Pure Mathematics 2

Worked examples (4)

• 1Single log expression from three terms (4 marks, P2)
• 2Solve an exponential equation using logs (4 marks, P2)
• 3Quadratic-in-exponential (5 marks, P2)
• 4Exponential decay model (7 marks, P2)

Worked examples (5)

• 1Expand a binomial fully (4 marks, P2)
• 2First four terms of $(1 + kx)^{n}$ (5 marks, P2)
• 3Find the coefficient of a particular term (5 marks, P2)
• 4Find $n$ from a given coefficient (6 marks, P2)
• 5Approximation using a binomial (4 marks, P2)

Worked examples (5)

• 1Algebraic long division of a cubic (4 marks, P2)
• 2Remainder theorem with unknown coefficient (5 marks, P2)
• 3Factor theorem with two unknowns (6 marks, P2)
• 4Improper algebraic fraction — split into polynomial + proper (5 marks, P2)
• 5Add two algebraic fractions and simplify (5 marks, P2)

Worked examples (4)

• 1Centre and radius from expanded form (4 marks, P2)
• 2Equation of a tangent to a circle (6 marks, P2)
• 3Centre via perpendicular bisector of a chord (6 marks, P2)
• 4Angle in a semicircle theorem (5 marks, P2)

Worked examples (5)

• 1Quadratic-in-$\\sin\\theta$ equation (5 marks, P2)
• 2Equation using $\\sin^{2} + \\cos^{2} = 1$ (5 marks, P2)
• 3Equation in $\\cos(\\theta + 30°)$ (4 marks, P2)
• 4Equation in $\\tan 2\\theta$ in radians (5 marks, P2)
• 5Mixed identity / equation — using $\\tan = \\sin/\\cos$ (5 marks, P2)

Worked examples (5)

• 1Arithmetic series — sum to $n$ terms (5 marks, P2)
• 2Geometric series — sum to infinity (5 marks, P2)
• 3Arithmetic-series modelling (savings) (6 marks, P2)
• 4Geometric-series modelling (depreciation) (5 marks, P2)
• 5Sigma notation — arithmetic and geometric (5 marks, P2)

Worked examples (5)

• 1Chain rule on $(3x^{2} - 1)^{5}$ (3 marks, P2)
• 2Product rule on $x^{2} e^{x}$ (3 marks, P2)
• 3Quotient rule on $\\dfrac{\\sin x}{x^{2}}$ (4 marks, P2)
• 4Stationary point of $f(x) = \\ln x - x$ (5 marks, P2)
• 5Chain rule on $\\sin(3x + 2)$ and second derivative (5 marks, P2)

Worked examples (5)

• 1Standard integrals (4 marks, P2)
• 2Definite trig integral (4 marks, P2)
• 3Integration by substitution (5 marks, P2)
• 4Integration by parts on $x e^{x}$ (5 marks, P2)
• 5Area between two curves (7 marks, P2)