Common Core State Standards for Mathematics
Sheltered Algebra I (V01) - Semester Two
Domain: Arithmetic With Polynomials and Rational Expressions (AAPR)
Learning Standard: Perform arithmetic operations on polynomials. Test Questions
AAPR09-12.01 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 10, 11, 12, 13, 14
Domain: Reasoning With Equations and Inequalities (AREI)
Learning Standard: Solve equations and inequalities in one variable. Test Questions

AREI09-12.04 Solve quadratic equations in one variable.

• Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
• Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
17, 18, 19, 20, 21, 22
Domain: Seeing Structure in Expressions (ASSE)
Learning Standard: Write expressions in equivalent forms to solve problems. Test Questions

ASSE09-12.03 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

• Factor a quadratic expression to reveal the zeros of the function it defines.
• Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
• Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
15, 16, 26, 32, 33
Domain: Building Functions (FBF)
Learning Standards: Build new functions from existing functions. Test Questions
FBF09-12.03 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 41, 42, 43, 44, 45, 46, 47
Domain: Interpreting Functions (FIF)
Learning Standard: Interpret functions that arise in applications in terms of the context. Test Questions
FIF09-12.04 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 23, 34, 39
FIF09-12.05 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. 48

FIF09-12.07 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

• Graph linear and quadratic functions and show intercepts, maxima, and minima.
• Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
• Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
24, 25, 27, 29, 36, 40
Learning Standard: Analyze functions using different representations. Test Questions

FIF09-12.08 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

• Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
• Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y= (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
8, 28, 31, 37, 38

FIF09-12.09 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum
30, 35
Domain: Linear, Quadratic, & Exponential Models (FLE)
Learning Standard: Construct and compare linear, quadratic, and exponential models and solve problems. Test Questions
FLE09-12.02 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). 9, 49
FLE09-12.03 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 50, 51
Domain: The Real Number System (NRN)
Learning Standard: Extend the properties of exponents to rational exponents. Test Questions
NRN09-12.02 Rewrite expressions involving radicals and rational exponents using the properties of exponents. 1, 2, 3, 4, 5, 6, 7

Multiple Choice: 51 points
Free Response: 10 points
Overall: 61 points