Mathematics
Form 5 · 22 topics available
Chapter 1 · Variation
Direct Variation
Model relationships where one quantity varies directly with another, find the constant, and use $y = kx$.
OpenInverse Variation
Model relationships where one quantity varies inversely with another using $y = \frac{k}{x}$.
OpenJoint Variation
Model quantities that vary with two or more variables at once, combining direct and inverse variation.
OpenChapter 2 · Matrices
Inverse Matrix and Simultaneous Equations
Find the inverse of a 2x2 matrix using its determinant, then use it to solve simultaneous linear equations.
OpenMatrices
A matrix is a rectangular array of numbers arranged in rows and columns. This section covers order, equal matrices and the identity matrix.
OpenBasic Operations on Matrices
Matrices can be added, subtracted, multiplied by a scalar and multiplied together. The inverse of a 2×2 matrix lets us solve simultaneous linear equations.
OpenChapter 3 · Consumer Mathematics: Insurance
Types of Insurance and Premiums
Learn life, medical, motor and fire insurance, how premiums are found, and how the average clause reduces a claim when property is under-insured.
OpenConsumer Mathematics: Insurance
How insurance works — premiums, sum insured and types of policy — for SPM Mathematics Form 5, with a worked example and an interactive exercise.
OpenChapter 4 · Consumer Mathematics: Taxation
Income Tax Computation
Compute chargeable income = gross income − reliefs, apply the tax bands, and subtract a rebate to find the tax payable.
OpenConsumer Mathematics: Taxation
Taxable income, tax reliefs and computing income tax for SPM Mathematics Form 5 — with a worked example and an interactive exercise.
OpenChapter 5 · Congruency, Enlargement and Combined Transformations
Congruency
Congruent figures have exactly the same shape and size. This section covers the tests for congruent triangles and how congruency differs from similarity.
OpenEnlargement
An enlargement changes the size of a figure using a centre and a scale factor. Lengths multiply by the scale factor and areas by its square.
OpenCombined Transformation
A combined transformation applies two or more transformations one after another. The order in which they are applied usually matters.
OpenTessellation
A tessellation covers a flat surface with shapes leaving no gaps and no overlaps. Whether a regular polygon tessellates depends on its interior angle.
OpenChapter 6 · Ratios and Graphs of Trigonometric Functions
Solving Trigonometric Equations
Solve sine, cosine and tangent equations for 0 to 360 degrees using the reference angle and the correct quadrants (CAST).
OpenValues of Sine, Cosine and Tangent for 0° ≤ θ ≤ 360°
The sign of a trigonometric ratio depends on the quadrant. A reference angle lets us find any value from the special acute angles.
OpenGraphs of Sine, Cosine and Tangent Functions
The graphs of sine, cosine and tangent are periodic. Each has a characteristic shape, period and range that we can read off directly.
OpenChapter 7 · Measures of Dispersion for Grouped Data
Comparing Grouped Data Dispersion
Find the mean, variance and standard deviation from a frequency table, and compare the spread of two data sets.
OpenDispersion for Grouped Data
When data are grouped into class intervals we use frequency tables, histograms, cumulative frequency and the ogive to display and read the distribution.
OpenMeasures of Dispersion for Grouped Data
For grouped data we estimate the mean using midpoints, compute variance and standard deviation, and read the interquartile range from an ogive.
OpenChapter 8 · Mathematical Modeling
Applying Mathematical Modeling
Follow the modeling steps — identify, form, solve, interpret, evaluate — and apply them to a real situation such as a taxi fare.
OpenMathematical Modeling
Using equations, functions and graphs to represent and solve real-world problems for SPM Mathematics Form 5 — with an interactive exercise.
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