Cambridge IGCSE™
* 7 8 7 6 4 3 4 7 5 0 *
ADDITIONAL MATHEMATICS 0606/11
Paper 1 April 2024
2 hours
You must answer on the question paper.
No additional materials are needed.
INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
● The total mark for this paper is 80.
● The number of marks for each question or part question is shown in brackets [ ].
This document has 18 pages.
DC (CJ/FC) 212434/2
© UCLES 2021 [Turn over
2
Mathematical Formulae
1. ALGEBRA
Quadratic Equation
For the equation ax 2 + bx + c = 0 ,
- b ! b 2 - 4ac
x=
2a
Binomial Theorem
n n n
(a + b) n = a n + e o a n - 1 b + e o a n - 2 b 2 + f + e o a n - r b r + f + b n
1 2 r
n
where n is a positive integer and e o =
n!
r (n - r) !r!
Arithmetic series un = a + (n - 1) d
1 1
Sn = n (a + l ) = n {2a + (n - 1) d}
2 2
Geometric series un = ar n - 1
a (1 - r n )
Sn = ( r ! 1)
1-r
a
S3 = ( r 1 1)
1-r
2. TRIGONOMETRY
Identities
sin 2 A + cos 2 A = 1
sec 2 A = 1 + tan 2 A
cosec 2 A = 1 + cot 2 A
Formulae for ∆ABC
a b c
= =
sin A sin B sin C
a 2 = b 2 + c 2 - 2bc cos A
1
T = bc sin A
2
© UCLES 2021 0606/11/A/24
3
1
y
0 x
- 360° - 270° - 180° - 90° 90° 180° 270° 360°
-2
-4
-6
x
The diagram shows the graph of y = a sin + c for - 360° G x G 360°, where a, b and c are integers.
b
x
(a) Write down the period of a sin + c. [1]
b
(b) Find the value of a, of b and of c. [3]
© UCLES 2021 0606/11/A/24 1 [Turn over
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2 Points A and C have coordinates (- 4, 6) and (2, 18) respectively. The point B lies on the line AC such
2
that AB = AC.
3
(a) Find the coordinates of B. [2]
(b) Find the equation of the line l, which is perpendicular to AC and passes through B. [2]
(c) Find the area enclosed by the line l and the coordinate axes. [2]
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5
(a) Find the vector which has magnitude 39 and is in the same direction as b
12 l
3 . [2]
-5
(b) Given that a = b
2
l and b = b - 4 l, find the constants m and n such that 5a + m e 4 o = nb . [4]
-1 5 6
6
q -2 pr
4 (a) Given that = p a q b r c , find the value of each of the constants a, b and c. [3]
r ` pqj
3 -3
4 2
(b) Solve the equation 3x 5 - 8x 5 + 5 = 0 . [4]
7
5. Find the possible values of the constant k such that the equation kx 2 +4kx +3k +1 = 0 has two
different real roots. [4]
8
d ` 2 3xj
6 (a) Find x e . [3]
dx
1
d ` 2 j3
(b) (i) Find 3x + 4 . [2]
dx
2
x `3x 2 + 4j
2 -
(ii) Hence find y
0
3
dx . [3]
9
7 (a) Show that the equation of the curve y = `x 2 - 4j`x - 2j can be written as y = x 3 + ax 2 + bx + 8 ,
where a and b are integers. Hence find the exact coordinates of the stationary points on the curve.
[4]
(b) On the axes, sketch the graph of y = `x 2 - 4j`x - 2j , stating the intercepts with the coordinate
axes. [4]
O x
(c) Find the possible values of the constant k for which `x 2 - 4j`x - 2j = k has exactly 4 different
solutions. [2]
10
8
A
C
10 cm
i
O rad
The diagram shows a circle, centre O, radius 10 cm. The points A and B lie on the circumference of the
circle. The tangent at A and the tangent at B meet at the point C. The angle AOB is i radians. The length
of the minor arc AB is 28 cm.
(a) Find the value of i. [1]
(b) Find the perimeter of the shaded region. [3]
11
(c) Find the area of the shaded region. [3]
12
9 A function f (x) is such that f (x) = ln (2x + 3) + ln 4 , for x 2 a , where a is a constant.
(a) Write down the least possible value of a. [1]
(b) Using your value of a, write down the range of f. [1]
(c) Using your value of a, find f - 1 (x) , stating its range. [4]
13
(d) On the axes below, sketch the graphs of y = f (x) and y = f - 1 (x) , stating the exact intercepts of
each graph with the coordinate axes. Label each of your graphs. [4]
O x
14
10 The first three terms of an arithmetic progression are lg x, lg x 5 , lg x 9 , where x 2 0 .
(a) Show that the sum to n terms of this arithmetic progression can be written as n (pn - 1) lg x ,
where p is an integer. [4]
(b) Hence find the value of n for which the sum to n terms is equal to 4950 lg x . [2]
(c) Given that this sum to n terms is also equal to -14850, find the exact value of x. [2]
15
11 A particle P moves in a straight line such that, t seconds after passing through a fixed point O, its
`2t + 1j2
3
displacement, s metres, is given by s = - 1.
t+1
`2t + 1j2
1
(a) Show that the velocity of P at time t can be written in the form (a + bt) , where a and b
are integers to be found. (t + 1) 2 [5]
(b) Show that P is never at instantaneous rest after passing through O. [1]
16
12
y y = x + 10
y = x2 – 4x + 10 B
O C x
The graph of y = x2 – 4x + 10 cuts the y-axis at point A. The graphs of y = x2 – 4x + 10 and
y = x + 10 intersect one another at the points A and B. The line BC is perpendicular to the x-axis.
Calculate the area of the shaded region enclosed by the curve and the line AB. [8]
17
Continuation of working space for question 12.
18
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