**Question of the Week – Week 51**

The diagram shows the curve and the straight line . Find the shaded area shown in purple to 3 decimal places.

**Question of the Week – Week 49**

Show that the difference between the squares of two consecutive odd numbers is always a multiple of 8.

**Question of the Week – Week 45**

Prove that the difference between a whole number and its cube is a multiple of 6.

**Question of the Week – Week 44**

The following table shows the prices in millions of pounds of some houses in a given postcode:

House Price, P (£m) | Frequency |

**Find an estimate for the interquartile range for this data.**

**Question of the Week – Week 43**

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

**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 . Find the area shaded shown in green.

**Question of the Week – Week 38**

Given that (and ), find the values of x for which f(x) is a decreasing function.

**Question of the Week – Week 36**

The points A and B have position vectors and respectively. The point P splits the line vector in the ratio 2:3. Find the position vector .

**Question of the Week – Week 35**

*A ship leaves a port and heads to its destination for 65 km on a bearing of 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 relative to the port. Calculate the distance between the vessel in distress and the ship.*

**Question of the Week – Week 32**

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