Lesson Packs · Grade 12
Grade 12 Mathematics
30 complete lessons. Each one has an editable PowerPoint with worked examples and a Word worksheet with a full answer key.
Unit 1Limits and Continuity
Lesson 1Limits of FunctionsStudents learn what the limit of a function means, estimate limits from tables and graphs, evaluate limits by substitution, factoring and rationalizing, and use one-sided limits to decide whether a limit exists.37 slides · 10 questions
Lesson 2Limits at Infinity and AsymptotesStudents evaluate limits at infinity by dividing by the highest power and by comparing degrees, find infinite one-sided limits, and use both to identify vertical, horizontal and oblique asymptotes from equations and graphs.39 slides · 11 questions
Lesson 3Continuity of FunctionsStudents learn the three conditions for continuity at a point, classify removable, jump and infinite discontinuities, find parameters that make piecewise functions continuous, and use the Intermediate Value Theorem to show that a root exists.39 slides · 11 questions
Unit 2Derivatives
Lesson 4The Derivative and Tangent LinesStudents move from the average to the instantaneous rate of change, see the tangent line as the limit of secant lines, find derivatives from first principles, write equations of tangent lines and meet a function that is continuous but not differentiable.38 slides · 10 questions
Lesson 5Rules of DifferentiationStudents learn the constant, power, constant multiple, sum and difference rules, then the product and quotient rules. They use them to differentiate polynomials, roots and rational functions, and to find slopes and tangent lines at given points.37 slides · 10 questions
Lesson 6The Chain RuleStudents learn to split a composite function into an inner and an outer function and differentiate it with the chain rule, including powers of functions, combinations with the product and quotient rules, tangent lines and rates of change.39 slides · 11 questions
Lesson 7Derivatives of Exponential and Logarithmic FunctionsStudents learn the derivatives of the natural exponential and logarithm functions, extend them to other bases and to composite functions with the chain rule, simplify with the laws of logarithms before differentiating, and find rates of growth and decay.40 slides · 11 questions
Lesson 8Derivatives of Trigonometric FunctionsStudents learn why calculus with angles uses radians, find the derivatives of sine, cosine and tangent, combine them with the chain, product and quotient rules, find second derivatives and tangent lines, and describe oscillating motion.37 slides · 10 questions
Unit 3Applications of Derivatives
Lesson 9Increasing and Decreasing Functions and ExtremaStudents use the sign of the first derivative to find where a function is increasing or decreasing, locate critical points, classify local maxima and minima with the first derivative test and a sign table, and find absolute extrema on a closed interval.38 slides · 10 questions
Lesson 10Concavity, Inflection Points and Curve SketchingStudents use the second derivative to find where a graph is concave up or concave down, locate inflection points, classify stationary points with the second derivative test, and sketch cubic and rational functions with a full curve-sketching checklist.39 slides · 10 questions
Lesson 11Optimization ProblemsStudents solve optimization problems with derivatives: they define variables, use a constraint to write a one-variable objective function with a realistic domain, find its critical points, and justify the maximum or minimum with the second derivative or the endpoints.40 slides · 10 questions
Unit 4Integration
Lesson 12Antiderivatives and Indefinite IntegralsStudents learn what an antiderivative is and why an indefinite integral always includes a constant C. They integrate powers, reciprocals, exponential and trigonometric functions term by term, and use an initial condition to find a particular antiderivative.39 slides · 11 questions
Lesson 13Integration by SubstitutionStudents learn to recognise an integrand that contains a composite function multiplied by the derivative of its inner function. They choose a substitution u, rewrite the integral in terms of u, adjust constant factors, and change the limits of definite integrals.39 slides · 11 questions
Lesson 14Integration by PartsStudents derive the integration by parts formula from the product rule and use the LIATE guideline to choose u. They integrate products of polynomials with exponential, trigonometric and logarithmic functions, integrate ln x, apply the formula twice and evaluate definite integrals.37 slides · 10 questions
Lesson 15Definite Integrals and the Fundamental Theorem of CalculusStudents estimate areas with rectangles, define the definite integral as a limit of Riemann sums and as net signed area, use its properties, and apply both parts of the Fundamental Theorem of Calculus to evaluate and differentiate integrals.43 slides · 12 questions
Lesson 16Area Between CurvesStudents find the area between a curve and the x-axis, including regions below the axis, by splitting at the roots and using absolute values. They then find the area between two curves by locating the intersection points and integrating top minus bottom.38 slides · 11 questions
Lesson 17Volumes of Solids of RevolutionStudents find the volumes of solids formed by rotating a region about the x-axis with the disk and washer methods, derive the volumes of a cone, a sphere and a paraboloid, and find volumes when a region is rotated about the y-axis.42 slides · 11 questions
Unit 5Differential Equations
Unit 6Vectors and 3D Geometry
Lesson 19Vectors in Space: Dot and Cross ProductStudents work with vectors in three dimensions: component form, magnitude and unit vectors, the dot product and the angle between two vectors, the perpendicular test, and the cross product with its use for areas of parallelograms and triangles.37 slides · 10 questions
Lesson 20Lines and Planes in SpaceStudents write vector and parametric equations of lines in space, find the equation of a plane from a point and a normal vector or from three points, find where a line meets a plane, and calculate the distance from a point to a plane and the angle between two planes.38 slides · 11 questions
Unit 7Probability and Statistics
Lesson 21Conditional Probability and Bayes' TheoremStudents find conditional probabilities from two-way tables and with the formula, use the multiplication rule and tree diagrams, test whether two events are independent, and apply the law of total probability and Bayes' theorem to problems such as screening tests.38 slides · 10 questions
Lesson 22Discrete Random Variables and the Binomial DistributionStudents build probability distribution tables, calculate the expected value and variance of a discrete random variable, recognise binomial situations, and use the binomial formula, its mean and variance, and cumulative probabilities to solve problems.38 slides · 10 questions
Lesson 23The Normal DistributionStudents describe the properties of the normal curve, use the 68–95–99.7 rule, standardise values with z-scores, find normal probabilities with a calculator or a z-table, and solve inverse problems that find a value from a given probability.38 slides · 10 questions
Unit 8Complex Numbers and Matrices
Lesson 24Complex NumbersStudents meet the imaginary unit i, calculate with complex numbers in the form a + bi (including division with the conjugate), plot them on an Argand diagram, find the modulus, argument and polar form, and solve quadratics with a negative discriminant.40 slides · 11 questions
Lesson 25Matrices and Systems of Linear EquationsStudents learn matrix notation and order, add and scale matrices, multiply matrices and see why the order matters, find 2 × 2 and 3 × 3 determinants and 2 × 2 inverses, and solve systems of linear equations with an inverse matrix and by elimination.38 slides · 10 questions
Unit 9Sequences, Series and Proof
Lesson 26Arithmetic and Geometric Sequences and SeriesStudents find the nth term and the sum of arithmetic and geometric sequences, read and evaluate sums in sigma notation, and decide when an infinite geometric series converges and find its sum to infinity.40 slides · 11 questions
Lesson 27The Binomial TheoremStudents build Pascal's triangle, calculate binomial coefficients C(n, r), expand (a + b)ⁿ with the binomial theorem, use the general term to find a specific coefficient or term, and make quick numerical approximations.39 slides · 11 questions
Lesson 28Mathematical InductionStudents learn why checking cases is not a proof, and use mathematical induction — a base case, an inductive hypothesis and an inductive step — to prove formulas for sums, divisibility results and inequalities for all positive integers.36 slides · 10 questions
Unit 10Further Complex Numbers and Statistics
Lesson 29Polar Form of Complex Numbers and De Moivre's TheoremStudents multiply and divide complex numbers in modulus–argument form, use De Moivre's theorem to find powers quickly, and find all the nth roots of a complex number and show them on an Argand diagram.39 slides · 11 questions
Lesson 30Sampling Distributions and Confidence IntervalsStudents learn how a sample mean and a sample proportion vary from sample to sample, find standard errors, use the central limit theorem, and build and interpret z-confidence intervals for a population mean and a population proportion.40 slides · 11 questions
For big organisations
For schools
For centers
For team leaders
For teachers
AI and resources
Printable worksheets
Lesson Packs
Interactive simulations
Teacher tools
AI studio
Ideas and research