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2024 AQA AS MATHEMATICS 7356/ 2 Paper 2
Verified Question Paper and Marking Scheme Attached May 2024
MATHEMATICS
Paper 2
Thursday 23 May 2024 Afternoon Time allowed: 1 hour 30 minutes
Materials
⚫ You must have the AQA Formulae for A‑level Mathematics booklet. ⚫ You should have a graphical or scientific calculator that meets the requirements of the specification.
Instructions
⚫ Use black ink or black ball‑point pen. Pencil should only be used for drawing. ⚫ Fill in the boxes at the top of this page. ⚫ Answer all questions. ⚫ You must answer each question in the space provided for that question. ⚫ If you need extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s). ⚫ Do not write outside the box around each page or on blank pages. ⚫ Show all necessary working; otherwise marks for method may be lost. ⚫ Do all rough work in this book. Cross through any work that you do not want to be marked.
Information
⚫ The marks for questions are shown in brackets. ⚫ The maximum mark for this paper is 80.
Advice
⚫ Unless stated otherwise, you may quote formulae, without proof, from the booklet. ⚫ You do not necessarily need to use all the space provided. G For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
TOTAL
Do not write outside the Section A
Answer all questions in the spaces provided.
1 Line L has equation
5 y = 4 x + 6
Find the gradient of a line parallel to line L
Circle your answer.
box
[1 mark]
2 One of the equations below is true for all values of x
Identify the correct equation.
Tick ( ) one box. [1 mark]
cos^2 x = – 1 – sin^2 x
cos^2 x = – 1 + sin^2 x
cos^2 x = 1 – sin^2 x
cos^2 x = 1 + sin^2 x
Do not write outside the
4 Curve C has equation y = 8 sin x
4 (a) Curve C is transformed onto curve C 1 by a translation of vector [
]
box
Find the equation of C 1
[1 mark]
4 (b) Curve C is transformed onto curve C 2 by a stretch of scale factor 4 in the y direction.
Find the equation of C 2 [1 mark]
4 (c) Curve C is transformed onto curve C 3 by a stretch of scale factor 2 in the x direction.
Find the equation of C 3 [1 mark]
Do not write outside the
5 A student suggests that for any positive integer n the value of the expression
4 n^2 + 3
is always a prime number.
Prove that the student’s statement is false by finding a counter example. Fully justify your
answer. [3 marks]
box
Turn over for the next question
Turn over (^) U
Do not write outside the
6 (b) (ii) Find the value of a
[3 marks]
box
Turn over for the next question
Turn over (^) U
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7 Point A has coordinates (4, 1) and point B has coordinates (– 8, 5)
7 (a) Find the equation of the perpendicular bisector of AB [5 marks]
box
Do not write outside the
x
8 Prove that the graph of the curve with equation
y = x^3 + 15 x –
box
has no stationary points. [5 marks]
Do not write outside the Turn over for the next question
DO NOT WRITE ON THIS PAGE
ANSWER IN THE SPACES PROVIDED
box
Turn over U
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9 (b) On the diagram, the region enclosed between the curve and the line y = 2 is shaded.
Show that the area of this shaded region is
box
Fully justify your answer. [6 marks]
Turn over for the next question
Turn over U
Do not write outside the
10 A singer has a social media account with a number of followers. The singer releases a
new song and the number of followers grows exponentially.
The number of followers, F , may be modelled by the formula
F = a e kt
where t is the number of days since the song was released and a and k are constants.
⚫ Two days after the song is released the account has 2050 followers.
⚫ Five days after the song is released the account has 9200 followers.
On the graph below ln F has been plotted against t for these two pieces of data.
A line has been drawn passing through these two data points.
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In F
O 1 2 3 4 5 t
Do not write outside the
10 (b) (i) Show that
d F
= kF
d t
[2 marks]
box
10 (b) (ii) Using the model, estimate the rate at which the number of followers is increasing
5 days after the song is released. [2 marks]
10 (c) The singer claims that 30 days after the song is released, the account will have more
than a billion followers.
Comment on the singer’s claim. [1 mark]
END OF SECTION A
Do not write outside the Section B
Answer all questions in the spaces provided.
11 The table below shows the daily salt intake, x grams, and the daily Vitamin C
intake, y milligrams, for a group of 10 adults.
Adult A B C D E F G H I J
x 5.3 6.2 3.6 10.4 2.4 9.4 6 5 7.1 11.
y 90 145 88 48 114 44 80 95 55 41
A scatter diagram of the data is shown below.
box
y 80
x
One of the adults is an outlier. Identify the letter of the adult that is the outlier.
Circle your answer below.
[1 mark]
A B E J
12 Which one of the following is not a measure of spread?
Circle your answer.
[1 mark]
median range standard deviation variance
Turn over U
Do not write outside the
14 The discrete random variables X and Y can be modelled by the distributions
X ~ B(40 , p )
Y ~ B(25 , 0.6)
It is given that the mean of X is equal to the variance of Y
14 (a) Find the value of p
[3 marks]
box
14 (b) Find P( Y = 17)
[1 mark]
Turn over U
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15 The number of flowers which grow on a certain type of plant can be modelled by the
discrete random variable X
The probability distribution of X is given in the table below.
box
x 0 1 2 3 4 5 or more
P ( X = x ) 0.03 0.15 0.22 0.31 0.09 p
15 (a) Find the value of p
[2 marks]
15 (b) Two plants of this type are randomly selected from a large batch received from a local
garden centre.
Find the probability that the two plants will produce a total of three flowers. [3 marks]
