Foundation June 2018 Paper 1 Q23
23 Here is a solid square-based pyramid, \(VABCD\).
The base of the pyramid is a square of side 6 cm.
The height of the pyramid is 4 cm.
\(M\) is the midpoint of \(BC\) and \(VM = 5\) cm.
(a) Draw an accurate front elevation of the pyramid from the direction of the arrow.
(b) Work out the total surface area of the pyramid. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| isosceles triangle, base 6 cm, height 4 cm | M1 | for drawing an isosceles triangle or for drawing a triangle of base 6cm and height 4cm |
| A1 | for a fully correct diagram |
Additional guidance
Accept a freehand drawing
Only a single triangle is acceptable;
do not accept any attempted nets or 3-D diagrams
Condone a perpendicular drawn from base to vertex
| Answer | Mark | Mark scheme |
|---|---|---|
| 96 cm2 | M1 | for a method to find the area of a triangular face eg \(\frac{1}{2} \times 6 \times 5\ (= 15)\) |
| M1 | (dep) for finding the total surface area eg \(4 \times \text{``}15\text{''} + 6 \times 6\) | |
| A1 | for a numerical answer of 96 SC B1 for an answer of 84 if M0 scored | |
| B1 | cm2 |
Additional guidance
A1: Ignore incorrect or absent units for this mark
[The SC is from: \(4 \times \frac{1}{2} \times 6 \times 4 + 6 \times 6\)]
B1: Ignore incorrect or absent numerical answer for this mark