Grade 11 math

Remainder & Factor Theorems

Use synthetic division and the Remainder and Factor Theorems to find remainders, test factors and find missing zeros.

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Zeros & Multiplicity

Find the zeros of a factored polynomial, their multiplicities, and whether the graph crosses or touches the x-axis.

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Polynomial Multiplication

Multiply two binomials with coefficients.

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Solving Quadratic Equations

Solve quadratic equations by factoring.

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Rational Expressions

Simplify rational expressions by canceling common factors.

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Quadratic Formula & the Discriminant

Solve quadratic equations using the quadratic formula and analyze the discriminant.

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Dividing Polynomials

Divide a polynomial by a linear binomial using synthetic division.

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Rational Exponents

Evaluate expressions with rational (fractional) exponents.

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Simplifying Rational Expressions with Binomials

Simplify rational expressions using the difference of squares and common-factor cancellation.

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Adding & Subtracting Rational Expressions

Add and subtract rational expressions with like and unlike denominators by building the least common denominator.

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Linear-Quadratic Systems of Equations

Solve nonlinear systems made of a line and a parabola by substitution, and decide how many solutions a system has.

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Quadratic Equations with Complex Solutions

Solve quadratic equations whose solutions are imaginary or complex numbers.

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Quadratic Inequalities

Solve quadratic inequalities by finding the roots and deciding where the parabola is above or below the x-axis.

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Solving Radical Equations

Solve square-root and cube-root equations and check for extraneous solutions.

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Solving Rational Equations

Solve equations with variables in the denominator and reject extraneous solutions.

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The Rational Root Theorem

List and test possible rational roots p/q of a polynomial and find its rational root.

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Solving Polynomial Equations by Factoring

Solve cubic and quartic equations by taking out common factors, factoring by grouping and using quadratic form.

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Systems of Three Equations

Solve systems of three linear equations in three variables by substitution and elimination.

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Exponential Expressions

Apply exponent rules with a numeric base.

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Function Composition

Evaluate the composition of two functions.

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Logarithm Basics

Evaluate simple logarithms.

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Exponential & Logarithmic Equations

Solve exponential and logarithmic equations for x.

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Arithmetic & Geometric Series

Find sums of arithmetic and geometric series, evaluate sigma notation, and sum infinite geometric series.

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Solving Exponential & Log Equations with Logarithms

Solve exponential equations by taking logarithms of both sides, and solve logarithmic equations while rejecting extraneous solutions.

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Exponential Growth, Decay & Compound Interest

Identify growth and decay rates and use y = a(1 ± r)^t, A = P(1 + r/n)^(nt) and A = Pe^(rt).

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Function Operations (Sum, Difference, Product & Quotient)

Add, subtract, multiply and divide functions: evaluate (f + g), (f - g), (f · g) and (f/g) at a number, write them as expressions, and find where f/g is undefined.

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Transformations of Functions

Shift, stretch and reflect parent functions like x², |x| and x³, and track how points move.

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Properties of Logarithms

Use the product, quotient and power rules to expand, condense and evaluate logarithms.

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Common Logs, Natural Logs & Change of Base

Evaluate common logarithms (base 10) and natural logarithms (base e), and use the change-of-base formula.

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Polynomial Degree & End Behavior

Find the degree and leading coefficient of a polynomial and use them to describe its end behavior and turning points.

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Rational Functions: Asymptotes & Holes

Find vertical and horizontal asymptotes and holes of rational functions, and write the equation of a graphed one.

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Vertex Form & Graphs of Parabolas

Find the vertex, axis of symmetry and extreme value of a parabola, and write equations in vertex form y = a(x - h)² + k.

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Equations of Circles

Find the center and radius of a circle from its equation, write equations of circles, and complete the square.

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Factoring Sums & Differences of Cubes

Factor sums and differences of cubes, including ones with a common factor or two variables.

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Conditional Probability & Independent Events

Find P(A and B) for independent and dependent events, P(A or B) with the addition rule, and conditional probabilities P(A | B) from two-way tables and formulas.

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Normal Distributions & z-Scores

Find z-scores and use the 68-95-99.7 rule to find percents and counts in a normal distribution.

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Counting: Permutations & Combinations

Use the counting principle, factorials, permutations (order matters) and combinations (order doesn't) to count outcomes.

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Coterminal & Reference Angles (Degrees & Radians)

Find coterminal angles, reference angles and the quadrant of an angle in standard position, in degrees and in radians.

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Radians, Arc Length & Sector Area

Convert between degrees and radians and use s = rθ and A = ½r²θ to find arc lengths and sector areas.

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Amplitude, Period & Midline of Sine and Cosine

Find the amplitude, period, midline and maximum of y = a sin(bx) + d and y = a cos(bx) + d from equations and graphs.

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Introduction to Complex Numbers

Simplify powers of i and perform operations with complex numbers.

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Dividing Complex Numbers

Multiply by complex conjugates and divide complex numbers, writing each result as a + bi.

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Word Problems

Exponential growth and quadratic word problems.

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