4MA0 Higher January 2014 Paper 3R Q18
18
Ivan is a shot putter.
The formula \(h = 2 + 6t - 5t^2\) gives the height, \(h\) metres, of the shot above the ground \(t\) seconds after he has released the shot.
(i) Solve \(\;2 + 6t - 5t^2 = 0\)
Give your solutions correct to 3 significant figures.
Show your working clearly.
Give your solutions correct to 3 significant figures.
Show your working clearly.
The shot hits the ground after \(T\) seconds.
(ii) Write down the value of \(T\).
Give your answer correct to 3 significant figures.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| (i) \(\dfrac{-6 \pm \sqrt{6^2 - 4 \times -5 \times 2}}{2 \times -5}\) | M1 |
| \(\dfrac{-6 \pm \sqrt{76}}{-10}\) or \(\dfrac{-6 \pm \sqrt{36 + 40}}{-10}\) | M1 |
| −0.272 1.47 | A1 |
| (ii) Answer: 1.47 | B1 |
| (4) | |
| (4 marks) |
Notes
M1: for correct substitution condone + in place of \(\pm\) and condone one sign error in substitution
M1: for correct simplification
A1: Award for answers which round to −0.272 (−0.2717...) and 1.47 (1.4717…)
Award 3 marks for correct answers, if at least M1 scored. Condone missing negative solution
B1: for answer which rounds to 1.47 ft from (i) if only one positive solution given
The mark scheme states that for this question the correct answer alone does not imply a correct method.