Higher November 2018 Paper 3 Q10
10 \(\mathrm{f}(x) = 4\sin x^\circ\)
(a) Find \(\mathrm{f}(23)\)
Give your answer correct to 3 significant figures. (1)
Give your answer correct to 3 significant figures. (1)
\(\mathrm{g}(x) = 2x - 3\)
(b) Find \(\mathrm{fg}(34)\)
Give your answer correct to 3 significant figures. (2)
Give your answer correct to 3 significant figures. (2)
\(\mathrm{h}(x) = (x + 4)^2\)
Ivan needs to solve the following equation \(\mathrm{h}(x) = 25\)
He writes
\((x + 4)^2 = 25\)
\(x + 4 = 5\)
\(x = 1\)
This is not fully correct.
(c) Explain why. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 1.56 | B1 | 1.56 to 1.563 |
| Answer | Mark | Mark scheme |
|---|---|---|
| 3.63 | M1 | for a complete method to find \(\mathrm{fg}(34)\) eg \(4 \sin 65\) (=3.625..) or \(\mathrm{fg}(x)\) eg \(4 \sin (2x - 3)\) |
| A1 | for answer in the range 3.6 to 3.63 |
Additional guidance
If an answer in the range is seen in working and then incorrectly rounded award full marks.
| Answer | Mark | Mark scheme |
|---|---|---|
| Statement | C1 | for statement eg positive and negative square root required. Acceptable examples The other answer is \(-9\) The quadratic should have 2 solutions. Not acceptable examples He has not expanded the brackets. He needed to \((x+4)\) twice as there is a squared sign. \((x+4)^2\) is 16 not 25. Didn’t expand the bracket. |