A. Algebra
- Animal Populations
- Delivery Trucks
- Delivery Trucks, assessment variation
- Exponential Parameters
- Increasing or Decreasing? Variation 1
- Kitchen Floor Tiles
- Mixing Candies
- Mixing Fertilizer
- Modeling London's Population
- Profit of a company, assessment variation
- Quadrupling Leads to Halving
- Radius of a Cylinder
- Seeing Dots
- The Bank Account
- The Physics Professor
- Throwing Horseshoes
- Graphs of Quadratic Functions
- Ice Cream
- Identifying Quadratic Functions (Standard Form)
- Increasing or Decreasing? Variation 2
- Profit of a company
- Profit of a company, assessment variation
- Vertex of a parabola with complex roots
A-SSE.A. Interpret the structure of expressions.
A-SSE.A.1. Interpret expressions that represent a quantity in terms of its context.
A-SSE.A.1.a. Interpret parts of an expression, such as terms, factors, and coefficients.
A-SSE.A.1.b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret $P(1+r)^n$ as the product of $P$ and a factor not depending on $P$.
A-SSE.A.2. Use the structure of an expression to identify ways to rewrite it. For example, see $x^4 - y^4$ as $(x^2)^2 - (y^2)^2$, thus recognizing it as a difference of squares that can be factored as $(x^2 - y^2)(x^2 + y^2)$.
A-SSE.B. Write expressions in equivalent forms to solve problems.
A-SSE.B.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A-SSE.B.3.a. Factor a quadratic expression to reveal the zeros of the function it defines.
A-SSE.B.3.b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
A-SSE.B.3.c. Use the properties of exponents to transform expressions for exponential functions. For example the expression $1.15^t$ can be rewritten as $(1.15^{1/12})^{12t} \approx 1.012^{12t}$ to reveal the approximate equivalent monthly interest rate if the annual rate is $15\%$.
A-SSE.B.4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.
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A-APR.A. Perform arithmetic operations on polynomials.
A-APR.A.1. 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.
A-APR.B. Understand the relationship between zeros and factors of polynomials.
A-APR.B.2. Know and apply the Remainder Theorem: For a polynomial $p(x)$ and a number $a$, the remainder on division by $x - a$ is $p(a)$, so $p(a) = 0$ if and only if $(x - a)$ is a factor of $p(x)$.
A-APR.B.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
A-APR.C. Use polynomial identities to solve problems.
A-APR.C.4. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity $(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2$ can be used to generate Pythagorean triples.
A-APR.C.5. Know and apply the Binomial Theorem for the expansion of $(x + y)^n$ in powers of $x$ and $y$ for a positive integer $n$, where $x$ and $y$ are any numbers, with coefficients determined for example by Pascal's Triangle.The Binomial Theorem can be proved by mathematical induction or by a com- binatorial argument.
A-APR.D. Rewrite rational expressions.
A-APR.D.6. Rewrite simple rational expressions in different forms; write $\frac{a(x)}{b(x)}$ in the form $q(x) + \frac{r(x)}{b(x)}$, where $a(x)$, $b(x)$, $q(x)$, and $r(x)$ are polynomials with the degree of $r(x)$ less than the degree of $b(x)$, using inspection, long division, or, for the more complicated examples, a computer algebra system.
A-APR.D.7. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
A-CED.A. Create equations that describe numbers or relationships.
A-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A-CED.A.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
A-CED.A.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law $V = IR$ to highlight resistance $R$.
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- No tasks yet illustrate this standard.