maths p1 cheat sheet

Grade 12 Mathematics: Paper 1 Cheat Sheet

General Information

  • Author: Nina Hanekom

  • Edition: 1st Edition, Published 2023

  • Copyright: All rights reserved; one copy per purchase; sharing leads to legal actions.

  • Acknowledgements: Questions sourced from NSC Examination Papers (detailed citations).

Contents Overview

  • Topics & Weightings:

    • Algebra, Equations & Inequalities - 25 Marks

    • Number Patterns - 25 Marks

    • Functions & Graphs - 35 Marks

    • Finance, Growth & Decay - 15 Marks

    • Differential Calculus - 35 Marks

    • Counting Principle & Probability - 15 Marks

  • Total Exam: 3-hour paper, total of 150 marks.

Using the Study Guide

  • Designed to mirror exam structure.

  • Use alongside past papers for practice.

  • Tip: Familiarize with question difficulty classifications (K, R, C, P).

    • K: Knowledge (20 marks)

    • R: Routine (52-53 marks)

    • C: Complex (45 marks)

    • P: Problem-solving (22-23 marks)

  • Emphasize exam guidelines during preparation.

Exam Topic Breakdown

  • Understanding Question Difficulty:

    • Knowledge - Recall and basic application of concepts.

    • Routine - Performing multi-step calculations and familiar procedures.

    • Complex - Higher-order thinking and multi-topic integration.

    • Problem-Solving - Novel contexts requiring existing knowledge.

Core Areas of Study

Algebra, Equations & Inequalities

  • Solve linear, quadratic, and exponential equations.

  • Quadratic equations can be solved via factorisation or quadratic formula.

  • Understand and solve inequalities.

Number Patterns

  • Identify types of patterns: arithmetic (constant difference), geometric (constant ratio).

  • Differentiate between terms of sequences vs. series.

  • Prove sum-formulae for patterns.

Functions & Graphs

  • Define functions, domains, ranges, and inverses.

  • Draw and interpret graphs for various functions (linear, quadratic, etc.).

Finance, Growth & Decay

  • Master key formulae for calculations regarding interest, loans, and investments.

Differential Calculus

  • Calculate derivatives, interpret graphs, and find tangents.

  • Understanding of concavity and inflection points.

Counting Principles & Probability

  • Apply counting principles (combinations and arrangements).

  • Use Venn diagrams and probability identities to solve problems.

Exam Preparation Tips

  • Regularly practice using past exam papers, paying close attention to the format.

  • Familiarize with question types and difficulty indicators.

  • Be proficient in formulae identification and application for all mathematical domains specified in the syllabus.

  • Don’t neglect practice on word problems, especially in calculus and finance topics.