Graph (2018-2020)
$\def\D{\displaystyle}$
| 1 | (CIE 2018/m/22/q4) (a) (i) State the amplitude of $15 \sin 2 x-5$. $[1]$ (ii) State the period of $15 \sin 2 x-5$. $[1]$ (b)  The diagram shows the graph of $y=|\mathrm{f}(x)|$ for $-180^{\circ} \leqslant x^{\circ} \leqslant 180^{\circ}$, where $\mathrm{f}(x)$ is a trigonometric function. (i) Write down two possible expressions for the trigonometric function $\mathrm{f}(x)$.[2] (ii) State the number of solutions of the equation $|f(x)|=1$ for $-180^{\circ} \leqslant x^{6} \leqslant 180^{*}$.$[1]$
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| 2 | (CIE 2018/s/11/ q3) Diagrams A to D show four different graphs. In each case the whole graph is shown and the scales on the two axes are the same.  Place ticks in the boxes in the table to indicate which descriptions, if any, apply to each graph. There may be more than one tick in any row or column of the table. $[4]$ $\begin{array}{|l|l|l|l|l|}\hline &A & B & C & D \\\hline \text{Not a function} & & & & \\\hline \text{One-one function} & && & \\\hline \text{A function that is its own inverse} & && & \\\hline \text{A function with no inverse} & & && \\\hline\end{array}$ |
| 3 | (CIE 2018, s, paper 11, question 4)> (i) The curve $y=a+b \sin c x$ has an amplitude of 4 and a period of $\frac{\pi}{3}$. Given that the curve passes through the point $\left(\frac{\pi}{12}, 2\right)$, find the value of each of the constants $a, b$ and $c$. $[4]$ (ii) Using your values of $a, b$ and $c$, sketch the graph of $y=a+b \sin c x$ for $0 \leqslant x \leqslant \pi$ radians. [3]  |
| 4 | (CIE 2018, s, paper 12 , question 1 ) It is given that $y=1+\tan 3 x$. (i) State the period of $y$. $[1]$ (ii) On the axes below, sketch the graph of $y=1+\tan 3 x$ for $0^{\circ} \leqslant x^{\circ} \leqslant 180^{\circ}$. $[3]$  |
| 5 | (CIE 2018, s, paper 21 , question 9) (i) Express $5 x^{2}-14 x-3$ in the form $p(x+q)^{2}+r$, where $p, q$ and $r$ are constants. $[3]$ (ii) Sketch the graph of $y=\left|5 x^{2}-14 x-3\right|$ on the axes below. Show clearly any points where your graph meets the coordinate axes. $[4]$  (iii) State the set of values of $k$ for which $\left|5 x^{2}-14 x-3\right|=k \quad$ has exactly four solutions. [2] |
Answers
1. $15,180, \tan x,-\tan x, 4$
$40 .$
2 . $-2,4,6$ 3.
4. (i) $\frac{\pi}{3}$ or $60^{\circ}$
5. $5(x-7/5)^2-64/5$
$0<k<64 / 5$
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