Claim 1Smarter Balanced Sample Items

High School - Target I

Solve equations and inequalities in one variable.

Questions courtesy of the Smarter Balanced Assessment Consortium Item Specifications – Version 2.0Slideshow organized by SMc Curriculum – www.ccssmathactivities.com

Enter the value for x that makes the given equation true.

48 = x − 3

Question 1a

Rubric: (1 point) The student enters the correct value for the variable x.

Answer: 51

Question 1a Answer

Enter the value for x that makes the given equation true.

20x 5(6x + 4) = 4x 6

Question 1b

Rubric: (1 point) The student enters the correct value for the variable x.

Answer: 1

Question 1b Answer

Solve the inequality for n. 45 ≥ −15n

Question 2a

Rubric: (1 point) The student enters the correct solution to the inequality.

Answer: n ≥ −3

Question 2a Answer

Which inequality represents all possible solutions of 3n < 12?

A. n < 36

B. n < 4

C. n > 36

D. n > 4

Question 2b

Rubric: (1 point) The student selects the correct option.

Answer: D

Question 2b Answer

Solve the inequality for w.

2w + 17 13

Question 2c

Rubric: (1 point) The student enters the correct solution to the inequality.

Answer: w 2

Question 2c Answer

Evaluate the claim as True or False for each set of numbers. Claim: All members of the set are solutions for w in the given inequality.

20 − 5(6 + 4) ≥ 4 − 6 𝑤 𝑤 𝑤Decide if all members of each set are solutions. Click True or False.

Question 2d

Rubric: (1 point) The student correctly matches true or false to each option.

Answer: F, F, F, T, T

Question 2d Answer

Question 3a

Rubric: (1 point each) The student enters the correct value for B.

Answers: Example 1: 2Example 2: 80Example 3: 100

Question 3a Answer

Question 3b

Solve the given equation for x.

20xB=

Rubric: (1 point) The student enters the correct equation.

Answer: x = 20B

Question 3b Answer

Question 3c

Solve the given equation for x.

6x + Cx = 11

Question 3c Answer

Rubric: (1 point) The student enters the correct equation.

Answer: 116

xC

=+

Question 3d

Question 3d Answer

Rubric: (1 point each) The student enters the correct solution.

Answer: Example 1: or 0.01Example 2: 25

1100

Question 4a

Question 4a Answer

Rubric: (1 point) The student enters the solution(s) to the equation.

Answer: and 3

5

3

5

Question 4b

Question 4b Answer

Rubric: (1 point) The student enters the solution(s) to the equation.

Answer: and i3

5 i3

5

Consider the equation: x2 − 14x + 45 = 0

Part A: Drag numbers into the boxes to rewrite the equation in the form shown.

Part B: Use the Add Point tool to place a point for each solution on the number line.

Question 4c

Rubric: (2 points) The student correctly rewrites the equation and correctly places both points on the number line (1 point) The student correctly rewrites the equation or correctly places both points on the number line(e.g., 7; 4; points at 5 and 9).

Answers:Part A: 7, 4Part B: 5 and 9

Question 4c Answer

Part A: Drag and drop numbers from the list to enter an equivalent equation for 3x2 + 2x − 225 = 0 into the quadratic formula.

Part B: Use the Add Point tool to place a point for each solution on the number line.

Question 4d

Rubric: (2 points) The student produces the correct quadratic formula and two correct values for n. (1 point) The student produces the correct quadratic formula or two correct values for n.

Answer:

Question 4d Answer

Drag and drop numbers from the list to enter an equivalent equation for 2(x + 1)2 = −3 into the quadratic formula.

Question 4e

Question 4e Answer

Rubric: (1 point) The student produces the correct quadratic formula.

Answer: ( ) ( ) ( )( )( )( )( )

24 4 4 2 5

2 2x

- ± -=

Question 4f

Use the drop down menu to enter an equivalent equation for n2 −3n = 10 by factoring, and the solutions for n and n2.

Rubric: (2 points) The student correctly factors the equation and provides the correct values for n. (1 point) The student correctly factors the equation or the student provides both values for n.

Answer: +1, +2, +1, 5; 2, +5

Question 4f Answer

Which equation has no real solutions?

A. 4x2 + 4x − 24 = 0

B. x2 + 4x + 16 = 0

C. 5x2 + 3x − 1 = 0

D. 3x2 − 4x + 1 = 0

Question 5a

Rubric: (1 point) The student selects the correct option.

Answer: B

Question 5a Answer

What are the solutions for the given equation?

x2 + 4x + 16 = 0

A. x = −2 ± 4i √3

B. x = −2 ± 2 √3

C. x = −2 ± 2i √3

D. x = −2 ± 4 √3

Question 5b

Rubric: (1 point) The student selects the correct option.

Answer: C

Question 5b Answer