Questions — AQA AS Paper 2 (143 questions)

Browse by module
All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 S1 S2 S3 S4 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 PURE S1 S2 S3 S4 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 Pre-U Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
Sort by: Default | Easiest first | Hardest first
AQA AS Paper 2 2023 June Q13
1 marks Easy -1.8
The table below shows the frequencies for a set of data from a continuous variable \(X\)
\(x\)Frequency
\(11 < x \leq 21\)7
\(21 < x \leq 24\)9
\(24 < x \leq 42\)36
\(42 < x \leq 50\)18
A histogram is drawn to represent this data. Find the frequency density of the bar in the histogram representing the class \(24 < x \leq 42\) Circle your answer. [1 mark] 2 \qquad 18 \qquad 36 \qquad 70
AQA AS Paper 2 2023 June Q14
4 marks Easy -1.8
The manager of a factory wants to introduce a bonus scheme. The factory has 65 employees who work in production and 28 employees who work in the office. The manager decides to collect the opinions of a sample of these 93 employees.
  1. Explain how the manager could collect a simple random sample of 20 employees. [3 marks]
  2. The manager collected a simple random sample of 20 employees. The manager noticed that all 20 of the employees in the sample worked in production and therefore the sample was not representative. State a different method of sampling that would give a representative sample. [1 mark]
AQA AS Paper 2 2023 June Q15
5 marks Moderate -0.8
Numbered balls are placed in bowls A, B and C In bowl A there are four balls numbered 1, 2, 3 and 7 In bowl B there are eight balls numbered 0, 0, 2, 3, 5, 6, 8 and 9 In bowl C there are nine balls numbered 0, 1, 1, 2, 3, 3, 3, 6 and 7 This information is shown in the diagram below. \includegraphics{figure_15} A three-digit number is generated using the following method: • a ball is selected at random from each bowl • the first digit of the number is the ball drawn from bowl A • the second digit of the number is the ball drawn from bowl B • the third digit of the number is the ball drawn from bowl C
  1. Find the probability that the number generated is even. [1 mark]
  2. Find the probability that the number generated is 703 [2 marks]
  3. Find the probability that the number generated is divisible by 111 [2 marks]
AQA AS Paper 2 2023 June Q16
4 marks Moderate -0.3
The discrete random variable \(X\) has probability distribution
\(x\)123456
P(X = x)0.30.10.20.10.10.2
The discrete random variable \(Y\) has probability distribution
\(y\)234567
P(Y = y)0.3p0.20.1p3p + 0.05
It is claimed that P(X ≥ 3) is greater than P(Y ≤ 4) Determine if this claim is correct. Fully justify your answer. [4 marks]
AQA AS Paper 2 2023 June Q17
5 marks Easy -1.3
An archer is training for the Olympics. Each of the archer's training sessions consists of 30 attempts to hit the centre of a target. The archer consistently hits the centre of the target with 79% of their attempts. It can be assumed that the number of times the centre of the target is hit in any training session can be modelled by a binomial distribution.
  1. Find the mean of the number of times that the archer hits the centre of the target during a training session. [1 mark]
  2. Find the probability that the archer hits the centre of the target exactly 22 times during a particular training session. [1 mark]
  3. Find the probability that the archer hits the centre of the target 18 times or less during a particular training session. [1 mark]
  4. Find the probability that the archer hits the centre of the target more than 26 times in a training session. [2 marks]
AQA AS Paper 2 2023 June Q18
3 marks Easy -1.2
It is believed that 25% of the customers at a bakery buy a loaf of bread. In an attempt to increase this proportion, the manager of the bakery provided free samples for the customers to taste. To decide whether providing free samples had been effective, a large random sample of customers leaving the bakery were asked whether they had purchased a loaf of bread. A hypothesis test at the 5% significance level was carried out on the data collected. The test statistic calculated was found to be in the critical region.
  1. State the Null and Alternative hypotheses for this test. [1 mark]
  2. State, in context, the conclusion to this test. [2 marks]
AQA AS Paper 2 2023 June Q19
4 marks Easy -1.3
A comparison of the masses (in kg) of convertible cars was made using the Large Data Set. A sample of 20 masses was chosen from both the 2002 data and the 2016 data. The masses of the 20 cars in each sample were used to create a box plot for each year. The box plots were labelled Box Plot A and Box Plot B as shown in the diagram below. \includegraphics{figure_19}
  1. Estimate the median of the masses from Box Plot A [1 mark]
  2. It is claimed that Box Plot B must be incorrectly drawn.
    1. Give a reason why this claim was made. [1 mark]
    2. Comment on the validity of this claim. [1 mark]
  3. It is claimed that Box Plot B must be from the 2002 data. Give a reason why this claim is correct. [1 mark]
AQA AS Paper 2 2024 June Q1
1 marks Easy -2.0
Line \(L\) has equation $$5y = 4x + 6$$ Find the gradient of a line parallel to line \(L\) Circle your answer. $$\frac{5}{4} \quad -\frac{4}{5} \quad \frac{4}{5} \quad \frac{5}{4}$$ [1 mark]
AQA AS Paper 2 2024 June Q2
1 marks Easy -1.8
One of the equations below is true for all values of \(x\) Identify the correct equation. Tick (\(\checkmark\)) one box. [1 mark] \(\cos^2 x = -1 - \sin^2 x\) \(\square\) \(\cos^2 x = -1 + \sin^2 x\) \(\square\) \(\cos^2 x = 1 - \sin^2 x\) \(\square\) \(\cos^2 x = 1 + \sin^2 x\) \(\square\)
AQA AS Paper 2 2024 June Q3
4 marks Moderate -0.8
It is given that $$3 \log_a x = \log_a 72 - 2 \log_a 3$$ Solve the equation to find the value of \(x\) Fully justify your answer. [4 marks]
AQA AS Paper 2 2024 June Q4
3 marks Easy -1.3
Curve \(C\) has equation \(y = 8 \sin x\)
  1. Curve \(C\) is transformed onto curve \(C_1\) by a translation of vector \(\begin{pmatrix} 0 \\ 4 \end{pmatrix}\) Find the equation of \(C_1\) [1 mark]
  2. 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]
  3. 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]
AQA AS Paper 2 2024 June Q5
3 marks Moderate -0.8
A student suggests that for any positive integer \(n\) the value of the expression $$4n^2 + 3$$ is always a prime number. Prove that the student's statement is false by finding a counter example. Fully justify your answer. [3 marks]
AQA AS Paper 2 2024 June Q6
7 marks Standard +0.3
In the expansion of \((3 + ax)^n\), where \(a\) and \(n\) are integers, the coefficient of \(x^2\) is 4860
  1. Show that $$3^n a^2 n (n - 1) = 87480$$ [3 marks]
  2. The constant term in the expansion is 729 The coefficient of \(x\) in the expansion is negative.
    1. Verify that \(n = 6\) [1 mark]
    2. Find the value of \(a\) [3 marks]
AQA AS Paper 2 2024 June Q7
9 marks Standard +0.3
Point \(A\) has coordinates \((4, 1)\) and point \(B\) has coordinates \((-8, 5)\)
  1. Find the equation of the perpendicular bisector of \(AB\) [5 marks]
  2. A circle passes through the points \(A\) and \(B\) A diameter of the circle lies along the \(x\)-axis. Find the equation of the circle. [4 marks]
AQA AS Paper 2 2024 June Q8
5 marks Standard +0.8
Prove that the graph of the curve with equation $$y = x^3 + 15x - \frac{18}{x}$$ has no stationary points. [5 marks]
AQA AS Paper 2 2024 June Q9
9 marks Standard +0.3
A curve has equation $$y = x - a\sqrt{x} + b$$ where \(a\) and \(b\) are constants. The curve intersects the line \(y = 2\) at points with coordinates \((1, 2)\) and \((9, 2)\), as shown in the diagram below. \includegraphics{figure_1}
  1. Show that \(a\) has the value 4 and find the value of \(b\) [3 marks]
  2. 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 \(\frac{16}{3}\) Fully justify your answer. [6 marks]
AQA AS Paper 2 2024 June Q10
11 marks Moderate -0.3
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 $$F = ae^{kt}$$ 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. \includegraphics{figure_2}
    1. Show that \(\ln F = \ln a + kt\) [2 marks]
    2. Using the graph, estimate the value of the constant \(a\) and the value of the constant \(k\) [4 marks]
    1. Show that \(\frac{dF}{dt} = kF\) [2 marks]
    2. Using the model, estimate the rate at which the number of followers is increasing 5 days after the song is released. [2 marks]
  3. 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]
AQA AS Paper 2 2024 June Q11
1 marks Easy -1.8
The table below shows the daily salt intake, \(x\) grams, and the daily Vitamin C intake, \(y\) milligrams, for a group of 10 adults.
AdultABCDEFGHIJ
\(x\)5.36.23.610.42.49.4657.111.2
\(y\)9014588481144480955541
A scatter diagram of the data is shown below. \includegraphics{figure_3} One of the adults is an outlier. Identify the letter of the adult that is the outlier. Circle your answer below. [1 mark] A \(\qquad\) B \(\qquad\) E \(\qquad\) J
AQA AS Paper 2 2024 June Q12
1 marks Easy -2.5
Which one of the following is not a measure of spread? Circle your answer. [1 mark] median \(\qquad\) range \(\qquad\) standard deviation \(\qquad\) variance
AQA AS Paper 2 2024 June Q13
4 marks Easy -1.8
The headteacher of a school wishes to collect the opinions of the students on a new timetable structure. To do this, a random sample of size 50, stratified by year group, will be selected. The school has a total of 720 students. The number of students in each of the year groups at this school is shown below.
Year group10111213
Number of students200240150130
  1. Find the number of students from each year group that should be selected in the stratified random sample. [3 marks]
  2. State one advantage of using a stratified random sample. [1 mark]
AQA AS Paper 2 2024 June Q14
4 marks Moderate -0.8
The discrete random variables \(X\) and \(Y\) can be modelled by the distributions $$X \sim \text{B}(40, p)$$ $$Y \sim \text{B}(25, 0.6)$$ It is given that the mean of \(X\) is equal to the variance of \(Y\)
  1. Find the value of \(p\) [3 marks]
  2. Find P(\(Y = 17\)) [1 mark]
AQA AS Paper 2 2024 June Q15
7 marks Moderate -0.3
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.
\(x\)012345 or more
P(\(X = x\))0.030.150.220.310.09\(p\)
  1. Find the value of \(p\) [2 marks]
  2. 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]
    1. State one assumption necessary for the calculation in part (b) to be valid. [1 mark]
    2. Comment on whether, in reality, this assumption is likely to be valid. [1 mark]
AQA AS Paper 2 2024 June Q16
5 marks Easy -1.8
An investigation into the hydrocarbon emissions, \(X\) g/km, from cars in the Large Data Set was carried out. The results are summarised below. $$\sum x = 128.657 \qquad \sum x^2 = 8.701 \, 707 \qquad n = 2405$$ where \(n\) is the total number of cars which had a measured hydrocarbon emission in the Large Data Set.
    1. Find the mean of \(X\) [1 mark]
    2. Find the standard deviation of \(X\) [2 marks]
    1. The Large Data Set is a sample taken from the entire UK Department for Transport Stock Vehicle Database. It is claimed that the values in part (a)(i) and part (a)(ii) obtained from the Large Data Set should be reliable estimates for the mean and standard deviation of the hydrocarbon emissions for the entire UK Department for Transport Stock Vehicle Database. State, with a reason, whether this claim is likely to be correct. [1 mark]
    2. State one type of emission where more than 80% of the data is known for cars in the entire UK Department for Transport Stock Vehicle Database. [1 mark]
AQA AS Paper 2 2024 June Q17
5 marks Moderate -0.3
The proportion of vegans in a city is thought to be 8% The owner of an organic food café in this city believes that the proportion of their customers who are vegan is greater than 8% To test this belief, a random sample of 50 customers at the café were interviewed and it was found that 7 of them were vegan. Investigate, at the 5% level, whether this sample supports the owner's belief. [5 marks]
AQA AS Paper 2 Specimen Q1
1 marks Easy -1.8
\(p(x) = x^3 - 5x^2 + 3x + a\), where \(a\) is a constant. Given that \(x - 3\) is a factor of \(p(x)\), find the value of \(a\) Circle your answer. [1 mark] \(-9\) \quad\quad \(-3\) \quad\quad \(3\) \quad\quad \(9\)