Everything You Need For a Grade 6-9 in Your GCSE Maths Exam in 30 Minutes! | Higher | 16th May 2024

This section covers combinations, fractional and negative indices, surds (addition, expansion, and rationalization), recurring decimals, reverse percentages, and bounds, emphasizing careful calculation and error interval understanding.

Key algebraic concepts discussed include expanding three brackets, rearranging formulas, factorizing expressions (including difference of two squares), nth term of quadratic sequences, plotting and interpreting quadratic and exponential graphs, finding the equation of perpendicular lines and tangents to circles, forming and solving quadratic equations (using factorization or the quadratic formula), completing the square, quadratic inequalities, and solving quadratic simultaneous equations.

This part explains how to evaluate functions with given values, composite functions (including f(g(x))), inverse functions, and solving equations involving composite functions. It also reviews factoring and simplifying algebraic fractions, including division and addition.

Covers the rules for graph transformations (affecting X and Y coordinates), and how to perform algebraic proofs, particularly for properties of even and odd numbers.

This segment tackles complex problems combining Pythagoras, sine rule, and cosine rule. It also delves into 3D trigonometry, exact trigonometric values (using standard triangles), and trigonometric graph transformations.

Topics include catch-recapture method, drawing and interpreting box plots (median and interquartile range comparison), cumulative frequency graphs, and histograms (calculating frequency density and estimating values).

Explains compound interest (working backwards to find rates), depreciation, working with fractions and ratios (using probability trees), and direct and inverse proportion (including algebraic variations). It also covers interpreting velocity-time graphs (area for distance, gradient for acceleration) and solving ratio equations with algebra.

Addresses calculating shaded regions, area and perimeter of circle sectors (finding angles), estimating volume of cones, sphere calculations, finding dimensions of similar cones, geometric transformations (negative scale factor, multiple transformations, invariant points), bearings (using parallel line properties and trigonometry), similar shapes with area/volume ratios, and various circle theorems and geometric proofs (congruence).

Covers constructing and interpreting Venn diagrams (three-way), using tables for probabilities (even when not explicitly given), probability trees (multiplying along branches and adding outcomes), and solving complex probability equations with algebraic expressions.