Mastering the TCAP TestsGrade 6

Practice by SPI

•SPI 06006.3.1: Represent on a number line the solution of an inequality.

•1. Which number line shows the solution for y-7>5?

A)B)C)D)

•2. Which number line shows the solution for 8c>40?

F)G)H)J)

•3. Which linear inequality has the solution drawn on the number line below?

A)w+6>8B)w+6<8C)w+6>8D)w+6<8

On Your Own

•4. Which number line shows the solution for 2w+3<11?

F)G)H)J)

On Your Own

•5. Which number line shows the solution for y/2>3?

A)B)C)D)

With Your Partner

•6. Which linear inequality has the solution shown on the number line below?

F) 9x+75<15G) 9x-75<85H) 9x+15<105J) 9X-85<10

Practice by SPI• SPI 0606.3.2: Use order of operations and parentheses to simplify

expressions and solve problems.Ana’s mother ordered the 4 pizzas shown below for a party.

1.Eight people at the party ate 3 slices each. The other 5 people at the party ate 1 slice each. To find the number of slices eaten at the party, Ana simplifies the expression below

32-(8x3+5)What result does she get?A)3 D)29B)4C)13

• 2. Which number equals this expression?56÷7x4-2x3F) 26G) 36H) 56J) 90• 3. What is the first step in evaluating13-8+6÷3x2?A) 13-8B) 8+6C) 6÷3D) 3x2

On Your Own•4. To evaluate the expression 21-6x3, Jun

subtracted 6 from 21 to get 15, and multiplied 15 by 3 to get 45. What should Jun have done differently?

F) Subtracted (6x3) from 21G) Subtracted 6 from (21x3)H) Subtracted 3 from (21x6)J) Subtracted (21x3) from 6

On Your Own •5. One day 145 adults and 248 students

visited Andrew Jackson’s home, The Hermitage. If adult admission is $17 and student admission is $11, which expression could be used to find the amount of money collected from those two groups?

A) (248+17) x (145x11)B) (145x17) + (248x11)C) (248÷11) + (145÷17)D) (145x11) + (248x17)

•On Your Own

•6. What is the simplest form of the expression below?

5(12+9) – 3(8-6)F)63G)75H)99J)204

On Your Own

•7. What is the value of the expression (18÷6) + 7 x 3A)33B)30C)24D)16

Practice by SPISPI 0606.3.3: Write equations that correspond to given situations or represent a given mathematical relationship.

• 1. The table below show’s Cami’s age compared to her sister Julie’s age at different times.

If c represents Cami’s age, which equation can be used to find j, Julie’s age?

A)j=c-5 D)j=c+3B)c=j+3C)j=c+5

Cami’s Age

Julie’s age

2 7

5 10

9 14

13 18

16 21

• 2. Matthew had $50 for his trip. He bought 2 ride tickets that cost $5.50 each. Then he used $9 for food. Which equation can be used to find x, the amount of money Matthew has left?

F)x=50.00-5.50-9G)x=50.00+5.50-9H)x=50.00-(2x5.50)-9J)x=50.00-(2x5.50)+9• 3. Which equation does the drawing below represent?

A)2x+4=6xB)6x=5 D)2x+4=6C)4x+2=6

x =x

•On Your Own•4. Some food prices at the county fair are

shown in the table below.

You buy s salads, b burgers, and d drinks. Which equation represents the t total cost, in dollars?

F)t=5s+4b+2dG)t=5s-4b-2dH)t=5s+4b-2dJ)t=5sx4bx2d

Food Item Price

Salad $5

Burger $4

Drink $2

On Your Own • 5. In Tennessee, when drivers see the speed limit sign

below, they must travel a minimum speed of 55 if they are in the left lane of an Interstate highway.

Which equation can be used to find d, the difference between the posted speed limit and the minimum speed limit?

A)70-d=55B)d-70=55C)55-d=70D)55-70=d

SPEEDLIMIT

70

Practice by SPI• SPI 0606.3.4: Rewrite expressions to represent quantities in

different ways.• 1. In the table below, which expression has been correctly

written in an equivalent form?

A)3x+5x+7B)4(2x+3y)C)2x+6y-2yD)7y-2y+3

Expression Equivalent Form

3x+5x+7 15x

4(2x+3y) 8x+3y

2x+6y-2y 6y

7y-2y+3 5y+3

• 2. Which of the following is an equivalent form of the expression below?

(5f+6) + (2f-1)F)12fG)5f+5H)7f+5J)10f• 3. Which expression represents (e x 9) + (e x 1) +

7 in a different way?A)10e+7B)9e+7C)9eD)17e

• 4. What is (6a+7b) + (8b+4a) in a different form?

F)14a+11bG)10a+15bH)14ab+11J)25ab• 5. Which expression below is equivalent to the

expression 5(4n-1)A)20n-1B)20n-5C)20nD)15n

•6. Kate correctly simplified the expression below on her math test. What was her correct answer?

(6a +3b + 5c) + (2b +7c)F)6a + 6b + 12xH)6a+5b+12cG)8a+5b+12cJ)23abc

With A Partner

•7. The lengths of the sides of a triangle are (3x +2), (2x+5), and 4x. Terrell correctly added the lengths of the three sides to find the perimeter. What expression did Terrell write for the perimeter?

A)7x+9B)5x+7C)9x+7D)16x

On Your Own

•8. What is the simplified form of the expression below?

(9y-3y) + 6y +8F)12y+8G)6y+14H)8y+12J)20y

Practice by SPI

•SPI 0606.3.5: Translate between verbal expressions/sentences and algebraic expressions/equations.

•1. The sum of 3 times a number m and 14 is equal to 29. Which equation could represent this situation?

A)14m+3=29B)29+3=4mC)3+m+14=29D)3m+14=29

• 2. For the past two weeks, Andrea has been collecting soft drink can tabs for charity. The table below show’s Andrea’s log of the number of tabs she collected.

Which equation can be used to find t, the number of tabs she collected during the first week?

F)425+t=80G)80-t=425H)t-80=425J)t+80=425

Can Tabs Collected

Week 1 t

Week 2 80

Total Collected 425

•3. Mr. Markus is 48 years old. This is 4 times the sum of his son’s age m and 3. Which equation could be used to find his son’s age?

A)4m+3=48B)48+3=4mC)4(m+3)=48D)m(4+3)=48

With Your Partner

•4. Which sentence best represents the equation

2x-8=28?F)The sum of twice a number x and 8 is 28.G)The difference between a number x and

28 is 8.H)Eight less than the product of 2 and a

number x is 28.J)Two times 8 is equal to a number x plus

28.

•On Your Own

•5. Hasina had $35 before she went shopping. She bought a book for $12 and a CD for c dollars. Which expression represents how much money Hasina had left after shopping?

A)35+12-cB)35-12+cC)35+12+cD)35-12-c

On Your Own

•6. Which phrase has the same meaning as the expression below?

g/2+5F)The product of a number g and 5 plus 2G)The quotient of a number g and 2

increased by 5H)The sum of a number g and 2 divided by

5J)The sum of a number g and the product of

5 and 2

Practice by SPI• SPI 0606.3.6: Solve two-step linear equations using number

sense, properties, and inverse operations.• 1. Look at the equation below. What value of n makes the

equation true?4n-1=11A)2B)3C)4D)12• 2. Rashida needs to solve the equation 4x+2=34. What value

of x makes the equation true?F)6G)8H)9J)16

• 3. An adult meal at a restaurant costs three dollars more than twice the cost of a children’s meal. The adult meal is $17. To find the cost of a child’s meal, Kamar wrote this equation

17=2c+3What value of c makes the equation true?A)7B)8C)10D)14• 4. What operation should you use first to find the value of g

that makes the equation true?125=g/115+30F)additionG)subtractionH)multiplicationJ)division

• On Your Own• 5. Which value of y makes the equation true?y/3-12=24A)108B)72C)36D)12• 6. What value of y makes the equation true?24+12y=72F)2G)4H)6J)8

On Your Own • 7. Which two inverse operations would be used to find

the value of e that makes the equation true?63+14E=91A)Addition and divisionB)Addition and multiplicationC)Subtraction and divisionD)Subtraction and multiplication

• 8. What value of p makes the equation true?12+p/6=48F)72G)216H)288J)360

Practice by SPI• SPI 0606.3.7: Use algebraic expressions and properties to

analyze numeric and geometric patterns.• 1. The table shows values for x and y.

Which expression can be used to find y in terms of x?A)x+6B)6xC)x-6D)6÷x

x y

16 10

14 8

12 6

10 4

• 2. Which list of numbers could be part of the number pattern created by the expression 2x+5 when x represents the previous number in the pattern?

F)1,7,9,32,69G)3,11,27,59,123H)2,9,21,45,93J)4,13,44,93,191• 3. The table shows values for x and y.Which expression can be used to findy in terms of x?A)7x-3B)7xC)7x+2D)8x-3

x y

4 30

7 51

11 79

13 93

• On Your Own • 4. Which expression can be used to find y in terms of x in the

table below?

F)x+11G)3x+1H)3x-1J)3x+3

• 5. Olivia created the pattern of numbers below by using an expression.5,9,17,33,65,129

Which expression could have been used to create the part of the number pattern above, when x represents the previous number in the pattern?

A)x+4B)3x-6C)2x+1D)2x-1

x 5 6 7 8

y 16 19 22 25

With Your Partner•6. Which expression can be used to find x

in terms of y in the table below?

F)6y-2G)4y+4H)5y+1J)2y+10

y x

3 16

5 24

8 36

12 52

Practice by SPI• SPI 0606.3.8: Select the qualitative graph that models a contextual situation (e.g.,

water filling then draining from a bathtub).• 1. An airplane leaves an airport, climbs to an altitude that it maintains for most of

the trip, and then lands at its destination. Which of these best represents this situation?

A) D)

B)

C)

Alt

itu

de

Distance

Distance

Alt

itu

de

Alt

itu

de

Distance

Distance

Alt

itu

de

• On Your Own• 2. Latoya works out by walking on a treadmill for 30

minutes. Which of these graphs best represents the number of miles she will have walked while working out on the treadmill?

F) J)

G)

H)

Miles

Minutes

Mile

s

Minutes

Miles

Minutes

Miles

Minutes

Practice by SPI• SPI 0606.3.9: Graph ordered pairs of integers in all four

quadrants of the Cartesian coordinate system.• 1. What are the coordinates of Point D on the grid below?

A)(-3,6)B)(-3,-6)C)(-6,-3)D)(3,6)

D

A

C

F

B

On Your Own• 2. Which point is located at (2,-5) on the grid below?

F)Point WG)Point XH)Point YJ)Point Z

Z

Y

X

W

On Your Own•3. Which point is located at (7,1) on the

grid below?A)Point EB)Point FC)Point GD)Point HE

F

H

G

•On Your Own•4. What are the coordinates of Point J on

the grid below?F)(5,-5)G)(-5,5)H)(-5,-5)J)(5,5)

J

K

ML

Closure- Ticket Out the Door: Select 3 Problems to Solve•1. SPI 0606.3.1: Represent on a number

line the solution of an inequality. Which linear inequality has the solution shown on the number line below?

•A. 9x + 75 < •B. 9x – 75 < 85•C. 9x + 15 < 105•D. 9x – 85 < 10

Ticket out the Door

•2. SPI 0606.3.2: Use order of operations and parentheses to simplify expressions and solve problems.

•What is the value of the expression (18 x 6) + 7 x 3?

Closure-Ticket Out the Door: Select 3 Problems to Solve • 3. SPI 0606.3.3: Write equations that go along

with situations or represent a given mathematical relationship. Some food prices at the grocery store are shown in the table below.

• You buy L lettuce heads, C bags of carrots, and B bunches of bananas. Which equation represents the t total cost, in dollars?

Food Item Price

Red leaf lettuce $3

Organic carrots $4

Bunch of bananas $2

Ticket Out the Door

•4. SPI 0606.3.4 Rewrite expressions to represent quantities in different ways.

• What is the simplified form of the expression below?

•(7y – 2y) + 4y + 6•A. 12y + 8•B. 6y + 14•C. 8y + 12•D. 9y + 6

Ticket Out the Door• 5. SPI 0606.3.5 : Translate between verbal

expressions/sentences and algebraic expressions/equations. Which phrase has the same meaning as the expression below?

• g/4 + 7• A. The product of a number g and 7 plus 4• B. The quotient of a number g and 4 increased

by 7• C. The sum of a number g and 4 divided by 7• D. The sum of a number g and the product of 4

and 7

Ticket Out the Door•6. SPI 0606.3.6: Solve 2 step linear equations

using number sense, properties, and inverse operations.

• What value of p makes the equation true?

•10 + P/4 = 50•A. 72•B. 160•C. 216•D. 100

Ticket Out the Door • 7. SPI 0606.3.7 : Use algebraic expressions and

properties to analyze numeric and geometric patterns. • Patrick created the pattern of numbers below by using

an expression.• 5, 11, 23, 47, 95, 191• Which expression could have been used to create the

part of the number pattern above, when x represents the previous number in the pattern?

• A. x + 4• B. 3x -6• C. 2x +1• D. 2x - 1

Ticket Out the Door

•8. SPI 0606.3.8: Select the graph that shows a situation.

•An airplane leaves an airport, climbs to an altitude that it maintains for half of the trip, and then lands at a midway point for refueling. It leaves the second airport, climbs to an altitude that it maintains for the second half of the trip, and then lands at its destination. Draw the graph that best represents this situation.

Ticket Out the Door

•9. SPI 0606.3.9: Graph ordered pairs on integers in all four quadrants of the coordinate system.

•Draw the points of the ordered pairs listed.

•(6, 3) , (-2, 4), (-4, -7) and ( -1, -1)