Mcas Review: Number Sense and Operations

MCAS REVIEW: NUMBER SENSE AND OPERATIONS 2007, Mathematics - Grade 10 Question 1: Multiple-Choice Reporting Category: Number Sense and Operations Standard: 10.N.2

What is the value of the expression below?

4(23 – 7) – 52 A. –21 B. –14 C. 1 D. 2 9

2007, Mathematics - Grade 10 Question 2: Multiple-Choice Reporting Category: Number Sense and Operations Standard: 10.N.3

Which of the following is closest to the value of ? A. 11 B. 12 C. 70 D. 72

C. 8 D. 14

Which of the following statements is true? A. π = B. π > C. π = D. π >

Which of the following is closest to the cube root of 150? A. 5 B. 12 C. 15 D. 50

2007, Mathematics - Grade 10 Question 14: Multiple-Choice

2 Reporting Category: Number Sense and Operations Standard: 10.N.2

What is the value of the expression below? 5|4 – 6| – (–3) A. –13 B. –7 C. 13 D. 17

2007, Mathematics - Grade 10 Question 21: Open-Response Reporting Category: Number Sense and Operations Standard: 10.N.2

The distance, d, in feet, that a dropped rock falls in t seconds can be estimated using the formula below.

d = 16t2

Use the formula to answer the following questions. a. What is the distance, in feet, that a dropped rock will fall in 10 seconds? Show your work. b. What is the ratio of the distance a dropped rock will fall in 30 seconds as compared to the distance a dropped rock will fall in 10 seconds? Show your work. c. How many seconds will it take a dropped rock to fall 144 feet? Show your work. d. To the nearest tenth of a second, how many seconds will it take a dropped rock to fall 80 feet? Show your work.

3 What is the value of the expression below?

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

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)

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 2006, Mathematics - Grade 10 Question 7: Multiple-Choice Reporting Category: Number Sense and Operations Standard: 10.N.1

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)

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

|−10 + 6| − |32 − 5| A. −17 B. −5

5 C. 0 D. 3

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

2006, Mathematics - Grade 10 Question 15: Short-Answer Reporting Category: Number Sense and Operations Standard: 10.N.2

(8 − 4)2 + 8 ÷ 4

2006, Mathematics - Grade 10 Question 20: Open-Response

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 and use them to show 7w + z is not equal to 7 + z. Show your that w work. 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.

Shirley bought a newspaper every day for 40 weeks.

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

7  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

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

2005, Mathematics - Grade 10 Question 4: Multiple-Choice Reporting Category: Number Sense and Operations

8 Standard: 10.N.2

|23 − 32| A. 0 B. 1 C. 2 D. 3

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)

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

|−10 + 6| − |32 − 5| A. −17 B. −5 C. 0 D. 3

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

10 C. 300 feet D. 400 feet

(8 − 4)2 + 8 ÷ 4

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 and use them to show 7w + z is not equal to 7 + z. Show your that w work. c. In Mistake C, Rick factored incorrectly.

11  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.

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

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

2005, Mathematics - Grade 10 Question 1: Multiple-Choice

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

|23 − 32| A. 0 B. 1 C. 2 D. 3

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

13 C. 2.1 D. 2.9

In which equation below is the solution equal to the multiplicative inverse of

? A. • r = 1 B. • r = C. • r = 0 D. • r = −1

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

At a fish market, Mr. Estes bought several pounds of cod that was on sale for

14 $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

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.

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?

15 In a report on the history of irrational numbers, Celine compared three different values that have been used to approximate π. The values are listed below.

Egyptian approximation

Chinese approximation

Archimedes’ approximation (Greek)

a. Celine compared , the approximation used by the Egyptians, to , a value that she

often uses for π. She converted both and to decimals rounded to four decimal places

(nearest ten-thousandth). To the nearest ten-thousandth, what is the absolute value of the

difference between and ? Show or explain how you got your answer.

b. Celine also compared , the approximation used by the Chinese, to . She converted

to a decimal rounded to four decimal places (nearest ten-thousandth). To the nearest

ten-thousandth, what is the absolute value of the difference between and ? Show or

explain how you got your answer.

c. Celine knows that π ≈ 3.1415927. Place the four numbers, , , , and π in order

from least to greatest. Explain your reasoning.

6(52 − 5) A. 25 B. 30 C. 120 D. 145

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

17 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

The Sun is approximately 93,000,000 miles from Earth. Light travels approximately 186,000 miles per second.

Which of the following is closest to the number of seconds it takes light to travel from the Sun to Earth? A. 0.005 second B. 0.050 second C. 500 seconds D. 5000 seconds

6(5 − 3) − 4(2 + 5 − (3 − 2))

18 A. −15 B. −12 C. 4 D. 8

Which of the following is closest to ? A. 6.7 B. 7.3 C. 7.7 D. 8.3

Each of the statements below is true for particular values of real numbers p, t, v, and z.

v • p = v and v ≠ 0 8 • z = p v + 5 = t t + p = p

a. What is the numerical value of p? Write the equation or equations you used to find its numerical value and explain your reasoning. b. What is the numerical value of t? Write the equation or equations you used to find its numerical value and explain your reasoning. c. What is the numerical value of v? Write the equation or equations you used to find its numerical value and explain your reasoning.

d. What is the numerical value of z? Write the equation or equations you used to find its numerical value and explain your reasoning.

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

Ralph simplified the expression

Which of the following properties of the real numbers did Ralph use? A. associative property of multiplication B. commutative property of multiplication C. distributive property D. multiplicative identity property

Bailey noticed that many of the students at her school had red hair. She randomly chose 25 of the students in her school and found that 2 of them had red hair. If Bailey’s sample is representative, which of the following is closest to the number of the 2200 students at her school who have red hair? A. 44 B. 88

20 C. 176 D. 200

Alison’s car gets about 32 miles per gallon of gas. If gas prices range from $1.80 to $2.10 a gallon, which of the following is closest to the amount of money Alison will spend on gas for a 1200-mile road trip this summer? A. $40 B. $55 C. $75 D. $240

A book is 1 inch thick, not including the cover. If the book contains 364 sheets of paper, which measure is closest to the thickness of one sheet of paper? A. 0.003 in. B. 0.030 in. C. 0.300 in. D. 0.364 in.

What is the simplified form of the expression ? A. 15 B. 45 C. 75

21 D. 225

Which point most closely indicates the location of on the number line below?

A. W B. X C. Y D. Z

Which of the following is closest to the value of ? A. 1.1 B. 2.8 C. 6.0 D. 6.3

What is the solution to the equation = 16?

22 2003, Mathematics - Grade 10 Question 22: Multiple-Choice Reporting Category: Number Sense and Operations Standard: 10.N.4

Water is flowing from a 1.5-inch nozzle with water pressure of 65 pounds per square inch. The rate (in gallons per minute) at which the water flows from this nozzle is represented by the expression 29.7 x (1.5)2 . What is the approximate rate at which the water flows? A. 239 gallons per minute B. 293 gallons per minute C. 359 gallons per minute D. 539 gallons per minute

Which of the following equations is false for all positive values of n? A. n2 = n(n) B. n2 = n(−n) C. n2 = −n(−n) D. n2 =

An art collector paid $7,000 for two paintings, a portrait and a landscape, at the same auction. Each painting cost $3,500.

a. The collector predicts that the portrait will increase in value by $600 per year. If she is correct, how many years after the date of purchase will the value of the portrait painting first be at least twice its original cost? Show or explain how you obtained your answer. b. Two years after the date of purchase, the portrait was appraised at $4900. What was the percent of increase from the collector’s purchase price to the appraised value? Show or explain how you obtained your

23 answer. c. The collector predicts that the value of the landscape painting will increase by 15% per year. If she is correct, what will its value be one year after the date of purchase? Show or explain how you obtained your answer. d. Assume that the landscape painting continues to increase in value according to the collector’s prediction. How many years from the date of purchase will its value first be twice its original cost? Show or explain how you obtained your answer.