Grade 12 Mathematics (Nsc): Exam Preparation

The complete Grade 12 Mathematics syllabus, with study and exam-writing tips

What you'll learn

Write the Grade 12 Mathematics Final Exam: Paper 1 and Paper 2 (NSC: CAPS)

Confidently and independently complete any Grade 12 Maths past paper as practice for the final exam

Structure your answers perfectly to achieve full marks in an exam

Solve a wide range of quadratic equations, simultaneous equations and nature of roots problems

Use logarithms to solve a problem and sketch logarithmic graphs

Find the inverse function of a linear, exponential, hyperbolic and parabolic graph

Understand and solve arithmetic, geometric and quadratic number pattern questions

Understand the differences between sequences and series, use the sum to infinity formula, use the sum to n-terms formula

Visualise, manipulate and solve multi-graph questions, where linear, parabolic, hyperbolic and exponential functions are involved

Understand the concept of limits as instantaneous gradient calculators

Differentiate a function using first principles

Differentiate a function using shortcut methods

Find the second derivative of a function and understand its meaning

Find equations of tangents to graphs of functions

Sketch functions and their derivatives, including turning points, points of inflection and points of intersection

Solve practical problems concerning optimisation and rate of change, including calculus of motion

Perform simple and compound interest calculations with any one variable unknown

Calculate future and present value annuities with monthly repayments (loans, investments, etc.)

Calculate growth and decay using investment principles

Differentiate between independent and dependent events, and apply the product rule

Utilise the sum rule for mutually exclusive events (P(A and B) = P(A) + P(B))

Utilise the addition rule for non-mutually exclusive events

Utilise the complementary rule for probability

Use the fundamental counting principle, factorial notation and permutations to solve Grade 12 probability questions

Visualise probability events using tree diagrams, contingency tables and Venn diagrams

Sketch sin, cos and tan graphs, shift them, reflect them and find their points of intersection

Use trigonometric compound angle identities to solve and simplify trigonometric equations

Use trigonometric double angle identities to solve and simplify trigonometric equations

Solve 2D and 3D trigonometric problems, making use of the sin, cos and area rule

Obtain the equation of a circle

Determine the equation of a tangent to a circle

Solve Euclidean geometry questions involving polygons and circles

Prove that two triangles are similar or congruent

Prove the midpoint theorem and its converse

Use and prove the Theorem of Pythagoras

Prove the required circle geometry theorems

Find the least squares regression line for bivariate data

Extrapolate and interpolate data given the least squares regression line

Generate a 5 number summary and box and whisker diagram for a set of data

Identify skewed and symmetric datasets

Comment on the strength of a correlation using the r-squared value

Requirements

Grade 11 Mathematics

Description

This course covers the entire Grade 12 Mathematics syllabus. We help you revise and solidify previous knowledge by providing realistic examples of what you are likely to see in tests and exams. We want to see you succeed and get the highest possible marks in your final exam. We focus on doing past paper questions to prepare you for your final exams. This aims to solve a common error amongst students, who only practise textbook examples before going into their final exams. Other students attempt past papers, which is statistically the best way to improve exam performance, but they struggle to understand the question and memo. By providing a tutorial video for each question and additional insight into each section, we believe that we have created the perfect product for you!We cover all the sections from Paper 1: factorisation and polynomials, sequences and series (geometric, arithmetic, quadratic), functions (hyperbolas, parabolas, exponential, logarithmic, linear, cubic), finance, differentiation and probability. We also cover all the sections from Paper 2: analytical geometry, Euclidean geometry (circles, ratio, proportion), trigonometry (expressions, graphs and 3D shapes) and statistics.   Bonus: Study and exam-writing tips from top students. So let's work on this together, because your final exam results can unlock countless opportunities for you!

Overview

Section 1: 2021 Paper 1

Lecture 1 2021 P1 Q1: Polynomials and factorisation

Lecture 2 2021 P1 Q2: Geometric series

Lecture 3 2021 P1 Q3: Quadratic sequences

Lecture 4 2021 P1 Q4: Linear sequences and series

Lecture 5 2021 P1 Q6: Inverse functions

Lecture 6 2021 P1 Q7: Parabolic and linear functions

Lecture 7 2021 P1 Q8: Finance

Lecture 8 2021 P1 Q9: Differentiation

Lecture 9 2021 P1 Q10: Cubic graphs

Lecture 10 2021 P1 Q11: Practical applications of calculus

Lecture 11 2021 P1 Q12: Probability

Section 2: 2019 Paper 1

Lecture 12 2019 P1 Q1: Polynomials and factorisation

Lecture 13 2019 P1 Q2: Quadratic sequences, geometric series

Lecture 14 2019 P1 Q3: Arithmetic series

Lecture 15 2019 P1 Q4: Hyperbolic and parabolic functions

Lecture 16 2019 P1 Q5: Inverse functions (log and exponential)

Lecture 17 2019 P1 Q6: Finance

Lecture 18 2019 P1 Q7: Differentiation

Lecture 19 2019 P1 Q8: Practical applications of calculus

Lecture 20 2019 P1 Q9: Cubic graphs

Lecture 21 2019 P1 Q10: Probability

Lecture 22 2019 P1 Q11: Probability (Venn diagrams, permutation)

Section 3: 2017 Paper 1

Lecture 23 2017 P1 Q1: Polynomials and factorisation

Lecture 24 2017 P1 Q2: Quadratic and arithmetic sequences

Lecture 25 2017 P1 Q3: Geometric series

Lecture 26 2017 P1 Q4: Parabolic functions

Lecture 27 2017 P1 Q5: Hyperbolic and logarithmic functions

Lecture 28 2017 P1 Q6: Finance

Lecture 29 2017 P1 Q7: Differentiation

Lecture 30 2017 P1 Q8: Cubic functions

Lecture 31 2017 P1 Q9: Practical applications of calculus

Lecture 32 2017 P1 Q10: Probability (Venn diagrams)

Lecture 33 2017 P1 Q11: Probability (Permutations)

Section 4: 2021 Paper 2

Lecture 34 2021 P2 Q1: Statistics

Lecture 35 2021 P2 Q2: Statistics (Linear Regression)

Lecture 36 2021 P2 Q3: Analytical geometry

Lecture 37 2021 P2 Q4: Analytical geometry (Circles)

Lecture 38 2021 P2 Q5: Trigonometric expressions

Lecture 39 2021 P2 Q6: Trigonometric identities

Lecture 40 2021 P2 Q7: Trigonometric graphs

Lecture 41 2021 P2 Q8: 3D trigonometry

Lecture 42 2021 P2 Q9: Euclidean geometry (Circles)

Lecture 43 2021 P2 Q10: Euclidean geometry (Circles)

Lecture 44 2021 P2 Q11.1: Euclidean geometry proof (Circles)

Lecture 45 2021 P2 Q11.2: Euclidean geometry (Circles, Ratio, Proportion)

Section 5: 2019 Paper 2

Lecture 46 2019 P2 Q1: Statistics (Linear regression)

Lecture 47 2019 P2 Q2: Statistics

Lecture 48 2019 P2 Q3: Analytical geometry

Lecture 49 2019 P2 Q4: Analytical geometry (Circles)

Lecture 50 2019 P2 Q5: Trigonometric expressions

Lecture 51 2019 P2 Q6: Trigonometric graphs

Lecture 52 2019 P2 Q7: 3D trigonometry

Lecture 53 2019 P2 Q8.1: Euclidean geometry (Circles)

Lecture 54 2019 P2 Q8.2: Euclidean geometry (Ratio, Proportion)

Lecture 55 2019 P2 Q9: Euclidean geometry proof (Circles)

Lecture 56 2019 P2 Q10.1: Euclidean geometry proof (Ratio, Proportion)

Lecture 57 2019 P2 Q10.2: Euclidean geometry (Circles)

Section 6: 2017 Paper 2

Lecture 58 2017 P2 Q1: Statistics (Linear regression)

Lecture 59 2017 P2 Q2: Statistics

Lecture 60 2017 P2 Q3: Analytical geometry

Lecture 61 2017 P2 Q4: Analytical geometry (Circles)

Lecture 62 2017 P2 Q5: Trigonometric expressions

Lecture 63 2017 P2 Q6: Trigonometric graphs

Lecture 64 2017 P2 Q7: 3D trigonometry

Lecture 65 2017 P2 Q8: Euclidean geometry (Circles)

Lecture 66 2017 P2 Q9: Euclidean geometry (Ratio, Proportion)

Lecture 67 2017 P2 Q10: Euclidean geometry (Circles)

Lecture 68 2017 P2 Q11.1: Euclidean geometry proof (Circles)

Lecture 69 2017 P2 Q11.2: Euclidean geometry (Circles)

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