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.
Answer/Explanation
(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 = ……………….
Answer/Explanation
(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