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A2 Unit 3 Pure Mathematics B

8 dot points across 8 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we handle the modulus function, composite and inverse functions, and split a rational expression into partial fractions?

The modulus function and its graphs and equations, composite and inverse functions, and resolving rational expressions into partial fractions.
A focused answer to WJEC A2 Unit 3 algebra and functions, covering the modulus function and its graphs and equations, composite and inverse functions, and resolving rational expressions into partial fractions.
13 min answer →

How do we differentiate products, quotients, composite functions and implicit relations, and the standard functions?

The chain, product and quotient rules, implicit differentiation, derivatives of exponential, logarithmic and trigonometric functions, and the second derivative and concavity.
A focused answer to WJEC A2 Unit 3 differentiation, covering the chain, product and quotient rules, implicit differentiation, the derivatives of exponential, logarithmic and trigonometric functions, and the second derivative for concavity.
14 min answer →

How do we integrate by parts, by substitution, and using partial fractions, and the standard functions?

Integrating standard functions, integration by substitution, integration by parts, integration using partial fractions, and definite integrals for areas.
A focused answer to WJEC A2 Unit 3 integration, covering integrating standard functions, integration by substitution, integration by parts, integration using partial fractions, and definite integrals for areas.
14 min answer →

How do we locate and approximate roots when there is no exact algebraic solution, and estimate an area numerically?

Locating roots by change of sign, iterative methods, the Newton-Raphson method, and the trapezium rule for numerical integration.
A focused answer to WJEC A2 Unit 3 numerical methods, covering locating roots by change of sign, iterative methods, the Newton-Raphson method, and the trapezium rule for estimating definite integrals.
13 min answer →

How do we describe a curve using a parameter, convert to Cartesian form, and find its gradient?

Parametric equations of curves, converting between parametric and Cartesian forms, and differentiating parametrically to find gradients and tangents.
A focused answer to WJEC A2 Unit 3 parametric equations, covering parametric equations of curves, converting between parametric and Cartesian forms, and parametric differentiation to find gradients and tangents.
12 min answer →

How do we prove a statement by assuming it is false and deriving a contradiction?

Proof by contradiction, the structure of the method, and the classic results proved this way (the irrationality of root 2, the infinitude of primes).
A focused answer to WJEC A2 Unit 3 proof by contradiction, covering the structure of the method, the irrationality of root 2, the infinitude of the primes, and how to set out a contradiction argument for full marks.
11 min answer →

How do we sum arithmetic and geometric series, handle infinite sums, and expand a binomial for any rational power?

Arithmetic and geometric sequences and series, sigma notation, the sum to infinity of a convergent geometric series, and the binomial expansion for any rational index.
A focused answer to WJEC A2 Unit 3 sequences and series, covering arithmetic and geometric sequences and series, sigma notation, the sum to infinity of a convergent geometric series, and the binomial expansion for any rational index.
13 min answer →

How do we use radians, the reciprocal ratios, and the compound and double-angle identities to simplify and solve trig problems?

Radian measure, the reciprocal functions secant, cosecant and cotangent, the compound and double-angle formulae, and the harmonic form R sin(theta + alpha).
A focused answer to WJEC A2 Unit 3 trigonometry, covering radian measure, the reciprocal functions secant, cosecant and cotangent, the compound and double-angle identities, and the harmonic form R sin(theta plus alpha).
14 min answer →