Answers in terms of π, surds kept exact, standard form by hand, and powers and roots of numbers you can work out in your head.
What you will learn
- Give areas and perimeters in terms of π
- Multiply and add surds (Higher)
- Multiply and divide in standard form by hand
- Work out powers and roots, including fractional and negative indices (Higher)
Leave π in the answer
"Give your answer in terms of π" means do not multiply by 3.14.
The answer 36π is exact; 113.04 is rounded.
The radius of a circle is the distance from its centre to its edge. The diameter is the distance right across through the centre, twice the radius. The circumference is the distance round the circle. The area of a circle is πr², where r is the radius, and the circumference is πd, where d is the diameter. A circle of radius 6 cm has exact area π × 6² = 36π cm².
- A semicircle with diameter 10 cm
- radius = 5 cm
- area = ½ × π × 5² = 12.5π cm²
- perimeter = ½ × π × 10 + 10 = 5π + 10 cm
A shaded area is often a square with a circle taken out. A circle that fits exactly inside a square of side 8 cm has diameter 8 cm, so radius 4 cm: the shaded area is 8² − π × 4² = 64 − 16π cm². A quarter circle of radius 8 cm centred on a corner has area ¼ × π × 8² = 16π cm².
The rest of this lesson and its 9 practice questions are locked.
In this lesson
- Leave π in the answer
- Surds kept exact (Higher)
- Standard form by hand
- Powers and roots
- Try it: Exact or rounded?
9 practice questions, marked as you go; about 25 minutes in all.
Key terms
Surd, Standard form
In this unit: Non-calculator methods
Everything Paper 1 asks you to do by hand: written multiplication and division, fractions and percentages, estimating and checking, exact answers, and multi-step problems without a calculator.