ACT Aspire Practice
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1.
If Sally walked 2 mile in 4 hour, how fast, in miles per hour, was she walking? Unit Rate
2.
You want to place a towel bar that is 8 1⁄4 inches long in the center of a door
that is 26 1⁄3 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?
𝐶 = 2𝜋𝑟 𝑎𝑛𝑑 𝐴 = 𝜋𝑟 2
5. If angle b = 18 degrees, what does angle “a” equal?
6. Find the value of x and the missing angle measure.
7.
Find the value of x and the missing angle measure.
ACT Aspire Practice
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.
10.
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. 𝑉 =
𝐵ℎ
3
13. Find the volume and surface area of the figure below.
17 cm
ACT Aspire Practice
14. Find the surface area and volume of the figure below.
15. Find the volume and surface area of the cylinder below.
ACT Aspire Practice
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.
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑢𝑒 𝑐𝑎𝑟𝑑𝑠
𝑡𝑜𝑡𝑎𝑙
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.
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑢𝑒 𝑐𝑎𝑟𝑑𝑠 𝑛𝑜𝑤
𝑛𝑒𝑤 𝑡𝑜𝑡𝑎𝑙
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.
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑦𝑜𝑢 𝑠𝑒𝑒
𝑡𝑜𝑡𝑎𝑙
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?
𝐶 = 2𝜋𝑟
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?
𝐴 = 𝜋𝑟 2
ACT Aspire Practice
23. The diameter of a bike wheel is 2.5 ft. How far will the bike go in one rotation of the wheel?
𝐶 = 2𝜋𝑟
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.
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑜𝑎𝑡𝑠 𝑓𝑟𝑜𝑚 𝑀𝑎𝑠𝑠𝑎𝑐ℎ𝑢𝑠𝑒𝑡𝑡𝑠
𝑡𝑜𝑡𝑎𝑙
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.
𝑦
Check each 𝑥
ACT Aspire Practice
26. The graph below represents the price of the bananas at one store. What is the constant of
proportionality?
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
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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.
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?
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.
30. 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.
ACT Aspire Practice
31. 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?
Hint: Remember to add the % of increase to 100%---then change this percent to a decimal –multiply it
by 48. This is your answer.
32. 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.
33. Is “p – q = p + (-q)?” Example: Is 54 – 82 = 52 + (-82)?
ACT Aspire Practice
34. If I have an expression such as 4 + -9, in what direction would I move on a number line and
why?
35. 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.
36.
-3 + (-5)
37. 7 – 12= ____________
38. -5 – (-9) =___________
39. 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)
ACT Aspire Practice
40. 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.
41. 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.
42. Write an equivalent expression for 3(x – 5) -12.
43. Suzanne thinks the two expressions 2(3a – 2) + 4a and 10a – 2 are equivalent? Is she correct?
Explain why or why not?
44. Can you write the perimeter of the following rectangle two different ways?
ACT Aspire Practice
45. 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.
46. The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
47. 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.
5
4
48. Solve 𝑛 − 9 = −24
ACT Aspire Practice
49. 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 tshirts she can purchase.
50. 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.
51. Solve
−3
𝑥
4
− 2 ≥ 11 and graph on a number line.
ACT Aspire Practice
52.
Find the dimensions of the master bedroom. Then calculate the actual area of the
master bedroom in the blueprint shown below?
53. If there are 180 degrees in a triangle, find the missing measure below.
ACT Aspire Practice
54. 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 supplementary to x.
55. 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.
ACT Aspire Practice
56. Find the area of a triangle with a base length of three units and a height of four units.
Formula is 𝐴 =
1
𝑏ℎ
2
𝑜𝑟
𝑏ℎ
2
57. Find the area of the trapezoid below.
Formula is 𝐴 =
1
ℎ
2
(𝑏𝑎𝑠𝑒 1 + 𝑏𝑎𝑠𝑒 2)
𝑏𝑎𝑠𝑒 1+𝑏𝑎𝑠𝑒 2
)
2
𝑜𝑟 ℎ (
The bases are the two parallel sides and “h” is height. The height will always form a right angle
with the bases.
58.
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
59.
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