The diagram shows a symmetrical plate ABCDEF. The line ABCD is straight and the length of BC is 2 cm. Each of the two sectors ABF and DCE is of radius r cm and each of the angles ABF and DCE is equal to ⅓π radians. [Figure 8.1]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [M1] XE/0.4 = sin(π/6) or XE/0.4 = cos(π/3) [XE = 0.2] A correct trig expression involving XE. Do not condone a mixture of degrees and radians.
2. [A1] Length EF = 2+2×0.2 = 2.4 AG
3. [B1] [CX =]0.4cos(π/3) or 0.4sin(π/6) or √(0.4²-0.2²) OE, SOI Expect √3/5 or 0.3464.
4. [B1] [Sector=]1/2×(0.4)²×π/3 SOI Expect 0.0838 or 2π/75
5. [M1] Area of their (rectangle + two triangles + two sectors) Or Area of their (trapezium + two sectors)
6. [A1] 0.930 AWRT
7. [B1] [Length AD =] 2+2r Must be seen alone or part of a list and not part of a product.
8. [B1] [Arc length =] r x π/3 May be implied by r x π/3 x 2. Must be seen alone or part of a list.
9. [B1] [EF =]2+2rsin(π/6) or 2+2rcos(π/3) or 2+r Must be seen alone or part of a list and not part of a product.
10. [B1] [4+ 3r + 2rπ/3 = 6 leading to ] 0.393 AWRT Condone 6/(2π+9) NB: Using EF = 2.4 gives 0.391.