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)}.