2011 Higher Maths Solutions

Paper 1 Paper 2

The Exponential & Logarithmic Function

New Topic: The Exponential and Logarithmic Functions By the end of this topic you will be able to: • recall and use the laws of logarithms • solve simple exponential and logarithmic equations • model mathematically situations involving the logarithmic or exponential function

Further Calculus

New Topic: Further Calculus, MiA Unit 3 Ch2 By the end of this topic you will be able to: • differentiate and integrate functions involving brackets • differentiate and integrate trig functions • apply these skills to solve problems

Compound Angle Formulae

New Topic: Compound Angle Formulae, MiA Unit 2 Ch3 By the end of this topic you will be able to: • know and apply the addition formulae: sin(A+B) = sinAcosB + cosAsinB sin(A–B)  = sinAcosB – cosAsinB cos(A+B) = cosAcosB – sinAsinB cos(A–B) = cosAcosB + sinAsinB • know and apply the double angle formulae: sin2A  [...]

Polynomials

New Topic: Polynomials, MiA Unit 2 Ch1.1 By the end of this topic you will be able to: • use the Remainder Theorem to find remainder when dividing by x – h

• determine the roots of a polynomial equation

• use the Factor Theorem to determine the factors of a [...]

Sequences

New Topic: Sequences, MiA Higher Ch4 By the end of this topic you will: • know the terms: sequence, nth term, limit as n tends to • use un notation for the nth term of a sequence • define and interpret recurrence relations of the form un+1 = mun + c • know condition for [...]

Differentiation

New Topic: Differentiation, MiA Higher Ch3 By the end of this topic you will: • be familiar with the terminology associated with differentiation • understand the principles of differentiation • be able to derive the gradient formula of a given function • be able to calculate the gradient of a tangent to a curve • [...]

Trigonometric Functions & Graphs

New Topic: Trigonometric Functions & Graphs By the end of this topic you will be able to: • convert Degrees to Radian measure and vice versa • recall exact values in and calculate using radian measure • translate graphs of trig functions • sketch trig functions given their equation • solve trig equations

Vertex, Focus & Directrix

Work with a partner to find the vertex, focus and directrix of a parabola. (you will be assigned a parabola in class) Solutions to be submitted by Friday 3 September. Here are a couple of links to get you started: http://www.ltcconline.net/greenl/courses/103b/Conics/PARAB.htm

Composite & Inverse Functions

By the end of this topic you will: know domain, range, inverse, composite functions be able to find f(g(x)) given f(x) and g(x)