Algebra Syllabus Template Page 2
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4A
Algebra
Seeing Structure in Expressions
A-SSE
Interpret the structure of expressions.
1. Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret
P(1+r)
as the product of P and a factor not depending on P.
n
2. Use the structure of an expression to identify ways to rewrite it. For example, see x
– y
as (x
)
– (y
)
, thus recognizing it
4
4
2
2
2
2
as a difference of squares that can be factored as (x
– y
)(x
+ y
).
2
2
2
2
Write expressions in equivalent forms to solve problems.
3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by
the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression
≈ 1.012
1.15
t
can be rewritten as (1.15
1/12
)
12t
12t
to reveal the approximate equivalent monthly interest rate if the
annual rate is 15%.
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.
Arithmetic with Polynomials and Rational Expressions
A-APR
Perform arithmetic operations on polynomials.
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.
Understand the relationship between zeros and factors of polynomials.
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).
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.
Use polynomial identities to solve problems.
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.
5. (+) Know and apply the Binomial Theorem for the expansion of (x + y)
in powers of x and y for a positive integer n,
n
where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
1
1. The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.
124 | Higher Mathematics Standards
Conceptual Category
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