A2 Assignment 3 Cover SheetName:

Question / Done / Backpack / Ready / Topic / Comment
Drill / 1i / Solving Trig Equations
1ii / Solving Trig Equations
1iii / Solving Trig Equations
2i / Algebraic Fractions
2ii / Algebraic Fractions
2iii / Algebraic Fractions
3i / e and ln equations
3ii / Differentiation of e and ln
4i / Differentiation
4ii / Differentiation
4iii / Product Rule
4iv / Quotient Rule
4v / Product Rule
4vi / Quotient Rule
C2 Practice / 1a / Logs
1b / Solving Log Equations
2 / Solving Exponential Equations
3 / Exponential Simultaneous Equations
4a / Graph Sketching
4b / Graph Sketching
4c / Graph Sketching
4d / Graph Sketching
5a / Differentiation/Integration
5b / Differentiation/Integration
5c / Differentiation/Integration
6 / Pythagorean Identities
C3 Practice / 7 / Pythagorean Identities
8 / Pythagorean Identities
9 / Pythagorean Identities
10a / Pythagorean Identities
10b / Pythagorean Identities
11 / Trig Differentiation
Diff’n / 12 / Chain Rule
13 / Chain Rule

Comments/Actions

A2 Maths Assignment 3

Hand in the week commencing3rd July 2016.

Start early (use the 24 hour rule) and use subject extensions for help.

Your UCAS predicted grade will be your AS grade unless you missed a grade by a few marks and your A2 teacher sees strong evidence that you will do better.

You should

1 Provide a full solution to EVERY question, showing all working.

2 Tick or cross each of your answers in a contrasting colour according to the answers given.

3 Find the mistakes which led to incorrect solutions.

4 Provide corrections to incorrect solutions.

Part A - Drill – to be tested in the week commencing 3rdJuly 2016.

1Trigonometry

Solve

i)for 0θ 360o giving your answer correct to 3 sf

ii)for 0θ 2π, giving your answer correct to 3 sf

iii)for –π θπ, giving exact answers in terms of π

2Algebra

Simplify

i)ii)iii)

3e and Natural Logarithms

i)Solve the equations, giving your answer to 3 s.f.

a)

b)

ii)Differentiate the following expressions with respect to x

a)b) c)

e) ln (4x – 2)f)

4Differentiation

, ,

, ,

Findi) f’(x)ii) g’(x) iii) h’(x) iv) i’(x) v) j’(x) vi) k’(x)

Drill Answers

1.i) 78.5o, 282oii) 3.48, 5.94iii)

2i) ii) iii)

3i) a) 1.13b) 1.07

ii)a) b) c) d) e) f)

4i) ii)iii)

iv) v)

vi)

Part B – C2 Practice - these questions provide an excellent foundation for the A2 course. If you can answer these questions easily you will be able to start your A2 course with confidence.

1a)Giventhat, show that

b)Hence or otherwise, find the roots and, where, of the equation

2Solve

3Solve the simultaneous equations and

4Sketch the following curves, not using your graphical calculator, but either by knowing their shape and finding their roots, or by considering them as transformations of,, and respectively.

a)b)

c)d)

You can use your graphical calculator to check your sketches, but it’s important that you can sketch them without it.

5The function f, defined for xR, x > 0, is such that

f(x) = x2 – 2 +.

(a)Find the value of f (4).

(b) Given that f(3) = 0, find f(x).

(c) Prove that f is an increasing function.

Part C – C3 Practice

6Given that , write the following in terms of a:

(a)(b)(c)

7Prove that

8Prove that

9Express + as a single fraction in its simplest form.

10(a)Express as a fraction in its simplest form

.

(b)Hence solve

.

Part D– Differentiation

11Given thatfind and show that

12On the curve with equation, the pointPhasx coordinates of 0. Find the equation of the tangent to the curve at P.

13What are the derivatives and of and? Show your method.

Answers

Part B

(1b) (2) -0.487, 1.12 (3)x = 4, y = 3

(4)(5a) (5b) (5c)

Part C

(6a)(b)(c)(7) Proof(8) Proof

(9)(10a)(10b)

Part D

(11) (12) 18x – y + 1 = 0

(13) and