year12+archives

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July
Use partial fractions to solve the integrals
 * 23rd July 2007**

Use partial fractions to solve the integrals
 * 16th July 2007**

math f:y\mapsto y^2, \, y \in \Re math math g:y\mapsto \sqrt{16-4y}, \, y\in \Re, \, y\leq 4 math math h:y\mapsto 5y+10, \, y\in \Re math find math f^{-1}, \, g^{-1} \,and \, h^{-1} math
 * 9th July 2007**

given that math f(x)=2x^2-14x+9, \, x \in \Re math math g(x)=x^3+6, \, x>0, \, x \in \Re math find math f(-1), \, g(5), \, fg(2) math
 * 2th July 2007**

**June**
Show that math \dfrac{4x^3-7x+5}{2x+3} math can be written as math Ax^2+Bx+C+\frac{D}{2x+3} math And calculate the values of A, B, C and D
 * 25th June 2007**

Simplify the following
 * 18th June 2007**

math \dfrac{2x^2-8}{4x^2+20x+24} math

math \dfrac{x^2-x-6}{x^3+6x^2+8x} math

math \dfrac{3(a+2)}{4b} \times \dfrac{b^2}{3(a^2-4)} math

Show that math (x+1) math is a factor of math x^3-x^2-50x-48 math
 * 11th June 2007**

hence or otherwise find all the solutions of math x^3-x^2-50x-48=0 math

Solve the following
 * 4th June 2007**

math \int\limits_{0}^{10} x^3+3x-\frac{1}{x^2}\, dx math

math \int \limits_{-5}^{5}2x^2-2x-\frac{1}{x}+\frac{1}{3x^3}\,dx math

math \int \limits_{1}^{3}\alpha^3-2\alpha^2-\frac{3}{\alpha}+\frac{2}{3\alpha^2}\,d\alpha math

**May**
The curve c has the equation f(//x//)= //x//³ - 7//x//² + 15//x// + 6 The point P has an x coordinate of 1 The point Q is a minimum turning point of the curve Find f'(//x//) and show that PQ is parallel to the //x//-axis
 * 28th May 2007**

math 3\sin x=6\cos x math find the value of math \tan x math
 * 21th May 2007**

solve for math 0^{\circ}<360^{\circ} math math 5 \sin^2 x=1+ \cos x math Giving your answer to the nearest degree
 * 14th May 2007**

Describe the circle with the equation math x^2+y^2=4x math
 * 7th May 2007**

**April**
A cylinder of radius x and height y has a surface area of 60cm². Calculate the maximum volume of the cylinder.
 * 30th April 2007**

Expand (4 + //a//x)⁶ in ascending powers of x up to the term in x³ if the coefficient of x³ is 20. what is the value of //a// Now substitute for //a// to work out the coefficients of the other three parts
 * 23rd April 2007**

Factorise math x^3- 7x - 6 math
 * 16th April 2007**

A circle C has centre math (4,3) math and radius math 5\sqrt{2} math A line **//L//** has the equation y=x+3 a) Write down the equation of circle C b) Calculate the exact coordinates of the two points where C intersects **//L//** c) Find the distance between the two points
 * 2nd April 2007**

**March**
The line math y=x+5 math cuts the line math y=x^2+6x-12 math at the points A and B (a) Find the coordinates of A and B (b) Calculate the area between the two lines
 * 26th March 2007**

If log3(x) = log5(y), find in the form of a single logarithm, the value of logx(y).
 * 19th March 2007**

The coefficient of x² in the binomial expansion of math (1+\frac{x}{2})^n math where n is a positive integer, is **9**. (changed coefficient to 9 to make life easier - but how to answer it is still your problem) a) find the value of n. b) Using the value of n found in part a, find the coefficient of x³.
 * 12th March 2007**

** Work out (a) The area and (b) The perimeter of the blue shape.
 * 5th March 2007

**February**
a) work out the other angles here: b) now work out its area.
 * 26th Feb 2007**

if math a+b+c=4 math math ab+bc+ca=6 math math abc=3 math Work out math \frac{1}{a}+\frac{1}{b}+\frac{1}{c} math math \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca} math math a^2+b^2+c^2 math
 * 19th Feb 2007**