ACT ASPIRE PRACTICE
Write Expressions:
1. The difference of 5 and a number.5 - x
2. A teacher split her students into 11 groups. Write an expression to show how to determine how many students would be in each group.x/11
3. Which expression is equivalent to 2x + 116? a. 2(x – 58)b. 2x – 58c. 2x + 58d. 2(x + 58)
4. Write an expression: A number subtracted from 20 20-x
5. Write an expression: 4 less than a number cubed x3-4
6. Apply the distributive property: (4x – 6) 1/2x – 3/4
7. Hannah babysits to earn money. She charges $6.50 for the first hour, and $5.75 for each additional hour. Let (n) equal the number of hours she works after the first hour. Write an expression to show how much Hannah charges.
5.75n + 6.50
8. What is the exponential notation of 6 x 6 x 6 x 6 x 6? 65
Equations:
9. Write an equation equivalent to 6(x – 3) = 4x + x 6x – 18 = 4x
10. As a class experiment, a cart was rolled at a constant rate along a straight line. Shawn recorded in the chart above the cart’s distance (x), in feet, from a reference point at the start of the experiment and for each of 5 times (y), in seconds. Which equation represents the data in the table? a. x = y + 10 b. x = 4y + 10 c. x = 4y + 6 d. x = 14y
y / 0 / 1 / 2 / 3x / 10 / 14 / 18 / 22
11. What is the value of 8x if x = 4? 32
12. Use the four operations and parentheses to complete this equations: 6 / 3 + (54) - 5 = 17
13. y = 8 – 3x if y = 2, what is the value of x? x = 2
14. Sochi had started reading a book. She had already read 11 pages, then she read 3 pages per minute. Write an expression to show how many pages Sochi has read total. 3x + 11
15. A rectangular parking lot has an area of 2/3 of a square km. The width is ½ km. What is the length? Explain.
L = 1 1/3 Since Area is length x width, and we’re given the width, I divided 2/3 by ½ to solve for Length.
16. Diana can use the equation y = 7x to calculate her pay, where y is the amount she is paid and x is the number of hours she works. How many hours did she work if she was paid $45.50? Explain
6.5 hours. Y is 45.50 so 45.50 = 7x . To solve for x, you must divide 45.50 by 7.
17. If y – 18 = 14, what is the value of 3(y+5)?Explain how you found your answer. 111, first I solved for y in the first equation. I added to 18 to both sides to get y by itself. Y = 32 Then, I replaced y with 32 in the expression. 3(32 + 5). I solved parentheses first, then I multiplied 3 x 37 to get 111.
18. Sandy’s workout consists of using the rowing machine for a certain number of minutes, and then uses the treadmill for a certain number of minutes. Each minute she uses the rowing machine, she burns 8 calories. Each minute that she uses treadmill, she burns 10 calories.
a) Assign variables for the number of minutes she uses each machine.R = rowing T = treadmill
b) Write an expression that represents the total number of calories that she burns during a workout.
8r + 10t
c) Evaluate your expression if Sandy uses the rowing machine for 19 minutes and the treadmill for 25 minutes. 8*19 + 10*25 = 402
Numbers and Operations:
19. The sides of a square on a coordinate plane are 3 cm long. One vertex of the square is located at the point (3, 0). What could the other three coordinates be? (3, 3), (6, 0), (3, -3), (0, -3), (0,0), (0, 3), or (6, -3)
20. A trapezoid has vertices at (-2, 5), (-3, -2), (2, -2), and (1, 5) on a coordinate plane. What is the height of the trapezoid? 7
21. The price of a movie theatre ticket increased from $7.50 to $7.75. The theatre sold 315 one night at the higher price. What is the difference in income the theatre would earn of the higher price and previous price?
$78.75
22. In which quadrant does a point lie if it has a negative x-coordinate and positive y-coordinate? II
23. What is the value of 32/15÷5/12? Explain how to solve.7 39/75. Change mixed number to 47/15 then cross multiply. 47*12/15*5, then reduce.
24. What is the GCF and LCM of 24, 12, and 32?GCF is 4. LCM is 96
25. The average annual temperature between 1971 and 2000 was -3 degrees Celsius in Alaska and 21.1 degrees Celsius in Hawaii. What is the difference in the average temperatures of Alaska and Hawaii? 24.1
26. Write 10% as a fraction in simplest form. 1/10
27. What is 1/3 + ¼? 7/12
28. Will needs 5/8 cup of milk for a recipe, but he only has 1/3 cup. How much more does he need? 7/24
29. How would you locate the point (-5, -4) on a coordinate plane? From the origin move 5 units left and then 4 units down. Which quadrant is it in? III
Ratios and Proportions:
30. A laundry detergent is sold at 2 stores. Store A is $6.50 for 60oz; B is $5.50 for 54 oz. Which storehas the best deal?B
31. The number of gallons is proportional to the number of pints. How many gallons are equal to 96 pints? 12
32. What is 40% of 25?10
33. Write an equivalent ratio to 3:5.6:10
Geometry:
38. What is the volume? 1 in.3
39. The box has a volume of 25,294.25 cm3. Its width is 11.5cm and height is 41.5cm. What is the missing length?
53 cm
40. How do you find the area of a triangle?Multiply base times height then half your answer by dividing by 2.
41. What is the surface area of a prism with length of 15m, width of 6m, and height of 10m?
150 + 150 + 60 + 60 + 90 + 90 = 600m2
42. What is the area of this figure?
120 m2
Statistics:
43. Which of these is NOT a statistical question?
a. How many students in each class enjoy doing long division?
b. What is the age of the youngest child in each student’s family?
c. How far did a five-person relay team run?
d. How many baskets did each player get this season?
44. The Yellow Jackets soccer team scored 6, 8, 5, 8, 5, 5 goals in those games. What is the mode goals?5
45. Solana is shopping for a new shirt. Here are the prices of shirts she likes: $50, $41, $40, $42, and $32. What is the median price of the five shirts? 32, 40, 41, 42, 50
46. What is the 1st quartile of a box-and-whisker plot with the following data:
42, 44, 46, 47, 50, 52, 56, 60, 64, 70, 71, 73, 76, 78, 80, 82, 86, 88
47. This semester Andrew has earned grades of 85, 83, 89, 81, and 89 on his math tests. What is his mean grade?
85.4