O-LevelMathematicsTrigonometry4024/23 · May/June 2025 · Q2211 Marks
The diagram shows a pyramid ABCV. The base of the pyramid is an equilateral triangle, ABC, with sides of length 34 cm. The height VO is perpendicular to the base of the pyramid. VA = VB = VC = 82 cm.
- (a)Write down the number of planes of symmetry of the pyramid.[1]
- (b)(i)M is the midpoint of AC. The ratio MO: OB is 1:2. Show that OB = 19.6 cm correct to 1 decimal place.[3]
- (b)(ii)Calculate the angle between the edge VB and the base of the pyramid.[2]
- (b)(iii)Calculate the volume of the pyramid.[5]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [1] 3
- [3] M1 Explicit method to find MB
- M1 Method to find OB, provided their MB found from Pythagoras or trigonometry
- A1 19.62 to 19.63
- [2] 76.1 to 76.2
- M1 for 82cos x = 19.6 oe
- [5] 13300 or 13281 to 13286
- M2 for [height =] √82²-19.6² oe
- or M1 for 19.6² + height² = 82²
- M1 for area of base = 1/2 × 34 × 34sin 60 oe
- Or 1/2 × 34 × their MB oe
- M1 for 1/3 × their base area × their height
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