Cambridge IGCSE: Additional Mathematics 0606/11
Cambridge IGCSE: Additional Mathematics 0606/11
Cambridge IGCSE: Additional Mathematics 0606/11
* 5 1 7 2 0 6 4 8 8 4 *
2 hours
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 [ ].
DC (CE/SG) 316817/2
© UCLES 2023 [Turn over
2
Mathematical Formulae
1. ALGEBRA
Quadratic Equation
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
1
y
2 The polynomial P (x) is such that P (x) = ax 3 - 11x 2 + bx + c , where a, b and c are integers. P (x) is
3
divisible by x and has a remainder of when divided by 2x + 1. It is also given that Pl (2) = 18 .
2
(a) Find the values of a, b and c. [6]
2 -3
3 The point A has position vector e o. The point B has position vector e o.
-6 6
(a) Find, in vector form, the displacement of B from A. [2]
x 1 2 3 4 5
y 20 57 104 160 224
The table shows values of the variables x and y, which are related by the equation y = Ax b , where A
and b are constants.
(a) Use the data to draw a straight line graph of ln y against ln x. [3]
ln y
–1
(b) Use your graph to estimate the values of A and b. Give your answers correct to 2 significant
figures. [4]
(c) Use your graph to estimate the value of y when x = 3.5. [2]
5 (a) A 4-digit code is to be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. No digit may be
used more than once in any code. A code may start with 0.
(iii) Find how many codes form a number greater than 1000. [2]
(b) A team of 9 people is to be chosen from a group of 15 people. The group includes a family of 4
people who must not be separated. Find the number of teams that can be chosen. [3]
1
6 (a) Write 3 lg x - lg 4 + 2 as a single logarithm to base 10. [3]
2
(b) Solve the equation 2 log a 4 - 3 log 4 a - 5 = 0, giving your answers in exact form. [5]
(a) Show that f l (x) can be written in the form 2 (3x - 2) (px + q) , where p and q are integers. [3]
(b) Hence find the coordinates of the stationary points on the curve. [2]
(c) On the axes below, sketch the graph of y = f (x), stating the intercepts with the coordinate axes.
[3]
O x
(d) Find the values of k such that the equation f (x) = k has 3 distinct solutions. [2]
8
y
A C
O x
y = 4x 2 - 6x - 5
B
y = 1 - 4x
The diagram shows the line y = 1 - 4x meeting the curve y = 4x 2 - 6x - 5 at the points A and B.
The tangent to the curve at B meets the horizontal line through A at the point C. Find the x-coordinate
of C, giving your answer correct to 2 decimal places. [10]
i i i
9 (a) The first three terms of an arithmetic progression are - 3 tan , - tan , tan ,
r 2 2 2
where 0 1 i 1 .
2
19 3
(i) Given that the 12th term of this progression is equal to , find the exact value of i. [4]
3
(ii) Hence find the exact value of the sum to ten terms of this progression. [2]
1 1
(b) The first three terms of a geometric progression are cosec 4 z , cosec 2 z , 1,
16 4
r r
where - 1z1 .
2 2
(i) Given that the sum of the 3rd and 4th terms of this progression is equal to 4, find the possible
values of z. [4]
(ii) Determine whether or not this progression has a sum to infinity. [2]
3x 2 - 2 dy Ax + B
10 (a) Given that y = , show that can be written in the form ,
x-4 dx (x - 4) 2 3x 2 - 2
where A and B are integers to be found. [5]
(b) Hence find, in terms of h, the approximate change in y when x increases from 3 to 3 + h, where h
is small. [3]
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