PSLE Maths circles: composite figures, perimeter and area
Circles is a P6 topic, and it carries more marks than any other topic in the P6 WA2 papers I have read. It is almost never a bare circle. It is a circle cut up and joined to squares and rectangles.
What the papers ask
- Circumference and area of a whole circle, from the radius or the diameter. The one-mark questions of Paper 1.
- Semicircles and quarter circles, where half or a quarter of the circle is taken and the straight edges must be added back for the perimeter.
- Composite figures: a semicircle on a rectangle, a running track, a ring, quarter circles in a square. Perimeter and area are often asked as parts (a) and (b).
- Areas found by adding and taking away, the hardest form, where the shaded part has no formula of its own. These sit among the last questions of Paper 2. See how those questions are built.
The mistakes that cost marks
| Mistake | What to do instead |
|---|---|
| Radius and diameter swapped | Write r = before starting. Area uses the radius twice; a figure labelled with the diameter needs halving first. |
| A straight edge inside the figure counted in the perimeter | Trace the outside with a finger. Only what is traced goes in. |
| The straight edges of a semicircle left out | A semicircle's perimeter is the curved half plus the diameter, unless the diameter is joined to something else. |
| The wrong value of pi | Use the one the question gives, 22/7 or 3.14, and nothing else. |
| Half the circle's area taken for a quarter circle | A quarter circle is a quarter: pi × r × r ÷ 4. |
A worked example: the leaf in a square
The figure shows a square of side 14 cm. A quarter circle of radius 14 cm is drawn from each of two opposite corners, and the leaf between them is shaded. Take pi as 22/7.
(a) Find the perimeter of the shaded leaf.
(b) Find the area of the shaded leaf.
(a) The leaf is bounded by two quarter circle arcs, each of radius 14 cm. One arc is 1/4 × 2 × 22/7 × 14 = 22 cm, so the perimeter is 2 × 22 = 44 cm. No straight edge is on the boundary.
(b) One quarter circle is 1/4 × 22/7 × 14 × 14 = 154 cm². The two quarter circles together cover the whole square, and they cover the leaf twice. So the leaf is 2 × 154 − 14 × 14 = 308 − 196 = 112 cm².
How to practise circles
- Do perimeter and area of the same figure one after the other. The perimeter is the harder half.
- Practise with both 22/7 and 3.14, and with the radius given as well as the diameter.
- End each session with one figure where the shaded part has no formula of its own.
Circles is in almost every paper in our March, June and August courses, marked before each lesson. See what WA2 tests, or see the course dates.
Common questions about PSLE circles
Should my child use 22/7 or 3.14 in PSLE Maths?
Whichever the question says. PSLE and school papers state the value of pi in each circles question, and an answer worked with the other value is marked wrong. When the radius or diameter is a multiple of 7, the question usually gives 22/7 so the working cancels neatly.
Why do children lose marks on circle perimeter questions?
Usually by counting a straight edge that is inside the figure, or by leaving out a straight edge that is on the boundary. The perimeter of a composite figure is only the edges you would walk round, and the answer depends on deciding which those are before doing any arithmetic.
Practise it, free
Each is a full Paper 1 and Paper 2, marked the moment it is handed in, with a report on what went wrong.
20 seats. One paper a day.
Online P6 Maths crash courses in the school holidays: one full paper a day, marked before class, a report to parents every night.
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