ACT Aspire Practice

1. If Sally walked mile in hour, how fast, in miles per hour, was she walking? Unit Rate

1 2. You want to place a towel bar that is 8 ⁄4 inches long in the center of a door 1 that is 26 ⁄3 inches long. How far should you place the bar from each edge of the door? (Write the answer as a mixed number.)

Step 1: Subtract the length of the towel bar from the length of the door.

Step 2: Divide the result in Step 1 by 2---this is your answer

3. As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $110. What is the minimum number of sales you must make to earn at least $110? Setup an inequality and solve. ACT Aspire Practice

4. What is the circumference and area of a circle with a radius of 3 inches?

5. If angle b = 18 degrees, what does angle “a” equal?

6. Find the value of x and the missing angle measure. ACT Aspire Practice

7. Find the value of x and the missing angle measure.

8. Find the value of x ONLY.

9. A scale drawing of a door is 3 cm high. If the scale is 1 cm = 2 meters, what is the actual height of the door? Setup a proportion. ACT Aspire Practice

11. Find the volume of a cube where the length of each side is 4 inches. V = Bh

12. Find the volume of the pyramid below. ACT Aspire Practice

13. Find the volume and surface area of the figure below.

14. Find the surface area and volume of the figure below. ACT Aspire Practice

15. Find the volume and surface area of the cylinder below.

16. A small deck of cards has 3 blue, 4 black, and 6 purple cards. What is the probability of picking two blue cards in a row if the first card is not returned to the deck after it is drawn? (Write your answer as a fraction.)

Total Number of Cards:

Step 1: Find the probability of picking a blue on the first draw. ACT Aspire Practice

Step 2: Find the probability of picking a blue card on the second draw. Remember the first blue card was not returned or put back. There are no longer 3 blue cards and there are no longer a total of 13 cards. There are now 12.

Step 3: Multiply the fraction from step 1 by the fraction in step 2 and simplify. This is your answer.

17. A number between 8 and 15 is picked at random. What is the probability that the number picked is an even number?

Total number of numbers BETWEEN 8 and 15: ______8, 9, 10, 11, 12, 13, 14, 15

Step 1: Find the probability of picking and even number and simplify. This is your answer.

ACT Aspire Practice

18. The cost of a 10 ½ pound turkey is $8.93. How much does one pound cost? Find the unit rate. It would easier if you changed 10 ½ to the decimal 10.5 and then divide.

19. When Ronnie woke up, it was – 4 degrees. The temperature dropped another 4 degrees. What

is the current temperature?

20. Multiply and write your answer as a decimal. - 3.4 x ½

Hint: Change ½ to a decimal –then multiply it by -3.4.

21. The circumference of a circle is 31.4 yards. What is the circle’s radius? What is the circle’s diameter? ACT Aspire Practice

22. A 360° rotating sprinkler that sprays water at a radius of 14 feet is used to water a lawn. What is the area of the lawn that is watered by this sprinkler?

23. The diameter of a bike wheel is 2.5 ft. How far will the bike go in one rotation of the wheel?

24. Boats from all along the Atlantic coast were moored at a busy marina one summer day. Of the 10 boats at the marina, 4 were from Massachusetts. What is the probability (in fraction form) that a randomly selected boat will be from Massachusetts?

Total number of boats: _____

Step 1: Find the probability of picking a boat from Massachusetts. Simplify the fraction if possible. ACT Aspire Practice

25. Do the numbers in the table represent a proportional relationship? If so, identify the unit rate or constant of proportionality. Then write an equation to represent the relationship.

Check each

26. The graph below represents the price of the bananas at one store. What is the constant of proportionality? ACT Aspire Practice

27. The graph below represents the cost of gum packs as a unit rate of $2 dollars for every pack of gum. The unit rate is represented as $2/pack. Represent the relationship using a table and an equation.

Table Equation : ______Graph

28. Games Unlimited buys video games for $10. The store increases the price 300%? What is the price of the video game?

Hint: Remember to add the % of increase to 100%---then change this percent to a decimal – multiply it by 10. This is your answer. ACT Aspire Practice

29. Gas prices are projected to increase 95% by April 2015. A gallon of gas currently costs $4.17. What is the projected cost of a gallon of gas for April 2015?

30. Hint: Remember to add the % of increase to 100%---then change this percent to a decimal – multiply it by $4.17. This is your answer.

31. A sweater is marked down 33%. Its original price was $37.50. What is the price of the sweater before sales tax?

Hint: Remember to subtract your % of decrease from 100%---then change this percent to a decimal---multiply it by $37. 50. This is your answer.

33. At a certain store, 48 television sets were sold in April. The manager at the store wants to encourage the sales team to sell more TVs and is going to give all the sales team members a bonus if the number of TVs sold increases by 30% in May. How many TVs must the sales team sell in May to receive the bonus? ACT Aspire Practice

Hint: Remember to add the % of increase to 100%---then change this percent to a decimal –multiply it by 48. This is your answer.

34. After eating at a restaurant, your bill before tax is $52.60. The sales tax rate is 8%. You decide to leave a 20% tip for the waiter based on the pre-tax amount. How much is the tip you leave for the waiter? How much will the total bill be, including tax and tip?

Hint: This is a multiple percent problem. DO NOT combine 8% and 20%.

Step 1: Add 20% to 100%--Change this to a decimal ---multiply the decimal by $52.60. This is the total amount you will pay including the tip.

Step 2: Add 8% to 100%---Change this to a decimal---multiply the decimal by the total amount in step 1. This is your total bill including tax, after the tip. ACT Aspire Practice

35. Is “p – q = p + (-q)?” Example: Is 54 – 82 = 52 + (-82)?

36. If I have an expression such as 4 + -9, in what direction would I move on a number line and why?

37. If I have an expression such as -2 + 7, in what direction would I move on a number line and why?

Use a number line to show each of the following.

38. -3 + (-5)

39. 7 – 12= ______

40. -5 – (-9) =______ACT Aspire Practice

41. You have $12. You must pay your friend $20. Which expression below represents the amount you still owe your friend?

a. 12 + 20 b. -12 + (-20) c. -12 + 20 d. 12 + (-20)

42. Your cell phone bill is automatically deducting $32 from your bank account every month. How much will the deductions total for the year? Keep in mind, that deducting $32 is negative and that there are 12 months in the year.

43. It took a submarine 25 seconds to drop to 225 feet below sea level from the surface. What was the rate of the descent? In other words, how many feet did the submarine drop per second? Divide---don’t forget 225 should be negative.

44. Write an equivalent expression for 3(x – 5) -12. ACT Aspire Practice

45. Suzanne thinks the two expressions 2(3a – 2) + 4a and 10a – 2 are equivalent? Is she correct? Explain why or why not?

47. Can you write the perimeter of the following rectangle two different ways?

48. The youth group is going on a trip to the state fair. The trip costs $52. Included in that price is $11 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes cost the same price. Write an equation to determine the price of one pass.

49. ACT Aspire Practice

50. The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

51. Amie had $26 dollars to spend on school supplies. After buying 10 pens, she had $14.30 left. How much did each pen cost? Setup an equation.

52. Solve

53. Florence has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 dollars and spend the rest on t-shirts. Each t-shirt costs $8. Write an inequality for the number of t- shirts she can purchase. ACT Aspire Practice

54. Steven has $25 dollars. He spent $10.81, including tax, to buy a new DVD. He needs to set aside $10.00 to pay for his lunch next week. If peanuts cost $0.38 per package including tax, what is the maximum number of packages that Steven can buy? Write an inequality.

55. Solve and graph on a number line.

56. ACT Aspire Practice

57. If there are 180 degrees in a triangle, find the missing measure below.

58. Find the measure of x. Remember there are 180 degrees in a triangle.

Step 1: Find the missing angle measure in the triangle. ACT Aspire Practice

Step 2: The angle measure you found in step 1 is supplementary to x.

59. Find the measure of x. Remember there are 180 degrees in a triangle.

Step 1: Find the missing angle measure in the triangle.

Step 2: The angle measure you found in step 1 is vertical to x.

60. Find the area of a triangle with a base length of three units and a height of four units.

Formula is ACT Aspire Practice

61. Find the area of the trapezoid below.

Formula is

The bases are the two parallel sides and “h” is height. The height will always form a right angle with the bases.

62. A store is having a sale on 3 different items. Each sign below show the original price of an item and how to calculate the discount for that item. Order the signs below from least amount of discount to greatest amount of discount.

Keep the same percent amount but change it to a decimal. Perform the steps in the order they are given to you.

ACT Aspire Practice

Setup two different inequalities using the sum of these two distances. Then solve each.

Distance Ryan walked: 2x + 2.3

Distance Tom walked: 2x + 2.7

Sum these two distances:______

______> 15 and ______< 21