# iGCSE Mathematics (0580) :E6.3 Recognise, sketch and interpret graphs of simple trigonometric functions..iGCSE Style Questions Paper 4

### Question

(a) (i) On the axes, sketch the graph of $$y=\sin x$$ for $$0^{\circ}\leq x\leq 360^{\circ}.$$

(ii) Describe fully the symmetry of the graph of y= sinx for $$0^{\circ}\leq x\leq 360^{\circ}.$$

……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
(b) Solve 4 sin x-1= 2 for $$0°\leq x\leq360^{\circ} .$$
x = …………………… and x = ……………………
(c) (i) Write $$x^{2}+10x+14$$ in the form $$(x+a)^{2}+b.$$
………………………………………….
(ii) On the axes, sketch the graph of $$y=x^{2}+10x+14$$, indicating the coordinates of the turning point.

(a)(i) Correct sketch
(ii) Rotational [symmetry] order 2 [centre] (180, 0)
(b) 48.6 or 48.59 to 48.60 and 131.4 or 131.40 to 131.41
(c)(i) (x + 5)2 – 11
(ii) Sketch of U-shaped parabola with a minimum indicated at (–5, –11) with no part of graph in 4th quadrant

### Question

(a)
The diagram shows a sketch of the curve $$y=x^{2}+3x-4.$$
(i) Find the coordinates of the points A, B and C.
A (………….. , …………..)
B (………….. , …………..)
C (………….. , …………..)
(ii) Differentiate $$x^{2}+3x-4.$$
………………………………………….
(iii) Find the equation of the tangent to the curve at the point (2, 6).
………………………………………….
(b)
(i) On the diagram, sketch the graph of y= tanx for $$0°\leq x\leq 360°.$$
(ii) Solve the equation 5tan x =-7  for $$0°\leq x\leq 360°.$$
x = ……………….. or x = ……………….

(a)(i) A(–4, 0)
B(1, 0)
C(0, –4)
(ii) 2x + 3 [ ± 0] final answer
(iii) y = 7x – 8
(b)(i) Correct sketch

(ii) 125.5 or 125.53 to 125.54
and
305.5 or 305.53 to 305.54

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