1. ACT ASPIRE EXPRESSIONS
DAY 1
PROBLEM SOLVING EXPRESSIONS

2. Multiple Choice #1
As the team’s fundraisers, Agnes and Betty both sold candy bars. At the end of the fundraiser, Agnes determined that she sold 8 more candy bars than Betty sold. If Agnes and Betty sold a total of 348 candy bars, how many did Betty sell?
A B C D E
Answer is E

3. Multiple Choice #2 Answer is B
Mrs. Salinas is making a test for her history class. There are these types of questions on the test: fill-in-the-blank, multiple-choice, and essay. So far, Mrs. Salinas has written 10 fill-in-the-blank, 21 multiple-choice, and 3 essay questions for the test. Which of the following can be added to the test so that exactly 3/5 of the test will be multiple-choice questions?
A 3 fill-in-the-blank and 2 essay questions
B 2 fill-in-the-blank, 3 multiple-choice, and 1 essay question
C 4 multiple-choice and 3 essay questions
D 2 fill-in-the-blank, 1 multiple-choice, and 3 essay questions
E 5 fill-in-the-blank, 2 multiple-choice, and 1essay question
Answer is B

4. Open-Ended #3
Sydney played a video game 43 times last year. He did not lose more than 2 games in a row last year. What is the greatest possible number of video games that Sydney could have lost last year? Show your work and explain your reasoning.
Answer is 29

5. Multiple Choice #4 A B C D E 432 348 347 300 288 Answer is B
Marina’s school filled 4⅚ buses to take people on a trip to the country. Each bus holds 72 people. How many people rode the buses on the trip?
A B C D E
Answer is B

6. Multiple Choice #5 A B C D E 400 330 210 100 21 Answer is C
Which number is closest to 33% of 700?
A B C D E
Answer is C

7. Open-Ended #6
A company that rents cars will rent a small car for $30 per day. Another company will rent the same type of car for $20 per day plus $0.08 for each mile driven. What is the number of miles per day at which the rental fees will be the same? Show your work and explain your reasoning.
Answer is 125

8. Multiple Choice #7 A B C D E 17 19 26 41 53 Answer is A
Ingrid’s favorite number is a prime number between 0 and 50. If 8 is subtracted from the number, it becomes a multiple of 9.
What is Ingrid’s favorite number?
A B C D E
Answer is A

9. Multiple Choice #8 A B C D E 6 ¼ 6 ¾ 7 ½ 6 7⅛ Answer is D
Mark shrunk a picture to ¾ of its original size. The height of the original picture was 8 ¼ inches. What is the height of the copy?
A B C D E
6 ¼ 6 ¾ 7 ½ ⅛
Answer is D

10. Constructed Response #9
The Venn Diagram represents students at XYZ Middle School. If one student is selected at random, what is the probability they will be high in writing only.
Answer is 12/200 or 6%

11. Constructed Response #10
There are three different flavors of fruit juice in a cooler. There is the same number of bottles of apple juice as bottles of grapefruit juice. There are 4 more bottles of orange juice than the other kinds of juice combined. There is a total of 60 bottles of juice. How many bottles of orange juice are in the cooler? Show your work and explain your reasoning.
Answer is 32

12. ACT ASPIRE EXPRESSIONS
DAY 2
Problems With Exponents
Look up the laws of exponents……and write down some info about each
(1) Product of Powers
(2) Quotient of Powers
(3) Power of Powers
Also what does it mean to have a negative exponent on a base such as 3⁻²?

13. Multiple Choice #1 A B C D E 2⁶ 2⁷ 2⁸ 2⁹ 2¹⁰ Answer is B
Which of the following is an equivalent way of expressing 2⁴ • 2 • 2²?
A B C D E
2⁶ 2⁷ 2⁸ 2⁹ 2¹⁰
Answer is B

14. Multiple Choice #2 A B C D E 616 164 6⁰ 610 6⁶ Answer is E
Which of the following is equivalent to 6⁸ ÷ 6²?
A B C D E
⁰ ⁶
Answer is E

15. Open-Ended #3
Simplify the following expression.
Answer is 62½

16. Answer is E Multiple Choice #4 A B C D E 48•42 44•44 4⁴•4⁵•4⁶ 432 421
Which of the following is equivalent to 416?
A B C D E
48•42 44• ⁴•4⁵•4⁶
Answer is E

17. Multiple Choice #5 A B C D E 10.27 1.0212 3 • 1.024 3 • 1.0212 NH
After 3 years, the value of a savings bond was (1.02⁴)³ times larger than its original value. What is the simplified form of (1.024)3
A B C D E
• • NH
Answer is B

18. Multiple Choice #6 A 405 ft wide by 405 ft long
Which of the following could be the length and width of a rectangular-shaped parking lot with an area of 1,048,576 square feet?
A 405 ft wide by 405 ft long
B 164 ft wide by 166 ft long
C 85 ft wide by 85 ft long
D 44 ft wide by 46 ft long
E 2⁸ ft wide by 4² ft long
Answer is D

19. Constructed Response #7
If ab and a = 7 and b = -2, what is the answer in simplest form.
1/49

20. Answer is C Multiple Choice #8 NH
Which of the following is equivalent to ?
A B C D E NH
Answer is C

21. Multiple Choice #9 A 26• 26• 26 B 219• 21 C 26• 23 D 29• 22• 21
A parking lot has an area of 218 square feet. Which of the following is equivalent to 218?
A 26• 26• 26
B 219• 21
C 26• 23
D 29• 22• 21
E 2¹²• 2⁸
Answer is A

22. Multiple Choice #10 A n + 5 B n x 5 C n + n + n + n + n
When n > 1, n⁵ = ?
A n + 5
B n x 5
C n + n + n + n + n
D n x n x n x n x n
E n⁵ x n⁵ x n⁵ x n⁵ x n⁵
Answer is D

23. Constructed Response #11
Simplify the following expression leaving your answer in terms of a fraction in simplest form:
-1³ + 3⁻¹ - 5⁻²
Answer is -53/75

24. ACT ASPIRE EXPRESSIONS
DAY 3
Problems With Order of Operations and Distributive Property

25. Multiple Choice #1 A 3k + 9 B 7k + 9 C 12k + 5 D 12k + 20 E 10k + 5
Each side of a square measures (3k + 5) units, and its perimeter can be expressed as 4(3k + 5) units. Which of the following is another way of expressing this perimeter?
A 3k + 9
B 7k + 9
C 12k + 5
D 12k + 20
E 10k + 5
Answer is D

26. Multiple Choice #2 A ⅜ of $1 million B ⅓ of $1 million
Diego is a contestant on a television show called “You Choose the Deal.”He must choose his prize from among the following dollar amounts. Which choice will give Diego the greatest dollar amount?
A ⅜ of $1 million
B ⅓ of $1 million
C 0.30 of $1 million
D 35% of $1 million
E $333,000
Answer is A

27. Multiple Choice #3 A 16m + 9 B 31m C 10m + 9 D 19m E 42m + 10.3
Which is equivalent to the expression below?
4(12m ÷ 3) + 9 — 2(3m)
A 16m + 9
B 31m
C 10m + 9
D 19m
E 42m
Answer is C

28. Open-Ended #4
If m = 4 and n = -5, what is the value of the expression below?
2m3 - 3n2
Answer is 53

29. Multiple Choice #5 A -12b B -3b C 6b D 2b E -2b Answer is A
Which is equivalent to the expression shown below?
4 • 3b — 6 • 4b
A -12b
B -3b
C 6b
D 2b
E -2b
Answer is A

30. Multiple Choice #6 A .95 B 3.8 C 4.1 D 7.4 E 9.8
What is the value of the expression below if x = 4, p = 9, and q = 12?
A .95
B 3.8
C 4.1
D 7.4
E 9.8
Answer is B

31. Open-Ended #7
If p = 3 and q = 2, what is the value of the expression below?
q⁻² — p⁴ + (p + q)3
Answer is 44¼

32. Multiple Choice #8 A 2x + 11 B 2x + 14 C 10x + 3 D 10x + 30 E 14x
Thomas and Audrey ordered 1 salad for $8, 2 pizzas for x dollars each, and 2 glasses of juice for $3 each. Their total cost in dollars can be represented by the expression 8 + 2(x + 3).
Which expression is equivalent to 8 + 2(x + 3)?
A 2x + 11
B 2x + 14
C 10x + 3
D 10x + 30
E 14x
Answer is B

33. Multiple Choice #9 A y + 5y B -2y² + 5y C -2y + 3y + 12 D 2y² + 5
Which is equivalent to the expression shown below?
4y — 2y(y) + 10y ÷ 2y
A y + 5y
B -2y² + 5y
C -2y + 3y + 12
D 2y² + 5
E -2y² + 4y + 5
Answer is E

34. Constructed Response #10
If k = 5 and m = 16, what is the value of the expression below?
k3 + [(m ÷ 4) + 32 • 20]
Answer is 309