MCAS Number Sense

Multiple Choice (No Calculators)

1. What is the value of the expression below?

15 (4 + 8) 2 (2 + 1) − 1 A. 17 B. 36 C. 45 D. 60

2. Which of the following expressions has the greatest value? A. (6 + 6) • 2 ÷ 3 − 1 B. 6 + 6 • 2 ÷ 3 − 1 C. 6 + 6 • 2 ÷ (3 − 1) D. 6 + 6 • (2 ÷ 3 − 1)

3. Which of the following is equivalent to the expression below?

(39 − 51)3

A. |51 − 39|3 B. −(39 − 51)3 C. (51 − 39)3 D. −|39 − 51|3 4. Laura correctly used a property of real numbers to calculate the exact value of the product shown below.

(840)(998)

Which of the following demonstrates a property that Laura could have used? A. (838)(1000) B. (838)(1000) + 2 C. (840)(1000) − (840)(2) D. (840)(1000) − (2) (1000)

5. Which of the following expressions has a value of 64? A.

|−10 + 6| − |32 − 5| A. −17 B. −5 C. 0 D. 3 7. The town park is shaped like a square and has an area of 43,560 square feet, as shown below.

Town Park

43,560 square feet

The expression below can be used to find the length, in feet, of one side of the park.

Which of the following is closest to the length of one side of the park? A. 100 feet B. 200 feet C. 300 feet D. 400 feet

8. Shirley bought a newspaper every day for 40 weeks.

 Monday through Saturday, she paid $0.35 each day for her newspaper.  Each Sunday, she paid $1.00 for her newspaper.

What total amount of money did Shirley pay for her newspapers during the 40-week period? A. $42.10 B. $124.00 C. $242.10 D. $324.00 9. Which of the following properties of real numbers is demonstrated by the equation below?

a(x + y) = ax + ay A. associative property of addition B. commutative property of addition C. inverse property of addition D. distributive property

(32 + 3)(32 − 3) A. 27 B. 72 C. 81 D. 90

|23 − 32| A. 0 B. 1 C. 2 D. 3

12. The Golden Ratio is defined by the expression shown below. Which of the following is closest to the value of the ratio? A. 1.1 B. 1.6 C. 2.1 D. 2.9

13. In which equation below is the solution equal to the multiplicative inverse of ? A. • r = 1 B. • r = C. • r = 0 D. • r = −1

14. Which of the following is closest to ? A. 5 B. 12 C. 120 D. 1200

15. At a fish market, Mr. Estes bought several pounds of cod that was on sale for $3.59 per pound. The total cost of the cod that he bought was $28.63.

Which of the following is closest to the amount of cod that Mr. Estes bought?

A. 6 pounds B. 7 pounds C. 8 pounds D. 9 pounds

16. Point X is graphed on the number line as shown below.

Which of the following numbers is closest to the location of point X? A. B. C. D.

6(52 − 5) A. 25 B. 30 C. 120 D. 145 18. Which statement is not true? A. 43 < 70 < 53 B. 2(52) < 70 < 3(52) C. 82 < 70 < 92 D. 33 < 70 < 43

−3 |6 − 10 | + 4 A. −16 B. −8 C. 12 D. 16

20. A certain car averages 28 miles per gallon. Gasoline costs $1.11 per gallon. Which of the following is closest to the number of miles the car would be expected to go on $250 worth of gasoline?

A. 400 miles B. 6,000 miles C. 12,000 miles D. 30,000 miles

Short Answer (No Calculators)

(8 − 4)2 + 8 ÷ 4 22. On an airline, approximately 10% of the airline passengers who are booked for a flight do not show up for the flight. The airline has booked 160 passengers for a flight with maximum seating of 135. How many of the 160 passengers booked for this flight will not have a seat, assuming 10% of the booked passengers do not show up?

23. A cube has a volume of 64 cubic inches. What is the length, in inches, of each edge of the cube?

24. What is the solution to the equation = 16?

Open Response (No Calculators)

1. Barry found the mistakes shown below when he checked his younger brother Rick's mathematics homework.

Rick's Homework Mistakes Mistake A: (x + y)2 = x2 + y2

7w  z Mistake B: = 7 + z w

Mistake C: n2 + n + 1 = (n + 1)(n + 1)

Barry explained that it would be possible to choose values for the variables, substitute them into Rick's equations, and show that the equations are not true. a. Barry asked his brother to let x = 3 and y = 4 and evaluate both sides of the equation in Mistake A.

 What is the value of (x + y)2 when x = 3 and y = 4? Show your work.  What is the value of x2 + y2 when x = 3 and y = 4? Show your work.

 Use your calculations to explain Rick's mistake. b. In Mistake B, Rick divided incorrectly. Choose a value for w and a value for z 7w  z and use them to show that is not equal to 7 + z. Show your work. w c. In Mistake C, Rick factored incorrectly.

 Choose a positive value for n and use it to show that n2 + n + 1 is not equal to (n + 1)(n + 1). Show your work.

 Choose a negative value for n and use it to show that n2 + n + 1 is not equal to (n + 1)(n + 1). Show your work.