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x = 0 (A1)(A1) (C2)

Note: Award (A1) for x = “a constant” (A1) for = 0. Award (A0)(A0) for an answer of “0”.

[2 marks]

f(x) = −2 (y = −2) (A1)(A1) (C2)

Note: Award (A1) for y = “a constant” (A1) for = −2. Award (A0)(A0) for an answer of “−2”.

[2 marks]

$\frac{3}{x} - 2 = 0$ (M1)

Note: Award (M1) for equating f(x) to 0.

$\left( {x = } \right)\frac{3}{2}\,\,\,\,\,\left( {1.5} \right)$ (A1) (C2)

[2 marks]

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Topic 6 - Mathematical models » 6.5 » Functions of this type and their graphs.

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18M.2.sl.TZ2.6f: Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.
18M.2.sl.TZ2.6e: Show that the stationary points of the curve are at x = 1 and x = 2.
18M.2.sl.TZ2.6d: Find $\frac{{{\text{dy}}}}{{{\text{dx}}}}$ .
18M.2.sl.TZ2.6c: Find the value of y when x = 1 .
18M.2.sl.TZ2.6b: A teacher asks her students to make some observations about the curve. Three students...
18M.2.sl.TZ2.6a: Sketch the curve for −1 < x < 3 and −2 < y < 12.
18M.1.sl.TZ2.11b: Write down the equation of the horizontal asymptote.
18M.1.sl.TZ2.11a: Write down the equation of the vertical asymptote.
18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...
18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
18M.2.sl.TZ1.4a: Find the value of k.
17N.1.sl.TZ0.14a: Write down the derivative of $f$ .
17N.2.sl.TZ0.5e: Write down the coordinates of the point of intersection.
17N.2.sl.TZ0.5d: Draw the graph of $f$ for $- 3 \leqslant x \leqslant 3$ and...
17N.2.sl.TZ0.5c: Use your answer to part (b)(ii) to find the values of $x$ for which $f$ is increasing.
17N.2.sl.TZ0.5b.ii: Find $f’(x)$ .
17N.2.sl.TZ0.5b.i: Expand the expression for $f(x)$ .
17N.2.sl.TZ0.5a: Find the exact value of each of the zeros of $f$ .
17M.2.sl.TZ2.6g: The equation $f(x) = m$ , where $m \in \mathbb{R}$ , has four solutions. Find the possible...
17M.2.sl.TZ2.6f: Write down the number of possible solutions to the equation $f(x) = 5$ .
17M.2.sl.TZ2.6e: Write down the range of $f(x)$ .
17M.2.sl.TZ2.6d.ii: Write down the intervals where the gradient of the graph of $y = f(x)$ is positive.
17M.2.sl.TZ2.6d.i: Write down the $x$ -coordinates of these two points;
17M.2.sl.TZ2.6c.ii: Find $f(2)$ .
17M.2.sl.TZ2.6c.i: Show that $a = 8$ .
17M.2.sl.TZ2.6b: Find $f'(x)$ .
17M.2.sl.TZ2.6a: Write down the $y$ -intercept of the graph.
16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
10M.2.sl.TZ1.3a: Write down the values of x where the graph of f (x) intersects the x-axis.
11N.2.sl.TZ0.4a: Write down (i) the equation of the vertical asymptote to the graph of $y = f (x)$ ...
07M.2.sl.TZ0.3i.a: Write down the equation of the vertical asymptote.
07N.1.sl.TZ0.5: The following curves are sketches of the graphs of the functions given below, but in a...
07N.2.sl.TZ0.1ii.a: Sketch the curve of the function $f (x) = x^3 − 2x^2 + x − 3$ for values of $x$ from −2...
08N.2.sl.TZ0.5a: (i) Write down the value of $y$ when $x$ is $2$ . (ii) Write down the...
08N.2.sl.TZ0.5b: Sketch the curve for $- 4 \leqslant x \leqslant 3$ and $- 10 \leqslant y \leqslant 10$ ....
15M.2.sl.TZ2.5a: Find $f( - 2)$ .

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Date	May 2018	Marks available	2	Reference code	18M.1.sl.TZ2.11
Level	SL only	Paper	1	Time zone	TZ2
Command term	Calculate	Question number	11	Adapted from	N/A

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