Cambridge AS Mathematics Workshops to Help Homeschoolers Succeed

Introduction

Let’s face it, Cambridge AS Mathematics (9709) is tough, especially when you’re a homeschooled learner without direct classroom access. Between dense textbooks, abstract concepts, and limited structured guidance, it’s easy for even the most capable Candidates to fall behind.

That’s why Tutors & Exams South Africa, in collaboration with Dynamic Learning, is proud to launch a new series of Cambridge AS Mathematics Workshops this August. Tailored for homeschooled Candidates preparing for the next exam series, these workshops go beyond revision; they’re a chance to build confidence, bridge knowledge gaps, and learn from experienced educators who know the syllabus inside out.

What are these Cambridge AS Mathematics Workshops?

Our workshops are curriculum-aligned, exam-focused sessions that cover all the key content in Pure Mathematics 1 and Probability & Statistics 1. Whether you’re struggling with sketching inverse functions or calculating standard deviation from scratch, these sessions break down complex topics into manageable, real-world explanations.

Each workshop is interactive, concept-driven, and aligned with the Cambridge International syllabus (9709). Candidates can attend individual sessions or save with a full package, with the option to include a marked mock paper for personalised feedback.

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The Real Problem: Why Homeschoolers Struggle with Cambridge AS Mathematics

Homeschooling offers flexibility, but when it comes to advanced mathematical concepts, many learners lack:

• Real-time feedback.
• Clear, structured explanations.
• Confidence in applying theory to exam-style questions.

Studies show that mathematics achievement strongly correlates with interactive learning environments and access to immediate feedback (EEF, 2021). Homeschoolers, while independent, often miss out on these essential learning conditions, especially for exam-heavy subjects like Cambridge AS Mathematics.

Why These Workshops Make a Difference

1. Topic-Specific Focus:

Each session targets one key topic, from functions and trigonometry to permutations and normal distribution. This prevents overload and allows for deeper understanding.

2. Exam-Focused Approach:

Workshops are tailored to Cambridge’s assessment structure, with plenty of time spent on exam-style questions, common pitfalls, and past paper techniques.

3. Qualified, Experienced Teachers:

Led by experienced Cambridge educators, including facilitators from Dynamic Learning, Candidates benefit from real exam insight and curriculum expertise.

4. Affordable, Flexible Packages:

With single sessions from just R500 and full packages starting at R2000, these workshops are cost-effective for families balancing multiple exam fees.

4. Personalised Feedback:

Choose a package that includes a marked mock paper to simulate real exam conditions, ideal for identifying final prep needs.

Cambridge AS Mathematics Workshop

Syllabus Code: 9709

Topics Covered: Pure Mathematics 1 & Probability and Statistics 1

Pricing Options:

Option 1 – R500 per individual session

Option 2 – Full Package (Content Only)

• Pure Mathematics 1 (All 7 sessions): R2800.
• Probability & Statistics 1 (All 5 sessions): R2000.

Option 3 – Full Package + Marked Mock Paper.

• Pure Mathematics 1 + Marked Mock Paper: R4000.
• Probability & Statistics 1 + Marked Mock Paper: R3200.

Week 1: Pure Mathematics 1

4th – 7th August 2025

Day 1 – Monday, 4 August 2025

10:00 am – 1:00 pm

• Functions

Learn how to:

• Factorise a quadratic and turn an equation into a completed square form.
• Draw and interpret quadratic functions including the domain, range and turning point.
• Draw and interpret a Hyperbola, including the domain and range.
• Determine whether a function is a one-to-one, many-to-one or one-to-many and if it has an inverse.
• Sketch an inverse function and determine its equation.
• Work with composite functions, solve for unknown values and determine whether or not a composite function can occur.
• Understand transformations including stretch, scale factors and translation.
• Determine how a transformation affects a graph and its equation.

2:00 pm – 5:00 pm

• Coordinate Geometry

Learn how to:

• Establish the equation of a circle in the form (x – a)² + (y – b)² = r.
• Use the equation of a circle, in any form, to determine the coordinates of the centre.
• Use the gradient formula and the equation of a straight line to determine the equation of a tangent or normal.
• Use the discriminant b² – 4ac to find unknown values where circles or lines intersect.
• Use the distance formula to determine the radius or diameter of a circle.
• Use the radius of a circle to determine the equation of a tangent or normal.

Day 2 – Tuesday, 5 August 2025

10:00 am – 1:00 pm

• Circular Measure

Learn how to:

• Understand the relationship between radians and degrees and how to convert one to the other.
• Find the length of an arc in a circle using a minor or major angle.
• Find the area of a sector in a circle.
• Find the area of a segment in a circle.
• Use trigonometry to find the area of a triangle as well as angles given known sides.
• Find the perimeter or area of a shape bounded by given lines or arcs.

2:00 pm – 5:00 pm

• Trigonometry

Learn how to:

• Sketch and interpret sine, cosine and tangent functions -in terms of coordinates, amplitude, period and translation.
• Determine the value of unknown angles from a function, in radians or degrees.
• Use sin^-1x; cos^-1x; tan^-1x to determine the value of an unknown angle.
• Use the identities sin 0/cos 0 = tan 0 and sin² 0 = 1.
• Find unknown values using sine, cosine and tangent on the Cartesian plane.

Day 3 – Wednesday, 6 August 2025

10:00 am – 1:00 pm

• Series

Learn how to:

• Determine the terms in the expansion of the expansion of (a + b)ⁿ.
• Determine the coefficients of a term given its exponent of x.
• Work with the general formula for an arithmetic or geometric sequence.
• Find the sum of an arithmetic or geometric series.
• Determine the sum to infinity of a geometric progression and work with the condition of convergence.

2:00 pm – 5:00 pm

• Differentiation

Learn how to:

• Find the first and second derivatives.
• Determine the gradient of a curve.
• Determine the equation for a tangent or normal to a curve at a specific point.
• Determine whether a point on a curve is a minimum or maximum.
• Find the derivative of an equation using the chain rule.
• Determine where a function is increasing or decreasing.
• Calculate rate of change.

Day 4 – Thursday, 7 August 2025

10:00 am – 1:00 pm

• Integration

Learn how to:

• Integrate an equation.
• Integrate an equation with a bracket using the reverse chain rule.
• Determine the equation of a function given its derivative.
• Determine the area under a curve, between a line and a curve, or between two curves.
• Determine the volume of a revolution.

Week 2: Probability & Statistics 1

11th – 13th August 2025

Day 1 – Monday, 11 August 2025

10:00 am – 1:00 pm

• Representation of Data

Learn how to:

• Draw and interpret stem-and-leaf diagrams, box-and-whisker plots, histograms and cumulative frequency graphs.
• Draw and interpret cumulative frequency tables and cumulative frequency graphs.
• Understand and use mean, median, mode, quartiles, percentiles, range, and interquartile range.
• Determine if a given value is an outlier and its effect.
• Calculate the mean, variance and standard deviation from data or given totals.

2:00 pm – 5:00 pm

• Permutations & Combinations

Learn how to:

• Work with arrangements with repeated letters and given restrictions.
• Work with groups given specific requirements where items can/cannot be together.
• Determine the probability that a certain arrangement occurs.

Day 2 – Tuesday, 12 August 2025

10:00 am – 1:00 pm

• Probability

Learn how to:

• Find and work with P(A); P(A U B); P(A Ո B); P(A’).
• Find the conditional probability given that a certain event occurs.
• Work with events if they are (not) mutually exclusive.
• Determine whether events are independent.

2:00 pm – 5:00 pm

• Discrete Random Variables

Learn how to:

• Draw up probability distribution tables and calculate the estimated mean, variance and standard deviation.
• Use the binomial distribution and geometric distribution in practical situations.
• Determine the expectation, variance and standard deviation of a binomial distribution.

Day 3 – Wednesday, 13 August 2025

10:00 am – 1:00 pm

• Normal Distribution

Learn how to:

• Find probabilities using the normal distribution.
• Determine a probability when x > x.
• Use probabilities to find z; x; µ or σ.
• Use an approximation when converting data from a binomial distribution to a normal distribution.

Schedule Summary:

Week 1: Pure Mathematics 1

Dates: 4th – 7th August 2025

Week 2: Probability & Statistics 1

Dates: 11th – 13th August 2025

Sources

• Education Endowment Foundation (2021). Feedback. https://educationendowmentfoundation.org.uk/education-evidence/teaching-learning-toolkit/feedback
• Bannier, B. (2016). Learning Outcomes and Homeschool Instructional Support, The Journal of Educational Research. https://www.jstor.org/stable/43526930