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51 resources.
What a quadratic equation is, solving by completing the square, the quadratic formula, and a real-life example.
The chain rule for differentiating composite functions, with two worked derivative examples.
What a definite integral is and how to evaluate one, with a worked trigonometric example.
How matrix addition and multiplication work, with a worked multiplication example.
Worked examples for checking whether an equation is quadratic, solving by factorization or completing the square, and using the discriminant.
Worked examples finding trigonometric ratios, evaluating standard-angle expressions, proving identities, and using co-function identities.
The power rule for differentiating x to a fixed exponent, with a worked example on a square root.
The product rule for differentiating a product of two functions, with worked examples including logarithmic differentiation.
The quotient rule for differentiating one function divided by another, with worked examples.
Using derivatives as rates of change, with worked examples on a growing circle's area and a particle's velocity and acceleration.
How to differentiate an equation that isn't already solved for y, with worked examples including an inverse trig identity.
How the sign of a function's derivative determines where it's increasing or decreasing, with worked examples including a cubic.
Finding local maxima and minima and solving optimization problems using derivatives, with worked examples.
What Rolle's theorem states and how to verify it for a function on a closed interval, with a worked example.
How the derivative gives the tangent's slope and the normal's slope is its negative reciprocal, with a worked example.
Finding the slope of a tangent line to a curve at a given point, with worked examples on a cubic and a rational function.
Splitting a rational function into simpler fractions before integrating, with worked examples.
Standard integration formulas for functions like 1/(x^2-a^2) and 1/(a^2-x^2), with worked examples.
Rewriting a trigonometric integrand with an identity before integrating, with worked examples on cos^2 x, sin^2 x, and a secant identity.
A shortcut formula for integrating e^x times a function plus its own derivative, with a worked example.
Using definite integrals to find area under a curve, including a full period of cosine and a classic circle-area derivation.
What probability measures, independent vs dependent events, and conditional probability, with worked card, dice, and survey examples.
What complex numbers are, the modulus-argument form, conjugates, and basic arithmetic on complex numbers, with worked examples.
How to count arrangements with permutations, with a worked dictionary-order example finding a specific word among all arrangements of a word's letters.
How to form a differential equation from a family of curves, and how to solve one by separating variables, with worked examples.
The integration by parts formula for integrating a product of two functions, with a worked example.
Left-hand and right-hand derivatives, spotting a point that's continuous but not differentiable, and finding a function's domain, with worked examples.
Diagonal, scalar, and identity matrices explained, with examples showing how each one is a more specific case of the last.
What symmetric and skew-symmetric matrices are, and how to split any square matrix into a sum of both, with a worked example.
Key facts about square matrices: the determinant scaling rule, idempotent matrices, and when a matrix equation has no solution.
How to solve a system of linear equations using the matrix method, with a fully worked three-variable example.
Solving for unknown entries in a matrix using a stated property or a matching determinant, with worked examples.
The negative of a vector, the scalar triple product identity, and using the dot product on unit vectors, with worked examples.
How to find the unit vector in a given direction, between two points, or scaled to a target magnitude, with worked examples.
What the projection of a vector onto a directed line means, including what happens at special angles, with a worked example.
The section formula for a point dividing a segment internally or externally, and finding a midpoint, with worked examples.
What direction cosines are and how to find them for a coordinate axis, a line through two points, or a line at given angles.
Writing a line's equation in vector and Cartesian form, given two points or a point and a parallel vector, with worked examples.
The equation of a coordinate plane, and finding a plane through the intersection of two others and a given point, with a worked example.
How to read a plane's intercepts on each axis straight from its equation, with a worked example.
How to find the angle between a line and a plane using their direction vector and normal vector, with a worked example.
The formula for the shortest distance between two skew lines in vector form, with two fully worked examples.
The determinant formula for the area of a triangle from its vertex coordinates, with a worked example.
Using the cross product to find the area of a triangle or parallelogram from vertex or side vectors, with worked examples.
Reflexive, symmetric, transitive, and equivalence relations defined and checked against worked examples.
One-one, onto, bijective, and invertible functions explained, with worked examples on checking each property and finding an inverse.
What a binary operation is, and how to check whether one has an identity element, is commutative, or is associative, with worked examples.
How to compute the composition of two functions in either order, with a worked example showing gof and fog can come out different.
Using differentials to approximate square roots and estimate small changes, with worked examples including a percentage-change setup.
Feasible regions, corner points, and finding the condition on an objective function's coefficients for it to be maximized at two corners at once.
Principal values, domains of inverse trig functions, and the complementary identity between tan⁻¹ and cot⁻¹, with worked examples.