IB Maths Foundations Course

IB Maths starts from the algebra you already know and extends it with functions, exponentials, logarithms, sequences and binomial expansions. These tools appear in both Analysis & Approaches and Applications & Interpretation papers.

• Solve quadratics, simultaneous equations and inequalities.
• Use exponent and logarithm laws.
• Work with arithmetic and geometric sequences.
• Apply binomial expansion and function notation.

Practice loop: solve a small set of quadratics, then a pair of simultaneous equations, then one inequality. Before moving on, write down the rule that let you solve each one; naming the rule turns a correct answer into a reusable method.

For exponentials and logarithms, keep the inverse relationship in mind: if b^x = y, then log_b(y) = x. This lets you switch forms whenever an equation is easier to solve as a logarithm. Check domain restrictions for logs, and remember that log(1) = 0 and log_b(b) = 1.

Functions and calculus are the heart of IB Maths. Practise composite and inverse functions, differentiation, integration, rates of change and optimization until each step feels automatic.

• Find composite functions, inverses and domains.
• Differentiate using product, quotient and chain rules.
• Find stationary points, tangents and areas.
• Use calculus for rates of change and optimization.

Differentiation checklist: identify the outer and inner function before applying the chain rule, then simplify carefully. For the product rule, write u and v first; for the quotient rule, keep the order of the subtraction straight.

Integration reverses this thinking. When you see a composite function, try substitution; when the integrand is a sum of simple powers, integrate term by term and check with differentiation.

IB Maths uses radians, exact values, identities and geometry together. Learn the sine and cosine rules, sector formulas and graph transformations because they connect directly to calculus and vectors.

• Convert between radians and degrees.
• Use exact values and trigonometric identities.
• Apply sine and cosine rules and sector formulas.
• Solve trigonometric equations in a given interval.

Exact value drill: memorise sin, cos and tan for 0, 30, 45, 60 and 90 degrees in both degrees and radians. Draw the unit circle when a sign is unclear: sine is positive in quadrants I and II, cosine in I and IV.

For equations like sin x = k, find the principal value first, then add the correct period and use the symmetry of the graph to list all solutions in the given interval.

Statistics and probability appear in every IB Maths route. Master measures of centre and spread, probability rules, binomial and normal distributions, and correlation before using a calculator.

• Calculate mean, median, mode, variance and standard deviation.
• Use addition and multiplication rules for probability.
• Apply binomial and normal distribution calculations.
• Interpret correlation and regression results.

Probability order of operations: decide whether events overlap before adding probabilities. Use the addition rule P(A or B) = P(A) + P(B) − P(A and B) for overlapping events, and the multiplication rule for independent events.

For distributions, always state the parameters first: X ~ Bin(n, p) or X ~ N(μ, σ²). Then decide whether the question asks for a probability, an expected value, or a boundary value before using your calculator.

IB maths papers award method marks and communication marks, not just final answers. Build a routine that shows clear reasoning, uses the calculator sensibly and avoids careless errors.

• Write every step with correct notation and units.
• Show substitutions and formulas to earn method marks.
• Check significant figures, signs and calculator settings.
• Review mistakes and repeat related practice sets.

Method-mark routine: write the formula, substitute values, simplify, then box the final answer with the required number of significant figures. If you cannot finish a question, still write the first step; method marks are often awarded for the setup.

During timed practice, mark questions you are unsure about and review them after the session. Track error types: sign slips, calculator mode, notation, and reading errors, then target the most frequent one in your next practice set.