A-Math 2021 Specimen Paper 2 Worked Solutions

Improper rational function

6 marks · algebra (partial fractions; improper rational function)

Log-linearising yx^n=k

10 marks: 3 + (2 + 2 + 3) · algebra (linear law; log-linearising and physical model)

Tangent at a point

10 marks: 5 + 5 · calculus (tangent to a curve; area between curve and line)

Line-and-curve non-intersection via discriminant

10 marks: 5 + (3 + 2) · algebra (non-intersection / discriminant; always-negative quadratic)

Algebraic division of a linear fraction

10 marks: 4 + 3 + 3 · calculus (algebraic division; product rule; integration by reversing)

Resolve a perpendicular distance into a - b

9 marks: 3 + 4 + 2 · trigonometry (modelling a perpendicular distance; r-formula)

Chain rule on e^f(x)

11 marks: 5 + 4 + 2 · calculus (chain rule on e^f(x); stationary point and nature)

Midpoint

12 marks: 5 + 5 + 2 · coordinate geometry (perpendicular bisector; equation of a circle; diameter)

Substitution u=2^x to a quadratic

12 marks: 4 + 4 + 4 · algebra (exponential equation by substitution; logarithm laws; no-solution argument)