2016-MATH 1 Released Form Revised...NC MATH 1—RELEASED ITEMS 3 Go to the next page. 2 What...

Remote Learning Packet #3

Math 1

Remote Day Activity Description

#21 Review Day 21: Linear Functions

#22 Review Day 22: Solving Systems of Equations and Inequalities

#23 Review Day 23: Sequences

#24 Review Day 24: Exponents and Exponential Functions

#25 Review Day 25: Geometry and Algebra

#26 Review Day 26: Quadratic Equations and Functions

#27 Mixed Review Day 27: One Hundred and Two(102) Problems (Part 1)

#28 Mixed Review Day 28: One Hundred and Two(102) Problems (Part 2)

#29 Mixed Review Day 29: NC Math 1 Released Items 2018

#30 Mixed Review Day 30: NC Math 1 Released Items 2016-2017

Linear Functions: EOC Prep Name: ___________________________

MATH 1 Day 21 Review

Directions: The following questions are sample items similar to those found on the EOC Exam. Answer each to

the best of your ability.

1.

2.

3.

4. *Which equation is equivalent to y + 2(x + 5) = 4x + 5

a) y = 2x + 20

b) y = -4x + 5

c) y = 2x – 5

d) y = 5x + 2

5. *

6. *

7. *

8.

9. *

10.

11. * 12. *

13.

14.

Systems of Equations & Inequalities: EOC Prep




1.

2.

3.

4.

5.

6.

7.

8. Which is the graph of the solution set of the system of inequalities?

x 2y 10

2x y 0

9.

10.

11.

Sequences: EOC Prep Name: ___________________________




1.

2.

3.

Exponents and Exponential Functions: EOC Prep




1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Geometry and Algebra: EOC Prep Name: ___________________________




1.

2.

3.

4. Find the length of the missing side of the triangle below.

5. Approximate the length of the perimeter of the quadrilateral below.

6.

7.

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11.

12.

Quadratic Equations and Functions: EOC Prep

Math 1 Review Day 26



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EOC Review Packet Name: ___________________________

Math 1

Directions: The following questions are sample items similar to those found on the EOC Exam. Answer each to the

best of your ability. Show all work on a separate sheet of paper.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

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97. 98.

99. 100.

101. 102.

Copyright 2016 by the North Carolina Department of Public Instruction. All rights reserved.�

Academic Services and Instructional Support

Division of Accountability Services | North Carolina Testing Program

Released Items

North Carolina

READY End-of-Course

Assessment

NC Math 1

2016–2017

NC MA T H 1—RE L E A S E D IT E M S

1 Go to the next page.

1 Jessie’s bus ride to school is 5 minutes more than 2

3 the time of Robert’s bus ride.

Which graph shows the possible times of Jessie’s and Robert’s bus rides?

Answer choices C and D are on the following page.

B

10

5

0

10

15

20

25

30

35

40

45

50

5 15 20 25 30 35 40 45 50x

y

Robert’s Bus Ride (minutes)

Jessie

’s B

us R

ide

(m

inutes)

A

10

5

0

10

15

20

25

30

35

40

45

50

5 15 20 25 30 35 40 45 50x

y


Jessie

’s B

us R

ide

(m

inutes)



10

5

0

10

15

20

25

30

35

40

45

50

5 15 20 25 30 35 40 45 50x

y


Jessie

’s B

us R

ide

(m

inutes)

10

5

0

10

15

20

25

30

35

40

45

50

5 15 20 25 30 35 40 45 50x

y


Jessie

’s B

us R

ide

(m

inutes)

D

C



2 What scenario could be modeled by the graph below?

A The number of pounds of apples, y, minus two times the number of pounds of oranges, x, is at most 5.

B The number of pounds of apples, y, minus half the number of pounds of oranges, x, is at most 5.

C The number of pounds of apples, y, plus two times the number of pounds of oranges, x, is at most 5.

D The number of pounds of apples, y, plus half the number of pounds of oranges, x, is at most 5.

3 Which expression is equivalent to t2 – 36?

A (t – 6)(t – 6)

B (t + 6)(t – 6)

C (t – 12)(t – 3)

D (t – 12)(t + 3)

0

1

1 2 3 4 5 6

2

3

4

5

6

y

x



4 Which is the graph of the function f(x) = 4x2 – 8x + 7?

Answer choices B, C, and D are on the following pages.

x

y

+8

+7

+6

+5

+4

+3

+2

+1

–1

–2

–3

–4

–5

–6

–7

–9

–8

+9

+10

+100 +8+7+6+5+4+3+2+1–1–2–3–4–5–6–7–8–9 +9–10

–10

A



Answer choices C and D are on the following pages.

x

y

+8

+7

+6

+5

+4

+3

+2

+1

–1

–2

–3

–4

–5

–6

–7

–9

–8

+9

+10

+100 +8+7+6+5+4+3+2+1–1–2–3–4–5–6–7–8–9 +9–10

–10

B



Answer choice D is on the following page.

x

y

+8

+7

+6

+5

+4

+3

+2

+1

–1

–2

–3

–4

–5

–6

–7

–9

–8

+9

+10

+100 +8+7+6+5+4+3+2+1–1–2–3–4–5–6–7–8–9 +9–10

–10

C



x

y

+8

+7

+6

+5

+4

+3

+2

+1

–1

–2

–3

–4

–5

–6

–7

–9

–8

+9

+10

+100 +8+7+6+5+4+3+2+1–1–2–3–4–5–6–7–8–9 +9–10

–10

D



5 The floor of a rectangular cage has a length 4 feet greater than its width, w. James

will increase both dimensions of the floor by 2 feet. Which equation represents the new area, N, of the floor of the cage?

A N = w2 + 4w

B N = w2 + 6w

C N = w2 + 6w + 8

D N = w2 + 8w + 12

Questions 6 through 13 require you to write your answers in the boxes provided on your answer sheet. Write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. Fill in only one circle in each column. 6 Two boys, Shawn and Curtis, went for a walk. Shawn began walking 20 seconds

earlier than Curtis.

• Shawn walked at a speed of 5 feet per second.

• Curtis walked at a speed of 6 feet per second.

For how many seconds had Shawn been walking at the moment when the two boys had walked exactly the same distance?

7 The math club sells candy bars and drinks during football games.

• 60 candy bars and 110 drinks will sell for $265.

• 120 candy bars and 90 drinks will sell for $270.

How much does each candy bar sell for?

(Note: Express the answer in dollars.cents.)



8 What is the smallest of 3 consecutive positive integers if the product of the smaller

two integers is 5 less than 5 times the largest integer?

9 The function

2( ) 5 20 60f t t t−= + + models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

10 Two times Antonio’s age plus three times Sarah’s age equals 34. Sarah’s age is

also five times Antonio’s age. How old is Sarah?

11 Suppose that the function f(x) = 2x + 12 represents the cost to rent x movies a

month from an internet movie club. Makayla now has $10. How many more dollars does Makayla need to rent 7 movies next month?

12 The larger leg of a right triangle is 3 cm longer than its smaller leg. The

hypotenuse is 6 cm longer than the smaller leg. How many centimeters long is the smaller leg?


10

13 Katie and Jennifer are playing a game.

• Katie and Jennifer each started with 100 points.

• At the end of each turn, Katie’s points doubled.

• At the end of each turn, Jennifer’s points increased by 200.

At the start of which turn will Katie first have more points than Jennifer?

This is the end of the calculator inactive released items.



14 A school purchases boxes of candy bars.

• Each box contains 50 candy bars.

• Each box costs $30.

How much does the school have to charge for each candy bar to make a profit of $10 per box?

A $0.40

B $0.50

C $0.80

D $1.25

15 Energy and mass are related by the formula E = mc2.

• m is the mass of the object.

• c is the speed of light.

Which equation finds m, given E and c?

A 2m E c= −

B 2m Ec=

C 2cm

E=

D 2Emc

=



16 Suppose that the equation V = 20.8x2 – 458.3x + 3,500 represents the value

of a car from 1964 to 2002. What year did the car have the least value? (x = 0 in 1964)

A 1965

B 1970

C 1975

D 1980

17 The table below shows the average weight of a type of plankton after several

weeks. Time

(weeks) Weight

(ounces) 8 0.04 9 0.07 10 0.14 11 0.25 12 0.49

What is the average rate of change in weight of the plankton from week 8 to

week 12?

A 0.0265 ounce per week

B 0.0375 ounce per week

C 0.055 ounce per week

D 0.1125 ounce per week



18 Dennis compared the y-intercept of the graph of the function f(x) = 3x + 5 to

the y-intercept of the graph of the linear function that includes the points in the table below.

x g(x) –7 2 –5 3 –3 4 –1 5

What is the difference when the y-intercept of f(x) is subtracted from the

y-intercept of g(x)?

A –11.0

B –9.3

C 0.5

D 5.5

19 Cell phone Company Y charges a $10 start-up fee plus $0.10 per minute, x.

Cell phone Company Z charges $0.20 per minute, x, with no start-up fee. Which function represents the difference in cost between Company Y and Company Z?

A f(x) = 0.10x− – 10

B f(x) = 0.10x− + 10

C f(x) = 10x – 0.10

D f(x) = 10x + 0.10



20 Monica did an experiment to compare two methods of warming an object. The

results are shown in the table below.

Time (Hours)

Method 1 Temperature (°F)

Method 2 Temperature (°F)

0 0 1.5 1 5 3 2 11 6 3 15 12 4 19 24 5 25 48

Which statement best describes her results?

A The temperature using both methods changed at a constant rate.

B The temperature using both methods changed exponentially.

C The temperature using Method 2 changed at a constant rate.

D The temperature using Method 2 changed exponentially.



21 Mario compared the slope of the function graphed below to the slope of the linear

function that has an x-intercept of 43 and a y-intercept of 2.−

What is the slope of the function with the smaller slope?

A 15

B 13

C 3

D 5

x

y

0

+6

+5

+4

+3

+2

+1

+1 +2 +3 +4 +5 +6–1

–1–2–3–4–5–6

–2

–3

–4

–5

–6



22 The boiling point of water, T (measured in degrees), at altitude a (measured in

feet) is modeled by the function ( ) 0.0018 212.T a a−= + In terms of altitude and temperature, which statement describes the meaning of the slope?

A The boiling point increases by 18 degrees as the altitude increases by 1,000 feet.

B The boiling point increases by 1.8 degrees as the altitude increases by 1,000 feet.

C The boiling point decreases by 18 degrees as the altitude increases by 1,000 feet.

D The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet.

23 A line segment has endpoints J(2, 4) and L(6, 8). The point K is the midpoint of

.JL What is an equation of a line perpendicular to JL and passing through K?

A y = x− + 10

B y = x− – 10

C y = x + 2

D y = x – 2

24 A triangle has vertices at (1, 3), (2, 3),−

and ( 1, 1).− − What is the approximate perimeter of the triangle?

A 10

B 14

C 15

D 16



25 The table below shows the area of several states.

State Area (thousands of square miles) Connecticut 6

Georgia 59 Maryland 12

Massachusetts 11 New Hampshire 9

New York 54 North Carolina 54 Pennsylvania 46

Delaware has an area of 2,000 square miles. Which is true if Delaware is included

in the data set?

A The mean increases.

B The range decreases.

C The interquartile range decreases.

D The standard deviation increases.

26 The table below shows the distance a car has traveled.

Minutes 25 50 75 100 125 Distance Traveled

(in miles) 20 40 60 80 100

What is the meaning of the slope of the linear model for the data?

A The car travels 5 miles every minute.

B The car travels 4 miles every minute.

C The car travels 4 miles every 5 minutes.

D The car travels 5 miles every 4 minutes.



27 The area of a trapezoid is found using the formula ( )1 2

12 ,A h b b= + where A is

the area, h is the height, and b1 and b2 are the lengths of the bases.

What is the area of the above trapezoid?

A A = 4x + 2

B A = 4x + 8

C A = 2x² + 4x – 21

D A = 2x² + 8x – 42

28 John mixed cashews and almonds.

• John bought 4 pounds of almonds for a total cost of $22.

• The cost per pound for cashews is 60% more than the cost per pound for almonds.

• John bought enough cashews that, when he mixed them with the almonds, the mixture had a value of $6.50 per pound.

Approximately what percent of the mixture, by weight, was cashews?

A 20%

B 25%

C 30%

D 35%

h = 4

x + 7b =2

x – 3b =1



29 Lucy and Barbara began saving money the same week. The table below shows the

models for the amount of money Lucy and Barbara had saved after x weeks.

Lucy’s Savings f(x) = 10x + 5

Barbara’s Savings g(x) = 7.5x + 25 After how many weeks will Lucy and Barbara have the same amount of money

saved?

A 1.1 weeks

B 1.7 weeks

C 8 weeks

D 12 weeks

30 Collin noticed that various combinations of nickels and dimes could add up to

$0.65.

• Let x equal the number of nickels.

• Let y equal the number of dimes.

What is the domain where y is a function of x and the total value is $0.65?

A {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

B {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

C {0, 1, 3, 5, 7, 9, 11, 13}

D {1, 3, 5, 7, 9, 11, 13}



31 The table below shows the cost of a pizza based on the number of toppings.

Number of Toppings (n) Cost (C)

1 $12 2 $13.50 3 $15 4 $16.50

Which function represents the cost of a pizza with n toppings?

A C(n) = 12 + 1.5(n – 1)

B C(n) = 1.5n + 12

C C(n) = 12 + n

D C(n) = 12n

32 There were originally 4 trees in an orchard. Each year the owner planted the same

number of trees. In the 29th year, there were 178 trees in the orchard. Which function, t(n), can be used to determine the number of trees in the orchard in any year, n?

A 17829( ) 4t n n= +

B 17829( ) 4t n n= −

C ( ) 6 4t n n= +

D ( ) 29 4t n n= −



33 The vertices of quadrilateral EFGH are ( 7, 3), ( 4, 6), (5, 3), and (2, 6).E F G H− − − −

What kind of quadrilateral is EFGH?

A trapezoid

B square

C rectangle that is not a square

D rhombus that is not a square

34 R is the midpoint of segment PS. Q is the midpoint of segment RS.

P is located at (8, 10), and S is located at (12, 6).− What are the coordinates of Q?

A (4, 2)

B (2, 8)−

C (11, 2)−

D (10, 2)

P

R

Q

S



35 The sequence below shows the total number of days Francisco had used his gym

membership at the end of weeks 1, 2, 3, and 4.

4, 9, 14, 19, ...

Assuming the pattern continued, which function could be used to find the total number of days Francisco had used his gym membership at the end of week n?

A f(n) = n + 5

B f(n) = 5n – 1

C f(n) = 5n + 4

D f(n) = n2

36 The number of points scored by a basketball player in the first eight games of a

season are shown below.

15, 35, 18, 30, 25, 21, 32, 16

What would happen to the data distribution if she scored 24, 22, 27, and 28 points in her next four games?

A The data distribution would become less peaked and more widely spread.

B The data distribution would become less peaked and less widely spread.

C The data distribution would become more peaked and less widely spread.

D The data distribution would become more peaked and more widely spread.



37 The table below shows the shoe size and age of 7 boys.

Name Shoe Size (x)

Age (y)

Tyrone 6 9 Marcel 6 11 Patrick 7 15 Bobby 8 11 Dylan 9 15 Mike 10 16

Jonathan 12 17 Approximately what percent of the boys’ ages is more than 1 year different from

the age predicted by the line of best fit for the data?

A 14%

B 29%

C 43%

D 57%


24

38 The scatterplot below shows the number of arithmetic errors 10 students made on

a quiz and the amount of time the students took to complete the quiz.

Which describes the relationship between the number of arithmetic errors the students made and the amount of time the students took to complete the quiz?

A There is a strong positive relationship between the variables.

B There is a strong negative relationship between the variables.

C There is a weak positive relationship between the variables.

D There is a weak negative relationship between the variables.

This is the end of the NC Math 1 released items.

Arit

hm

eti

c E

rro

rs

Time (minutes)

1

2

3

4

5

6

7

8

9

10

5 10 15 20 25 30 35 40 45 50 55 600

NC MATH 1—RELEASED ITEMS


NC Math 1 Released Items 2016–2017 Answer Key

Calculator Inactive

Question Number Question Type* Correct Answer Standard

1 MC B NC.M1.A-CED.2

2 MC C NC.M1.A-REI.12

3 MC B NC.M1.A-SSE.3

4 MC D NC.M1.F-IF.7

5 MC D NC.M1.A-CED.2

6 GR 120 NC.M1.A-CED.1

7 GR 0.75 NC.M1.A-REI.6

8 GR 5 NC.M1.A-CED.1

9 GR 6 NC.M1.F-IF.8a

10 GR 10 NC.M1.A-REI.6

11 GR 16 NC.M1.F-IF.2

12 GR 9 NC.M1.F-IF.8a

13 GR 4 NC.M1.F-LE.3



Calculator Active


14 MC C NC.M1.A-CED.1

15 MC D NC.M1.A-CED.4

16 MC C NC.M1.F-IF.4

17 MC D NC.M1.F-IF.6

18 MC C NC.M1.F-IF.9

19 MC B NC.M1.F.BF.1b

20 MC D NC.M1.F-LE.1

21 MC B NC.M1.F-IF.9

22 MC D NC.M1.F-LE.5

23 MC A NC.M1.G-GPE.5

24 MC B NC.M1.G-GPE.4

25 MC D NC.M1.S-ID.2

26 MC C NC.M1.S-ID.7

27 MC B NC.M1.A-APR.1

28 MC C NC.M1.A-CED.1


27


29 MC C NC.M1.A-REI.11

30 MC D NC.M1.F-IF.5

31 MC A NC.M1.F-BF.1a

32 MC C NC.M1.F-BF.1a

33 MC C NC.M1.G-GPE.4

34 MC C NC.M1.G-GPE.6

35 MC B NC.M1.F-BF.1a

36 MC C NC.M1.S-ID.3

37 MC C NC.M1.S-ID.6b

38 MC B NC.M1.S-ID.8

*Question Type: MC = multiple choice GR = gridded response (requiring numerical response)

Released Items

Published October 2018

Copyright 2018 by the North Carolina Department of Public Instruction. All rights reserved.�

Public Schools of North Carolina

Department of Public Instruction | State Board of Education

Division of Accountability Services/North Carolina Testing Program

North Carolina

End-of-Course

Assessment

NC Math 1



1 Which choice is the graph of y = (4 – x)(x + 2)?

A B

C D

x

y

0

+1

–1+1

–2–3–4–5–6–7–8

–1–2–3–4–5–6–7–8 +2 +3 +4 +5 +6 +7 +8

+2

+3

+4

+5

+6

+7

+8

x

y

0

+1

–1+1

–2–3–4–5–6–7–8

–1–2–3–4–5–6–7–8 +2 +3 +4 +5 +6 +7 +8

+2

+3

+4

+5

+6

+7

+8

x

y

0

+1

–1+1

–2–3–4–5–6–7–8

–1–2–3–4–5–6–7–8 +2 +3 +4 +5 +6 +7 +8

+2

+3

+4

+5

+6

+7

+8

x

y

0

+1

–1+1

–2–3–4–5–6–7–8

–1–2–3–4–5–6–7–8 +2 +3 +4 +5 +6 +7 +8

+2

+3

+4

+5

+6

+7

+8

RELEASED



2 In which graph does the shaded region represent the solution set for the inequality shown below?

2x – y < 4

A B C D

2

1

0

234567

89

10

1 3 4 5 6 7 8 9 10x

y

2

1

0

234567

89

10

1 3 4 5 6 7 8 9 10x

y

2

1

0

234567

89

10

1 3 4 5 6 7 8 9 10x

y

2

1

0

234567

89

10

1 3 4 5 6 7 8 9 10x

y

RELEASED



3 Which expression is equivalent to (x + 2)(3x – 3)?

A 3x2 – 6

B 3x2 + 3x – 6

C 3x2 + 6x – 6

D 3x2 + 9x – 6

RELEASED



Questions 4 through 6 are gridded response items that require you to write your answers in the boxes provided on your answer sheet. Write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. Fill in only one circle in each column. 4 A line, y = mx + b, passes through the point (1, 6) and is parallel to y = 4x + 6. What is the value of b?

5 Two functions are shown below.

f(x) = 12 • 2x

g(x) = 5x + 2

What is the largest integer value of x such that f(x) ≤ g(x)?

6 A company models its net income, in thousands of dollars, with the function f(x) = 9x2 – 54x – 144, where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0?

RELEASED



7 Joanna has a total of 50 coins in her purse.

• The coins are either nickels or quarters.

• The total value of the coins is $7.10.

Which system of equations can be used to determine the number of nickels, n, and quarters, q, that Joanna has in her purse?

A n + q = 50 0.05n + 0.25q = 7.10

B n + q = 7.10 50n + 50q = 7.10

C 0.05n + 0.25q = 50 n + q = 7.10

D 0.05n + 0.25q = 7.10 50n + 50q = 7.10

8 The function f(x) = –0.25x + 5 models the height of a candle x seconds after it is lit. What is the meaning of the y-intercept of the function?

A the initial height of the candle

B the final height of the candle

C the rate at which the candle is burning

D the amount of time it will take the candle to burn

RELEASED



Questions 9 and 10 are gridded response items that require you to write your answers in the boxes provided on your answer sheet. Write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. Fill in only one circle in each column. 9 The total cost, in dollars, of membership in a fitness center is given by the function c(m) = 20m + 40, where m is the number of months a person is a member. In dollars, how much is the cost of a membership for 1 year?

10 Water is being pumped into a 10-foot-tall cylindrical tank at a constant rate.

• The depth of the water is increasing linearly.

• At 1:30 p.m., the water depth was 2.4 feet.

• It is now 4:00 p.m., and the depth of the water is 3.9 feet.

What will the depth (in feet) of the water be at 5:00 p.m.?

RELEASED



11 Sally works at a store.

• x represents Sally’s monthly paycheck, and y represents her monthly savings.

• Sally will save at least $20 more than half of her paycheck each month.

• She can save at most $80 more than two-thirds of her paycheck each month.

• Her paycheck each month is at least $1,200, but no more than $1,850.

Which system of inequalities represents these constraints?

A

1223

20

801,2001,850

x y

x yyy

≤ +

≥ +≤≥

B

1223

20

801,2001,850

y x

y xxx

≥ +

≤ +≥≤

C

1223

20

801,2001,850

y x

y xxx

≤ +

≥ +≤≥

D

1223

20

801,2001,850

x y

x yyy

≥ +

≤ +≥≤

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12 A company uses the formula T = 581s + 150p to determine the total cost to purchase s computers and p printers. Which formula can be used to determine the number of printers purchased, given the total cost, T, and the number of computers purchased?

A 581150Tp s= −

B 581150

sp T= −

C 581150

T sp −=

D 581 150p T s= − −

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9

Questions 13 through 15 are gridded response items that require you to write your answers in the boxes provided on your answer sheet. Write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. Fill in only one circle in each column. 13 What is the value of the positive zero of the function, f, defined by f(x) = x2 – 121?

14 What is the value of x in the system of equations shown below?

5x + 4y = 1

y = 1 – x

15 What is the value of the smaller zero of the function f(x) = 2x2 – 8x – 24?

This is the end of the calculator inactive released items.

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10

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16 A statistician collected the following data to explore the relationship between two variables, x and y.

x y

2.3 11.0

4.2 16.5

5.1 19.2

6.4 23.1

8.2 24.3

8.5 29.5

The statistician performed a linear regression and also plotted the residuals.

• Based on the residual plot, the statistician decided to exclude one data point.

• The statistician then performed linear regression on the set of remaining data points.

• The result was that the new linear model fit the remaining data more closely than the original model fit the original data.

Which data point did the statistician exclude?

A (2.3, 11.0)

B (4.2, 16.5)

C (6.4, 23.1)

D (8.2, 24.3)

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17 A set of nine data points is shown below.

8, 11, 12, 10, 9, 7, 5, 3, 9

Which statement is true if a tenth data point of 45 is added to the data set?

A The mean and median will both increase.

B The mean will increase and the median will decrease.

C The mean will increase and the median will remain the same.

D The mean and median will both decrease.

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Questions 18 and 19 are gridded response items that require you to write your answers in the boxes provided on your answer sheet. Write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. Fill in only one circle in each column. 18 What is the distance, in units, between the y-intercept of f(x) = x2 + 7x – 18 and the y-intercept of the linear function that passes through the points shown in the table below?

19 What is the value of x in the equation shown below?

2(x + 8) – 4x = 10x + 4

x g(x) –5 2

10 11

25 20

60 41

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20 This is a paper/pencil copy of an online technology enhanced item.

21 Which equation represents the line that is perpendicular to the graph of 4x + 3y = 9 and passes through (–2, 3)?

A 3x – 4y = –18

B 3x + 4y = 18

C 3x – 4y = –6

D 3x + 4y = 6

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22 A club began with 3 members. Each month, each member brought one new member. Which function can be used to determine the number of members x months after the club began?

A f(x) = 2x + 3

B f(x) = 3x + 1

C f(x) = 1.5(2)x

D f(x) = 3(2)x

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Questions 23 through 25 are gridded response items that require you to write your answers in the boxes provided on your answer sheet. Write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. Fill in only one circle in each column. 23 Every ten years, the Census counts how many people are living in every town in the United States.

• The 2010 Census showed that 1,000 people were living in Appleville, and 4,000 people were living in Bridgetown.

• The population of Appleville is predicted to double every ten years.

• The population of Bridgetown is predicted to increase by 1,000 every ten years.

If the predictions come true, what will be the first census year that will show Appleville with a larger population than Bridgetown?

24 Two stores have movies to rent.

• The first store charges a $12.50-per-month membership fee plus $1.50 per movie rented.

• The second store has no membership fee but charges $3.50 per movie rented.

What is the minimum number of movies a person would need to rent in a month for the first store to be a better deal?

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25 Karen has two dogs. The larger dog weighs 1.4 pounds more than the smaller dog. The combined weight of the two dogs is 12.6 pounds. What is the weight, in pounds, of the smaller dog?

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26 Which choice could be modeled by a linear function?

A the amount of money, y, in an account after x years earning 4% interest compounded annually

B the monthly cost, y, to use a cell phone for x minutes at a rate of 4 cents per minute

C the height, y, of a ball after bouncing x times, if each bounce reaches 23

the previous height

D the amount, y, of radioactive material remaining after x years when decay occurs at a rate of 30% each year

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27 Oscar planted a tomato seed in his garden. Each day he recorded the height of the tomato plant.

During which interval did the tomato plant grow the fastest?

A Day 4 to Day 6

B Day 6 to Day 8

C Day 8 to Day 10

D Day 10 to Day 12

4

1

0

2

34

56

78

9

10

2 6 8 10 12 14 16 18 20x

yIn

ches

Days

Growth of Tomato Plant

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Questions 28 and 29 are gridded response items that require you to write your answers in the boxes provided on your answer sheet. Write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. Fill in only one circle in each column. 28 The function a(n) = 3n – 7 represents the value of the nth term in a sequence. What is the sum of the 1st and 5th terms of the sequence?

29 The width of a rectangle is 34 its length. The perimeter of the rectangle is 420 ft.

What is the length, in feet, of the rectangle?

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31 The table below shows the U.S. average life expectancy at birth, in years, in various decades.

What is the meaning of the slope of the linear best-fit equation for the data?

A The predicted average life expectancy at birth in 1930 was about 62.7 years.

B The predicted average life expectancy at birth in 1930 was about 57.6 years.

C The average life expectancy at birth increases by about 6.7 each year.

D The average life expectancy at birth increases by about 0.2 each year.

Years since 1930

Life Expectancy at

Birth

10 62.9

20 68.2

30 69.7

40 70.8

50 73.7

60 75.4

70 77.0

80 78.7

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32 The choices below are data sets. In the choices, w is a constant. Each choice has the same mean. Which choice has the greatest standard deviation?

A w – 2, w – 1, w, w + 1, w + 2

B w – 2, w – 2, w, w + 2, w + 2

C w – 3, w – 1, w, w + 1, w + 3

D w – 3, w, w, w, w + 3

33 Abby scored 87, 93, 96, and 89 on her first four history quizzes. What score does Abby need to get on her fifth quiz to have an average of exactly 91 on her history quizzes?

A 90

B 94

C 98

D 100

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34 The perimeter of the triangle below is 8x – 6.

Which expression represents the length of QR?

A 4x – 4

B 4x – 6

C 6x – 4

D 6x – 8

35 What are the solutions to the equation 4x2 – 52x + 169 = 121?

A {1, –12}

B {–1, 12}

C {–1, –12}

D {1, 12}

P

Q

R3 – 1x

x + 1

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36 David has a rectangle and a right triangle.

• The length of the rectangle is 5 more than its width, w.

• The length of the shorter leg of the triangle is equal to the rectangle’s width.

• The length of the longer leg of the triangle is twice the length of the rectangle.

Which function, f(w), represents the combined area of the rectangle and the triangle?

A f(w) = 2w2 + 10w

B f(w) = 3w2 + 15w

C f(w) = w2 + 10w + 25

D f(w) = w2 + 15w + 50

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37 The table below shows the number of hours 7 students studied for a math test and the grade each student earned on the test.

How does Amanda’s test score compare to the score predicted using the linear best-fit model of data for a student who studied 3.50 hours?

A Amanda scored about 5 points lower than the score predicted for a student who studied 3.50 hours.

B Amanda scored about 5 points higher than the score predicted for a student who studied 3.50 hours.

C Amanda scored about 2 points lower than the score predicted for a student who studied 3.50 hours.

D Amanda scored about 2 points higher than the score predicted for a student who studied 3.50 hours.

Student Hours

Studied (x)

Test Grade

(y)

Mary 2.00 84

Jonathan 1.75 86

Susan 2.00 88

Terry 3.00 94

Patrick 3.50 95

Amanda 3.50 93

Darius 2.25 89

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39 Two functions are shown below.

f(x) = 3x + 7

g(x) = 2x + 12

What is the value of x where the graphs of f(x) and g(x) intersect?

A –22

B –5

C 5

D 22

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40 Marcus measured the height, in inches, y, of plants over the course of 3 weeks. The correlation coefficient between the number of days, x, and the height of the plants is 0.85. Which could be concluded based on the correlation coefficient of the data?

A There is a strong relationship showing that as the number of days increases, the height of the plants increases.

B There is a strong relationship showing that as the number of days increases, the height of the plants decreases.

C There is a weak relationship showing that as the number of days increases, the height of the plants increases.

D There is a weak relationship showing that as the number of days increases, the height of the plants decreases.

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Question 41 is a gridded response item that requires you to write your answer in the boxes provided on your answer sheet. Write only one number or symbol in each box and fill in the circle in each column that matches what you have printed. Fill in only one circle in each column. 41 A function is shown below.

g(x) = 19.60 + 1.74x

What is the value of g(30)?

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42 The table below shows the weights of 8 different bears at a zoo.

Type of Bear Weight (pounds)

Asiatic Black Bear 225

Black Bear 300

Brown Bear 550

Panda Bear 200

Polar Bear 1,000

Sloth Bear 300

Spectacled Bear 280

Sun Bear 100

If the weight of the polar bear is removed, which statement is true?

A The mean decreases more than the median because the polar bear is a high outlier.

B The mean decreases less than the median because the polar bear is a high outlier.

C The mean decreases more than the median because the high value balances the low value.

D The mean decreases less than the median because the high value balances the low value.

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43 The vertices of a rectangle are located at (1, 2), (5, 0), (2, –6), and (–2, –4). What is the area of the rectangle?

A 20 square units

B 30 square units

C 35 square units

D 45 square units


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45 What is the distance between the y-intercept of the function f(x) = 2x2 – 6x + 3 and the y-intercept of the linear function g represented by the table below?

A 2 units

B 3 units

C 8 units

D 9 units

x g(x) –5 15 –2 3

2 –13

5 –25

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46 The table below displays the walking heart rate and running heart rate of eight girls in beats per minute (bpm).

Using the linear best-fit model for the data, what is the predicted running heart rate of a girl whose walking heart rate is 100 bpm?

A 161 bpm

B 163 bpm

C 165 bpm

D 167 bpm

Walking Heart Rate

Running Heart Rate

66 128

72 136

74 134

78 138

80 142

84 146

86 148

88 152

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48 A rectangle has a perimeter of 64.

• Let x equal the width of the rectangle.

• Let y equal the area of the rectangle.

Which equation can be used to find the area of the rectangle?

A y = x2 – 64x

B y = –x2 + 64x

C y = x2 – 32x

D y = –x2 + 32x

49 What is the midpoint of the longest side of the triangle with vertices (1, 4), (3, 4), and (3, 6)?

A (1, 1)

B (2, 4)

C (2, 5)

D (3, 5)

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36

NC MA T H 1—RE L E A S E D IT E M S 50 The table below shows the hours, x, spent working on a new road and the distance, y, of finished road.

What is the slope of the line that fits these data?

A 3400

B 3100

C 325

D 3

This is the end of the NC Math 1 released items.

Time (hours)

Distance (miles)

50 1.5

200 6

350 10.5

400 12

650 19.5

RELEASED



NC Math 1 Released Items 2018–2019 Answer Key

Calculator Inactive

Question Number

Question Type1

Correct Answer Standard DOK2

1 MC A NC.M1.F-IF.7 2

2 MC D NC.M1.A-REI.12 2

3 MC B NC.M1.A-APR.1 1

4 GR 2 NC.M1.G-GPE.5 2

5 GR 6 NC.M1.F-LE.3 1

6 GR 8 NC.M1.F-IF.8.a 2

7 MC A NC.M1.A-CED.3 2

8 MC A NC.M1.F-LE.5 1

9 GR 280 NC.M1.F-IF.2 1

10 GR 4.5 NC.M1.A-CED.1 2

11 MC B NC.M1.A-CED.3 3

12 MC C NC.M1.A-CED.4 1

13 GR 11 NC.M1.A-SSE.3 1

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Calculator Inactive

Question Number

Question Type1


14 GR 3− NC.M1.A-REI.6 1

15 GR 2− NC.M1.F-IF.8.a 2

Calculator Active

Question Number

Question Type1


16 MC D NC.M1.S-ID.8 3

17 MC C NC.M1. S-ID.3 2

18 GR 23 NC.M1.F-IF.9 2

19 GR 1 NC.M1.A-REI.3 1

20 DD Online Only

NC.M1.A-REI.6 2

21 MC A NC.M1.G-GPE.5 2

22 MC D NC.M1.F-BF.2 2

23 GR 2040 NC.M1.F-LE.3 3

24 GR 7 NC.M1.A-CED.1 2

25 GR 5.6 NC.M1.A-REI.6 2

26 MC B NC.M1.F-LE.1 2

27 MC C NC.M1.F-IF.6 2

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Calculator Active

Question Number

Question Type1


28 GR 4 NC.M1.F-IF.2 1

29 GR 120 NC.M1.A-CED.1 2

30 TI Online Only

NC.M1.A-REI.11 1

31 MC D NC.M1.S-ID.7 2

32 MC C NC.M1.S-ID.2 3

33 MC A NC.M1.A-CED.1 2

34 MC B NC.M1.A-APR.1 1

35 MC D NC.M1.A-REI.4 1

36 MC A NC.M1.F-BF.1.b 2

37 MC C NC.M1.S-ID.6 b 2

38 TD Online Only

NC.M1.G-GPE.5 2

39 MC C NC.M1.A-REI.11 1

40 MC A NC.M1.S-ID.8 2

41 GR 71.8 NC.M1.F-IF.2 1

42 MC A NC.M1.S-ID.3 2

43 MC B NC.M1.G-GPE.4 2

44 TI Online Only

NC.M1.F-LE.1 2

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40

Calculator Active

Question Number

Question Type1 Correct Answer Standard DOK2

45 MC C NC.M1.F-IF.9 2

46 MC B NC.M1.S-ID.6.a 2

47 DD Online Only

NC.M1.S-ID.2 2

48 MC D NC.M1.A-CED.2 2

49 MC C NC.M1.G-GPE.6 2

50 MC B NC.M1.F-IF.4 1

Question Technology Enhanced Item Solution 20 One solution, infinitely many solutions, no

solution 30 (–3, –20), (2, 35) 38 3x – 13 44 Sentence 1, 3, 4 47 [15, 25, 35, 45, 55, 65],

[15, 75, 85, 95, 105, 115], [15, 25, 35, 45, 55, 115]

1Question Type: MC = multiple choice GR = gridded response (requiring numerical response)

DD = drag and drop TI = text identify TD = targeted drop

2DOK: 1 = Recall 2 = Skill/Concept

3 = Strategic Thinking

Note for Gridded Response Items: Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, . , -, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or decimal.

RELEASED

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