22M-TZ2-Paper2
17. 21M.1.AHL.TZ1.6
- & -&
It is given that cosec " = %, where % < " < %
. Find the exact value of cot ".
[4]
18. 21M.2.SL.TZ1.4
A Ferris wheel with diameter 110 metres rotates at a constant speed. The lowest
point on the wheel is 10 metres above the ground, as shown on the following
diagram. P is a point on the wheel. The wheel starts moving with P at the lowest point
and completes one revolution in 20 minutes.
The height, ℎ metres, of P above the ground after ) minutes is given by ℎ()) =
, cos(0)) + 2, where ,, 0, 2 ∈ ℝ.
Find the values of ,, 0 and 2.
[5]
22M-TZ1-Paper2 –4– 2222 – 7110
3. [Maximum mark: 6]
A company is designing a new logo. The logo is created by removing two equal segments
from a rectangle, as shown in the following diagram.
diagram not to scale
The rectangle measures 5 cm by 4 cm . The points A and B lie on a circle, with centre O
and radius 2 cm , such that AÔB = θ , where 0 < θ < π . This information is shown in the
following diagram.
diagram not to scale
O θ 5
(a) Find the area of one of the shaded segments in terms of θ . [3]
(b) Given that the area of the logo is 13.4 cm2 , find the value of θ . [3]
(This question continues on the following page)
12EP04
19M-TZ2-Paper2
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16EP05
13M-TZ2-Paper 2
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16EP05
HL 1.7-1.8 COMPLEX NUMBERS - CARTESIAN FORM - POLYNOMIALS
' ()(#
• − ))
• . #' + +6
1)
2)
4)
2) (17 Marks)
5)
2.
13. 23M.1.AHL.TZ1.8
Part of the graph of a function, !, is shown in the following diagram. The graph of " =
!(%) has a "-intercept at (0, 3), an %-intercept at (+, 0) and a horizontal asymptote
" = −2.
Consider the function .(%) = |!(|%|)|. [N/A]
[[N/A]]
(a) On the following grid, sketch the graph of " = .(%), labelling any axis intercepts
and giving the equation of the asymptote.
[4]
(b)
Find the possible values of 0 such that (.(%))' = 0 has exactly two solutions.
[3]
14. 22N.1.SL.TZ0.7
(a)
The graph of a quadratic function ! has its vertex at the point (3, 2) and it
intersects the %-axis at % = 5. Find ! in the form !(%) = +(% − ℎ)' + 0.
[3]
