O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2018 · Q1011 Marks
The diagram shows a prism with a rectangular base of length 15 cm and width x cm. The cross section of the prism is a right-angled triangle. The height of the prism is 4 cm less than its width. The volume of the prism is 440 cm³. [Figure 10.1]
- (a)Show that 3x² - 12x - 176 = 0.[3]
- (b)Solve the equation 3x² - 12x – 176 = 0. Show your working and give your answers correct to 2 decimal places.[3]
- (c)Find the height of the prism.[1]
- (d)A line is drawn on the surface of the prism from B to F. Another line is drawn on the surface of the prism from A to F. Calculate angle AFB.[4]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [M2] 1/2 x (x - 4) × 15 = 440
- B1 for height = (x - 4)
- [A1] Correct expansion and simplification leading to 3x^2 - 12x - 176 = 0
- [B2] -(-12) ± √((-12)^2 – 4 × 3 × -176) / (2 × 3)
- B1 for √((-12)^2 – 4 × 3 × -176)
- or for (-(-12) ± √their 2256) / (2 × 3)
- [B1] 9.92 and -5.92
- [1] 5.92
- FT (their positive root – 4) if result positive
- [4] 18.2 or 18.21 to 18.22...
- M2 for [AF = ] √15^2 + their 9.92^2
- Or for [BF = ] √their 9.92^2 + their 5.92^2 + 15^2 oe
- or M1 for AF^2 = 15^2 + their 9.92^2 soi
- or for BF^2 = their 9.92^2 + their 5.92^2 + 15^2 oe
- AND
- M1 for tan [AFB] = their 5.92 / their 17.98
- or sin [AFB] = their 5.92 / their 18.93
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