A-Math 2021 Paper 1 Worked Solutions

Rationalising a denominator

3 marks · algebra (surds: rationalising a quotient)

Simultaneous equations (one non-linear)

3 marks · algebra (curve and line intersection)

Completing the square

4 marks · algebra (completing the square; turning point)

Integrate x^-2

4 marks · calculus (integration of x^-2 and 1/ax+b)

Partial fractions

6 marks · algebra (partial fractions with a repeated factor)

Remainder theorem

6 marks: 2 + 4 · algebra (remainder & factor theorem)

Amplitude

6 marks: 2 + 2 + 2 · trigonometry (amplitude, period, midline of a sine curve)

Area as rectangle minus corner triangles

7 marks: 3 + 4 · calculus (area model; stationary value)

Axis of symmetry of a kite

9 marks: 3 + 4 + 2 · coordinate geometry (kite)

Prove a trig identity

8 marks: 4 + 4 · trigonometry (prove an identity, then apply it)

Alternate segment theorem

7 marks: 4 + 3 · geometry (tangents, alternate segment theorem)

Index laws

8 marks: 4 + 4 · algebra (exponential & logarithmic equations)

Related rates with dV/dt

9 marks: (2 + 3) + 4 · calculus (connected & related rates of change)

Chain rule for (4+3x)^1/2

10 marks: 5 + 5 · calculus (normal to a curve; area by integration)