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Math Challenges and Solutions

Solve inequalities, linear equations, functions, and more math problems with step-by-step solutions. Improve your math skills today!

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Math Challenges and Solutions

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  1. Content 1.1a Roberto is packing a van with suitcases. The van has 15 storage units. Each large suitcase uses 2 storage units, and each small suitcase uses 1 storage unit. If l is the number of large suitcases and s is the number of small suitcases, which inequality represents the number of suitcases he can fit in the van? 1. A B C D  Page 1

  2. Content 1.1d 2. • Jonas is buying ice and soda for a barbecue.Ice costs $2 per bag, and soda costs $3 per case. Jonas has $18 to spend. Which of the following combinations is he able to buy if he is to stay within his budget? F 2 cases of soda and 6 bags of ice G 3 cases of soda and 5 bags of ice H 4 cases of soda and 4 bags of ice J 1 case of soda and 8 bags of ice  Page 2

  3. Content 1.2a • When x = 2 and y = -3, what is the value of the expression: x (3x – 2y) + xy ? 3. A B -18 6-618 C  D Page 3

  4. Content 1.2b 4. • (2x – 5) + (2 – x) – (3 + x) • What is the simplified value of this expression? F 2x + 6 G 2x - 6 H -6 J 6  Page 4

  5. Content 1.2c 5. • Which expression is the factored equivalent of: 6t – 5t– 25 2 A (2t + 5) (3t + 5) B (2t – 5) (3t – 5)C (2t – 5) (3t + 5)D (2t + 5) (3t – 5)  Page 5

  6. Content 2.1a • Which situation CANNOT be representedby a linear function? 6. F G H J A worker’s monthly earnings include a bonus of $25 and pay at a rate of $6 per hour he worked that month. A student collects 15 pounds of cans every 2 weeks for a fundraiser.  A writer uses twice as many pencils each week as he did the week before. A student gets 5 points for each correct answer on a test. Page 6

  7. Content 2.1b 7. • Identify the mapping diagram that represents the relation and determine whether the relation is a function. A C The relation is not a function The relation is a function  B D Page 7 The relation is a function The relation is not a function

  8. Content 2.2a 8. • Which linear equation goes throughthe points (–2, –7) and (3, 8)?  F y = x – 1G y = –2x – 7H y = 3x – 1 J y = 3x – 3 Page 8

  9. Content 2.2b 9. • The graph of which function appearsto be shifted 3 units down from thegraph of y = x2 + 3?  A y = x2 – 3 B y = x2C y = x2 + 3D y = x2 + 6 Page 9

  10. Content 2.1c.I 10. • The graph shows the wages earned by a cashier during a week. Which of the following best describes the slope of the line?  F The cashier earns $6 per hour.G The cashier earns $6.25 per hour.H The cashier earns $12 per hour.J The cashier earns $12.50 per hour. Page 10

  11. Content 2.2c.III 11. • An air conditioner cools a room from80oF to 74oF in 15 minutes. What is the rate of cooling?  A 0.4oF per minuteB 2.0oF per minuteC 4.0oF per minuteD 6.0oF per minute Page 11

  12. Content 2.2d 12. • What is the equation of the line that passes through (6,0) and (0,4) F x + 3y = 6G 2x + y = 6H 3x + 2y = 12J 2x + 3y = 12  Page 12

  13. Content 2.2e • Lisa can spend $400 on her summer vacation. If the plane ticket costs $200 and the hotel costs $40 per day, which inequality represents the number of days, d, that she can stay on vacation? 13. A B C D  Page 13

  14. Content 2.3a 14. What values of x represent the solutions to the inequality -3x + 6 < 12  F x > -2G x > 2H x < -2 J x < 2 Page 14

  15. Content 2.3b 15. Which inequality is represented by the number line?  A x > -8B x < -8C x< -8D x> -8 Page 15

  16. Content 2.4 16. • Find the value of b that makes the system of equations have the solution (3, 5). • y = 3x– 4 • y = bx + 2  F 1G 2H 0J -1 Page 16

  17. Content 3.1a 17. • Which graph or graphs would be best for showing the depth of water in a pond over a period of time? III. I. II. A IB II or IIIC IIID I or II  Page 17

  18. Content 3.1b • The chart shows the naptimesof 100 children. • For the next 1000 children surveyed, what is the best prediction of how many willhave a naptime at 1:30 P.M.? 18. F 170G 220H 260J 350  Page 18

  19. Content 3.1c 19. • Angela’s average for six math tests is 87. On her first four tests she had scores of 93, 87, 82, and 86. On her last test, she scored 4 points lower than she did on her fifth test. What scores did Angela receive on her fifth and sixth tests?  A Fifth test = 89 ; sixth test = 85 B Fifth test = 85 ; sixth test = 89 C Fifth test = 85 ; sixth test = 81 D Fifth test = 90 ; sixth test = 86 Page 19

  20. Content 3.2 20. • Gloria makes and sells handmade greeting cards. The scatter plot shows the number of cards she made over a 10-hour period. Find the equation of a trend line and use it to predict the number of cards Gloria can make in 12 hours F y = 2x ; 24 cards G y = 2.5x ; 30 cards H y = 3x ; 36 cards J y = 3.5x ; 42 cards  Page 20

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