Extra Math Answers
Answers are in Bold.
Links to corresponding mathematical concepts are in Bold.
Questions 1 – 5: Calculator-Prohibited
1. At a restaurant, a sandwich costs $2.25, a cup of soup costs $1.79, and a drink costs $0.99. The restaurant also offers the above items together as a special at a cost of $4.39.
How much money is saved by ordering the special instead of ordering each item separately?
2. A telephone company charges $45.00 a month for cell phone usage that does not exceed 750 minutes. Any usage over 750 minutes is charged at a rate of $0.55 a minute.
If a customer uses a cell phone for 863 minutes in a month, how much will that monthly cell phone bill be?
3. What is -9 squared?
4. What is 74 × 75 ? Give your answer in exponent form.
5. What is the simplified version of √6 × √18 ?
Questions 6 – 49: Calculator-Allowed
6. At a restaurant, a customer can order 6 different soups, 5 different salads, and 3 different desserts. How many different combinations of this food can the customer order?
7. The probability of snow is 60% on Friday, 70% on Saturday, 55% on Sunday, and 80% on Monday. In percent terms, what is the probability of snow on all four days?
8. A plane departed from New York City at 7:30 PM Eastern Standard Time (EST) and arrived in Los Angeles at 10:30 PM Pacific Standard Time (PST). Taking into account the different time zones as depicted in the map above, how many hours did the flight take?
9. A chili supper is held at a cost of $6.75 per person. What is the total cost of 135 people?
10. A car traveled 55 miles per hour for from 8 a.m to 7 p.m. What distance did it travel?
A. 605 kilometers
B. 650 miles
C. 605 miles
D. 650 kilometers
11. A teenager babysits for 10 different children of various ages. The median age of the children is 6.5. The mode age of the children is 5. Place two additional X marks on the graph below consistent with this age information.
12. In fractional terms, what is the probability of picking 35 green balls out of a total of 100 balls, the rest of which are not green?
13. The cost of Bob’s groceries before the sales tax was $12.50. If the sales tax rate was 6%, how much change did Bob receive after paying for his groceries with a twenty-dollar bill?
14. In the image below, two boxes are in proportion. How long is W?
Ratio and Proportion
15. In the map above, the scale is 1 inch : 250 miles.
Also in the map, Raleigh, North Carolina and Springfield, Illinois are approximately 3.5 inches apart. In the real world, approximately how many miles are Raleigh and Springfield apart?
16. A transistor is 3.2 × 10-8 mm wide. If a microchip is 12 mm wide, how many transistors can be fitted into the microchip side by side? Express your answer in scientific notation.
A. 3.8 × 10-8
B. 3.84 × 10-7
C. 3.75 × 108
D. 3.0 × 10-9
17. What is the value of 12y + 3x² when x = 9 and y = 4?
18. The cumulative rent R for an apartment is $1100 a month times the number of months m the apartment is rented plus a one-time deposit of $550.
What is the value of R where R = 1100m + 550 and the apartment is rented for 6 months?
19. $7500 is deposited in a bank at a rate of 3% for 5 years.
How much interest is earned over this time?
20. What is |-5|?
21. The number of mice in our neighborhood is 14 less than 5 times the number of cats c. Which expression represents the number of mice in our neighborhood in terms of c?
A. 14 < 5c
B. 5(c – 14)
C. 5c < 14
D. 5c – 14
22. A law firm employs 5 full partners and 12 associates. An associate earns $9500 a month less than a full partner. Let y represent the law firm’s total salaries in any given month and x represent the salary of a full partner in any given month. Which expression represents y in terms of x?
A. y = 12x + 5(x – 9500)
B. y = 17x – 9500
C. y = 5x + 12(x – 9500)
D. y = 17x + 9500
23. A teacher concocted 8 original test questions an hour minus 2 duplicate questions for a total of 64 test questions. Given the equation 8h – 2 = 64, how many hours h did the teacher spend concocting questions?
24. A shopper spent $155.00 at the mall, including $11.00 for parking. The shopper spent $16.00 apiece on accessories. Given the equation 16a + 11 = 155, how many accessories a did the shopper buy?
25. A shopper can spend $115.00 or less on paperback books from an online vendor. Each book costs $9.99. Regardless of how many books are ordered, shipping and handling costs $7.95. Which inequality represents the number of books b the shopper can order?
A. 9.99b + 7.95 ≥ 115
B. 7.95b + 9.99 ≤ 115
C. 7.95b + 9.99 ≥ 115
D. 9.99b + 7.95 ≤ 115
26. A special dinner must generate more than $3000.00 in order to raise money for charity. The dinner organizers spend $2000.00 on room rental and food. They expect 55 attendees. Which inequality represents the amount x the dinner organizers must charge each attendee in order to raise money for charity?
A. 55x + 2000 ≥ 3000
B. 55x + 2000 > 3000
C. 2000x + 55 ≥ 3000
D. 2000x + 55 > 3000
27. Which expression represents 10x + 4 > 9 multiplied by -3?
A. -30x – 12 > -27
B. -30x + 12 > -27
C. -30x – 12 < -27
D. -30x + 12 < -27
28. A baseball card aficionado can spend up to $415.00 at a show. The show charges a $10.00 entrance fee. The collector plans to spend $50.00 on each card x at the show.
Thus, the inequality 50x + 10 ≤ 415 expresses the number of baseball cards the aficionado can buy. Plot all possible points representing the number of baseball cards the collector can buy within the parameters of the number line below.
29. A kiosk must generate more than $160.00 in order to make a profit. It spends $60.00 on supplies. The kiosk will charge $20.00 for every item x it sells. Thus, the inequality 20x + 60 > 160 expresses the number of items the kiosk must sell in order to make a profit. Plot all possible points representing the number of items the kiosk must sell within the parameters of the number line below.
30. According to the line graph above, the stock price of Facts and Figures Corporation:
A. increased from 2000 to 2003
B. decreased from 2009 to 2010
C. decreased from 2011 to 2013
D. increased from 2003 to 2005
Facts and Figures
31. Bob planted some prairie grass to beautify a corner of his yard. After 2 weeks, the grass was 4 inches tall. After 6 weeks, the grass was 16 inches tall. If it grows at the same rate, how many inches tall will the grass be at week 10?
32. Which of the following pairs of lines are parallel?
A. y = x + 2 and y = -3x – 4
B. y = 3x – 4 and x + 2
C. y = 3x + 5 and y = 3x – 3
D. y = 3x + 5 and y = -3x – 3
33. Which of the following represents the point-slope form of the equation of a line passing through point (-3, 5) with a slope of 6?
A. y + 5 = 6(x + 3)
B. y + 5 = 6(x + 3)
C. y – 5 = 6(x + 3)
D. y – 5 = 6(x – 3)
34. With reference to Question 33, which of the following represents the
slope-intercept form of the equation of the line?
A. y = -6x + 23
B. y = -6x – 23
C. y = 6x – 23
D. y = 6x + 23
35. The following table shows the age in years and height in inches of a boy and a girl. On the accompanying x-y coordinate grid, plot the points for the girl at ages 3 and 8.
36. With reference to Question 35, which of the following is the correct linear equation passing through the points plotted?
A. y = -2.6x + 29.2
B. y = -2.6x – 29.2
C. y = 2.6x + 29.2
D. y = 2.6x – 29.2
37. With reference to Question 35, the girl is given the present of a giant beach ball whose diameter is as tall as she is at age 8.
To the nearest tenth of cubic foot, what is the volume of the beach ball?
38. The fireman’s ladder in the image below is leaning against a wall. Its base is 50 feet from the wall. Its top is 120 feet up the wall. How long in feet is the ladder?
39. As in the image below, a snail can crawl 4.4 meters along a wall and then turn 90° to the left and crawl 3.3 meters along another wall. If the snail took a straight shortcut from the starting to the ending point of these two walls, how much shorter in meters was the shortcut than sticking to the walls?
40. For the quadratic equation y = 4x² – 18x + 20, what is y when x = -3?
41. As in the image below, a pizza has a diameter of 15 inches. To the nearest hundredth of a square inch, what is its area?
42. As in the image below, a triangular billboard has a base of 4.4 meters and a height of 3.3 meters. What is its area in square meters?
43. As in the image below, the side of a square postage stamp is 2.25 cm. What is the postage stamp’s area in square centimeters?
44. As in the image below, a solar panel in the shape of a parallelogram has a base of feet and height of feet. What is its area in square feet in decimal form?
45. As in the image below, a cinder block has a length of 120 centimeters, width 50 centimeters, and height 70 centimeters. What is its volume in cubic meters?
Right Rectangular Prism
46. The President of Facts and Figures Corporation keeps breath mints in a cylindrical jar on his desk. As in the figure below, the diameter of the cylinder is 5 inches and the height of the cylinder is 9 inches. To the nearest hundredth of a cubic foot, what is the volume of the cylinder?
47. The following table shows the year and corresponding stock price for Facts and Figures Corporation. On the accompanying x-y coordinate grid, plot the points for the years 2002 and 2003.
|Facts and Figures Corporation|
48. With reference to Question 47, which of the following is the correct linear equation passing through the points plotted?
A. y = -4x – 8033
B. y = -4x + 8033
C. y = 4x + 8033
D. y = 4x – 8033
49. Because of the poor performance of the stock price from 2002 to 2003, the shareholders present the President of Facts and Figures Corporation with a conical dunce cap. As in the image below, the cone has a diameter of inches, height inches, and slant height inches. To the nearest hundredth of a cubic inch, what is its volume?