# Core 2 Useful Workings For Challenging Questions With Explanations

It contains questions from past papers that people may find challenging, with working and explanations at the side :)

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• Created by: George
• Created on: 14-05-11 18:51

## Pages in this set

### Page 1

Mathematics Core 2 Exam Style Questions that are considered challenging

Logarithms
Given that 0 < x < 4 and: log 5 (4 ­ x) ­ 2log 5 (x) = 1, solve for x

Solution
log 5 (4 ­ x) ­ 2log 5 (x) = 1

log 5 (4 ­ x)…

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Polynomials
f(x) = x 4 + 5x3 + ax + b, where a and b are constants

The remainder when f(x) is divided by (x ­ 2) is equal to the remainder when f(x) is divided by
(x + 1)

(a) Find the value of a

Given that (x +…

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Trigonometrical Identities
Show that the equation

(a) 4sin 2 x + 9cos x ­ 6 = 0, can be written as, 4cos 2x ­ 9cos x + 2 = 0

Hence solve, for 0 x < 720

(b) 4sin 2 x + 9cos x ­ 6 = 0

Solution
4sin…

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Look where cos is positive (1/4 is positive) cos and all functions

x = 75.5, 284.5, 435.5, 644.5

Geometric Series
The first three terms of a geometric series are (k + 4), k and (2k ­ 15) respectively, where k is a
positive constant.

(a) Show that k 2 ­…

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16 / ¼

64

Differentiation
A solid right circular cylinder has radius r cm and height h cm.

The total surface area of the cylinder is 800 cm 2

(a) Show that the volume, V cm 3 , of the cylinder is given by, V = 400r ­ r 3…