## Question of the Week – Week 43

Find, in terms of m, the coordinates of the point (1,0) after being reflected in the line $y=mx$.

## Question of the Week – Week 42

Find rational numbers x and y such that $4^x\times 3^y=24$.

## Question of the Week – Week 41

Solve $\frac{1}{3^{x}-1}+3^{1-x}=1.5$

## Question of the Week – Week 40

The points (0,6), (9,0), (0,-6) and (-k,0) lie on the circumference of a circle. Find the value of k.

## Question of the Week – Week 39

The diagram shows the curve with equation $y=-x(x-2)(x+1)$. Find the area shaded shown in green. ## Question of the Week – Week 38

Given that $f(x)=x^{\frac{1}{2}}+9x^{-\frac{1}{2}}$ (and $x\ne 0$), find the values of x for which f(x) is a decreasing function.

## Question of the Week – Week 37

Prove that $\frac{\cos^4(\theta)-\sin^4(\theta)}{\cos^2(\theta)}\equiv 1-\tan^2{\theta}$.

## Question of the Week – Week 36

The points A and B have position vectors $3{\bf i}-4{\bf j}$ and $2{\bf j}-7{\bf i}$ respectively. The point P splits the line vector $\overrightarrow{AB}$ in the ratio 2:3. Find the position vector $\overrightarrow{OP}$.

## Question of the Week – Week 35

A ship leaves a port and heads to its destination for 65 km on a bearing of $071^\circ$ before receiving a distress signal. The distress signal is sent from a vessel with a position that is 54km away from and at a bearing of $122^\circ$ relative to the port. Calculate the distance between the vessel in distress and the ship.

## Question of the Week – Week 34 From C2 Edexcel Paper June 2013.

## Question of the Week – Week 33 From C2 Edexcel Paper May 2014.

## Question of the Week – Week 32

Point P with x-coordinate 0.5 lies on the curve with equation $y=2x^2$. The normal to the curve at point P intersects the curve at points P and Q. Find the coordinates of Q.

## Question of the Week – Week 31 From Edexcel C2 June 2017 exam.

## Question of the Week – Week 30 From Edexcel C2 January 2010 exam.

## Question of the Week – Week 29

The gradient of a curve is given by $\frac{dy}{dx}=\frac{\left(3-\sqrt{x}\right)^2}{\sqrt{x}}$ for $x\textgreater 0$. Given that $y=\frac{2}{3}$ when $x=1$, find y in terms of x.

## Question of the Week – Week 28

Given that the equation $20x^2=4kx-14kx^2+2$, where k is a constant, has no real roots, find the set of possible values of k.

## Question of the Week – Week 27

Simplify $x\left(2x^{-\frac{1}{4}}\right)^4$.

## Question of the Week – Week 26

Given that $f$ for $x\textgreater 0$, and the point $(4,-8)$ lies on the graph of $y=f(x)$, find $f(x)$ simplifying each term.

## Question of the Week – Week 25

Solve $3^xe^{4x-1}=5$, giving your answer in the form $\frac{a+\ln(b)}{c+\ln(d)}$.