17 resources.
What a quadratic equation is, solving by completing the square, the quadratic formula, and a real-life example.
How the zeroes of a quadratic polynomial relate to its coefficients, plus building a polynomial from a given sum and product of zeroes.
Worked examples for checking whether an equation is quadratic, solving by factorization or completing the square, and using the discriminant.
Simplifying and rationalizing expressions with square roots, with worked examples including a telescoping sum.
Dividing one polynomial by another to find a quotient and remainder, and using that to find missing zeroes, with worked examples.
Using the Remainder Theorem to find a remainder without dividing, and factoring with the sum/difference-of-cubes identities, with worked examples.
What a logarithm is, common vs natural vs binary logarithms, and the core logarithm rules, with worked examples.
What complex numbers are, the modulus-argument form, conjugates, and basic arithmetic on complex numbers, with worked examples.
How to solve a one-variable linear equation, including fractional coefficients, with worked examples translating word problems into equations.
What a binary operation is, and how to check whether one has an identity element, is commutative, or is associative, with worked examples.
Turning a word problem into a pair of linear equations, and checking whether two lines intersect, are parallel, or coincide by comparing coefficient ratios.
Solving a pair of linear equations by substitution and by elimination, including recognizing when a system has infinitely many solutions.
The cross-multiplication formula for solving a pair of linear equations, and reducing an equation that isn't linear yet into one that is, with worked examples.
Translating age and money word problems into a pair of linear equations and solving them, including a classic problem with two valid cases.
The core rules for combining and simplifying exponents, including negative exponents, with worked examples.
Five worked Math Olympiad-style problems for grade 7: a Fibonacci-like sequence, an exponent equation, percentages with overlap, consecutive integers, and clock arithmetic.
What makes an expression a polynomial, the monomial/binomial/trinomial distinction, and how to find the degree of a polynomial in one or more variables.