 7) = 0. a) 1/3, 6, 7/2 b) 3, -6, -7 c) 1/3, -6, -7/2 d) 3, -6, -2/7 37) Solve the following system of equations: 3x + 2y = 6 x - 2y = 10 38) Solve the following system of equations: 2x + 2y = 8 x - y = 4 a) (0, 4) b) (4, 0) c) (-2, 0) d) (0, -4) 39) The formula C = $0.48n gives the cost, C, of developing a set of prints where n represents the number of prints completed at the local Kodak print shop. What is the total cost of printing 36 pictures? a) $20.48 b) $21.12 c) $21.60 d) $ ) Solve for Celsius when the temperature is 72 F using C = 5/9(F 32) 41) Mr. O Harris figures that 12.4% of his weekly gross income was spent on food. If he spent $96.72 on food, how much is his weekly gross income? 5

6 42) If each measure of the triangle below is given as an algebraic expression, what is the measure of angle A? A 10x - 6 C 5x + 6 9x - 12 B 43) Translate as an expression: Eight times the sum of a number and 3. 44) Translate. The sum of five and a number is forty- five. 45) Translate. Twenty minus the sum of four- ninths of a number and three. 46) Translate and find the number. Twenty less than four times a number is equal to the product of 3 times the sum of the number and ) Translate and find the numbers. The sum of two numbers is fifteen. One less than three times the smaller is equal to the larger. a. 8 and 7 c. 6 and 9 b. 4 and 11 d. 10 and 5 48) Solve - (2x + 8)=86 for x. 49) Solve 3(2n + 4) 2(3n +6)=75 for n. 50) Solve 4( 2d 2)= 7(2d 10) for d. 6

7 Part II: OPEN ENDED QUESTIONS: YOU MUST PICK THREE (3) TO ANSWER (20%): 1. A computer repairman charges a flat fee of $75 for a service call plus $55 per hour. Any fractional part of an hour is considered a whole hour of labor. This can be written as formula where T is the total cost and h is the number of hours. Complete the following formula: T = Find the total charge if the repair takes five hours. If the total charge of a service call was $240, for how many hours did he charge? Is it possible for a service charge to be $65. Explain why or why not. 2. In most states the amount of a fine for speeding on turnpikes or parkways is determined by the speed. For example, in one state, the speeding fine can be determined by the following formula: F = 2(S 65) +78, where F is the fine in dollars and S is the speed the car was going in miles per hour (mph). Find the speeding fine if the driver were stopped while going 100 mph. Suppose a speeder was given a ticket for $110. What was their speed? Explain how you found your answer. Why is it unlikely for someone to receive a $40 speeding ticket? 3. Ashraf applied for a job as a salesperson. He was offered two options. Plan A: $ % of monthly sales Plan B: 8% of monthly sales Sales for the previous employee was as follows: January: $50,000 February: $45,000 March: $60,000 April: $65,000 Based on this information: Which option would he select? Explain your answer. 4. A shopper compared the cost of the same three items among different stores. Food Basics was selling 3 pounds of apples for $2.79. Shoprite was selling 5 pounds of apples for $3.50. Pathmark was selling 2 pounds of apples for $4.10. If x represents the number of pounds and y represents the cost, interpret how the slope of the lines is related to the cost per pound. Write an equation for each store. Determine the best buy possible for the shopper. Explain your reasoning. Determine the most expensive buy. Explain your reasoning 7

8 5. Your cellular phone company charges $29.95 per month and gives you 300 minutes of free calls per month. Additional minutes cost $0.32 per minute. Your last bill came to $ Let x represent the number of minutes you talked last month. Write an equation that models this situation. Approximately how many minutes did you use the phone? Round to the nearest tenth. How many minutes did you have to pay extra money for? 6. You re a stocker at a grocery store. The store received a shipment of 1500 heads of lettuce. You sample 50 heads of lettuce and find that 4 heads were brown. Write a ratio that would estimate the number of heads of lettuce in the shipment that were brown. About how many heads of lettuce were brown? If the store has a policy of accepting any shipment of produce if damaged produce is 7% or less of the shipment, should you reject or accept this shipment? Explain your answer. 8

Ask questions such as If you ate a total of 30 cookies, some in the morning and 12 in the afternoon, how many crackers did you eat in the morning?

Ask questions such as If you ate a total of 30 cookies, some in the morning and 12 in the afternoon, how many crackers did you eat in the morning? Welcome to Summer Vacation! Your child has worked hard this school year to strengthen their ability as a young Mathematician. Remember that learning does not stop outside the classroom. Daily routines