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John has twin sisters. The sum of the ages of John and his twin sisters is 39. In 4 years’ time the twins will be 18. How old will John be in 4 years’ time?

With a problem like this first you must pull the necessary information out of the question. It can make it more familiar if we assign single letters to the unknowns. In this case the unknowns are, Johns age ...
FW
Answered by Finlay W. • Maths tutor
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Calculate the area of a sector which has an acute angle of 30 degrees and a radius of 5cm.

Sector area = (angle/360) + πr 2 Therefore the answer would be: Area = (30/360) + (π x 5 2 ) = 78.62 degrees to 2dp
PH
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P (–1, 4) is a point on a circle, centre O which is at the origin. Work out the equation of the tangent to the circle at P. Give your answer in the form y = mx + c

A tangent makes an angle of 90 degrees with the radius of a circle.Using this fact, we find the gradient of the radius going through P = -4Therefore gradient of the tangent to the circle at P is -1/-4 = 1/4T...
CG
Answered by Charlie G. • Maths tutor
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n is an integer greater than 1. Prove algebraically that n^2-2-(n-2)^2 is always an even number

We want to show that this gives an even number, so we need to get it into a form that it is 2 multiplied by some positive integer. We start by expanding the (n-2) 2 out, remember that (n-2) 2 =(n-2)(n-2). Th...
JC
Answered by Jacob C. • Maths tutor
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Nancy is driving and makes a wrong turn. The satnav indicates that her journey will take an extra 7 minutes. Nancy drives at an average speed of 60km/h to the nearest 5km/h. What's the greatest possible distance traveled in this detour in km to 2.d.p?

Start by selecting useful information in the text.time = 7 minutesspeed = 60km/h to the nearest 5km/hmaximum possible distance travelled = ? kmWe know a time and speed and want to know a distance. So we can ...
LG
Answered by Louis G. • Maths tutor
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