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.