The students solve problems involving the Major Content with connections to the Standards for Mathematical Practice
Type of items: Type 1
Color Code: Peach
Evidence Statement Key: A-SSE.2-4
Y = Yes; Assessed on Calculator Section
X = Calculator is Specific to Item
N = No; Assessed on Non-Calculator Sections
Z = Calculator Neutral (Could be Calculator or Non-Calculator Sections)
Point: 1 each (1:26)
Evidence Statement Text:
Use the structure of a numerical expression or polynomial expression in one variable to rewrite it, in a case where two or more rewriting steps are required.
Clarifications, limits, emphases, and other information intended to ensure appropriate variety in tasks:
i) Example: Factor completely: x^2 - 1 + (x - 1)^2 . (A first iteration might give (x+1)(x-1) + (x-1)(x-1), which could be rewritten as (x-1)(x+1+x-1) 1) on the way to factorizing completely as 2x(x-1). Or the student might first expand, as x^2 – 1 + x^2 -2x+1, rewriting as 2x^2- 2x, then factorizing as 2x(x-1).)
ii) Tasks do not have a real-world context.
Sample Questions (taken from PARCC’s Practice Tests and Released Items):
EOY Released Test Item 20
Paper Test, Unit 1, Item 6
1. EOY Released Test Item 20
Complete the sentence by selecting the correct phrase.
The expression (a2)2 - (b2)2 is an example of:
A. a system of equations
B. a polynomial of degree 2
C. a difference of squares
D. a completely factored expression
E. an exponential function
Which of the listed expressions are equivalent to (a2)2 - (b2)2? Select all that apply.
A. a4 - b4
B. a4 + b4
C. (a2 + b2)(a2 - b2)
D. (a2 + b2)(a + b) (a - b)
E. (a - b)4
2. Paper Test, Unit 1, Item 6Use the information provided to answer Part A and Part B. Consider the function f(x) = 2x2 + 6x - 8.
What is the vertex form of f(x)?
A. f(x) = 2(x - 3)2 - 4
B. f(x) = 2(x + 3)2 - 4
C. f(x) = 2(x - 1.5)2 - 12.5
D. f(x) = 2(x + 1.5)2 - 12.5
What is a factored form of f(x)?
A. f(x) = (2x + 1) (x - 8)
B. f(x) = (2x -1) (x + 8)
C. f(x) = 2(x + 4) (x - 1)
D. f(x) = 2(x - 4) (x + 1)
3. 2016 #21
Enter your answers in the boxes to show the complete factorization of the expression -5x3 + 30x2 + 35x. Enter your answers on the blanks.
-5x3 +30x2+ 35x
-5x (x2 + ___x + ___)
-5x (x + ___) (x + 1)
...to be posted soon
PARCC. (n.d.). Retrieved January 13, 2017, from http://www.aps.edu/assessment/parcc