Grade 11
Math AA HL - Term II – OBT1
Date: 5 February 2026
Name: ___________________________
Note: Calculator is allowed for this paper.
1.
The diagram below shows a fenced triangular enclosure in the middle of a grassy
field where AC = 3 m, DC = 2m, angle CBA = radians and ACB =
radians.
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One end of a rope is attached to point D on the outside edge of the enclosure, and the
other end is attached to a goat G. Given that the rope is 6 m long and the area of the
field outside the enclosure that the goat is able to graze is 74 m2,
find the value of .
2.
1
Given that sin x − cos x = , find cos 8x, rounding your answer to 3 significant figures.
4
Show all the workings. Don’t write answer directly from GDC.
3.
A function, f, is defined by f ( x) = 6.2sin ( x − 7.5 ) + c, for 0 x 15, where c R .
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(a)
Find the period of f.
The function f has a minimum at A(3, 11.8) and maximum at B(12, 24.2).
(b)
(i)
Find the value of c.
(ii)
Hence, find the value of f(9).
A second function, g, is defined by
2
g ( x) = a sin
( x + 2.25) + b for 0 x 15, where a, b R
15
The function g passes through the points P(1.5, 14.5) and Q(14, 10.2).
(c)
Find the value of a and the value of b.
(d)
Find the value of x for which the functions have the greatest difference.
4.
In a triangle ABC,
5sin( ABC ) − 6 cos( BCA) = 7
6sin( BCA) − 5cos( ABC ) = 2
(a) Show that sin( ABC + BCA) =
1
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James claims that CAB can have two solutions.
(b) Show that James is wrong by proving that CAB has only one possible value.
5.
A group of designers are creating a knife holder.
The diagram on the left shows a knife inside the holder and the diagram on the right
shows the empty holder.
The lengths of the holder, AB = 28 cm, AD = 20 cm, and CD = 20 cm and angle
CXB = radians. The designers can move the vertex X anywhere along the line
AD. Market research suggests that the most appealing design is such that the value of
is maximised. Find the length of AX which maximizes the value of .
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