Questions AS Paper 2 (315 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 2019 June Q13
6 marks Easy -1.2
13 Denzel wants to buy a car with a propulsion type other than petrol or diesel.
He takes a sample, from the Large Data Set, of the CO2 emissions, in \(\mathrm { g } / \mathrm { km }\), of cars with one particular propulsion type. The sample is as follows $$\begin{array} { l l l l l l l l } 82 & 13 & 96 & 49 & 96 & 92 & 70 & 81 \end{array}$$ 13
  1. Using your knowledge of the Large Data Set, state which propulsion type this sample is for, giving a reason for your answer.
    13
  2. Calculate the mean of the sample.
    13
  3. Calculate the standard deviation of the sample.
    13
  4. Denzel claims that the value 13 is an outlier. 13 (d) (i) Any value more than 2 standard deviations from the mean can be regarded as an outlier. Verify that Denzel's claim is correct.
    13 (d) (ii) State what effect, if any, removing the value 13 from the sample would have on the standard deviation.
AQA AS Paper 2 2019 June Q14
4 marks Easy -1.2
14 A probability distribution is given by $$\mathrm { P } ( X = x ) = c ( 4 - x ) , \text { for } x = 0,1,2,3$$ where \(c\) is a constant.
14
  1. Show that \(c = \frac { 1 } { 10 }\) 14
  2. Calculate \(\mathrm { P } ( X \geq 1 )\)
AQA AS Paper 2 2019 June Q15
6 marks Moderate -0.3
15 Two independent events, \(A\) and \(B\), are such that $$\begin{aligned} \mathrm { P } ( A ) & = 0.2 \\ \mathrm { P } ( A \cup B ) & = 0.8 \end{aligned}$$ 15
    1. Find \(\mathrm { P } ( B )\) 15
      1. (ii) Find \(\mathrm { P } ( A \cap B )\) 15
    2. State, with a reason, whether or not the events \(A\) and \(B\) are mutually exclusive.
AQA AS Paper 2 2019 June Q16
9 marks Moderate -0.3
16
16
Andrea is the manager of a company which makes mobile phone chargers.
In the past, she had found that \(12 \%\) of all chargers are faulty.
Andrea decides to move the manufacture of chargers to a different factory.
Andrea tests 60 of the new chargers and finds that 4 chargers are faulty.
Investigate, at the \(10 \%\) level of significance, whether the proportion of faulty chargers has reduced.
[7 marks] \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\) \(\_\_\_\_\)
16
  • State, in context, two assumptions that are necessary for the distribution that you have used in part (a) to be valid.
    •
    AQA AS Paper 2 2021 June Q1
    1 marks Easy -1.8
    1 Express as a single power of \(a\) $$\frac { a ^ { 2 } } { \sqrt { a } }$$ where \(a \neq 0\) Circle your answer. \(a ^ { 1 }\) \(a ^ { \frac { 3 } { 2 } }\) \(a ^ { \frac { 5 } { 2 } }\) \(a ^ { 4 }\)
    AQA AS Paper 2 2021 June Q2
    1 marks Easy -1.3
    2 One of the diagrams below shows the graph of \(y = \sin \left( x + 90 ^ { \circ } \right)\) for \(0 ^ { \circ } \leq x \leq 360 ^ { \circ }\) Identify the correct graph. Tick ( \(\checkmark\) ) one box. \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-03_451_465_568_497} \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-03_124_154_724_1073} \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-03_458_472_1105_495}
    □ \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-03_453_468_1647_497} \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-03_117_132_1809_1091} \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-03_461_479_2183_488}
    AQA AS Paper 2 2021 June Q3
    3 marks Easy -1.8
    3 It is given that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \sqrt { x }$$ Find an expression for \(y\).
    [0pt] [3 marks]
    L
    AQA AS Paper 2 2021 June Q4
    6 marks Moderate -0.8
    4
    1. Find the binomial expansion of \(( 1 - 2 x ) ^ { 5 }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 2 }\) 4
    2. Find the first two non-zero terms in the expansion of $$( 1 - 2 x ) ^ { 5 } + ( 1 + 5 x ) ^ { 2 }$$ in ascending powers of \(x\).
      4
    3. Hence, use an appropriate value of \(x\) to obtain an approximation for \(0.998 ^ { 5 } + 1.005 ^ { 2 }\) [2 marks] \(5 A B C\) is a triangle. The point \(D\) lies on \(A C\). \(A B = 8 \mathrm {~cm} , B C = B D = 7 \mathrm {~cm}\) and angle \(A = 60 ^ { \circ }\) as shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-06_604_978_486_532}
    AQA AS Paper 2 2021 June Q5
    4 marks Easy -1.2
    5
    1. Using the cosine rule, find the length of \(A C\).
      5
    2. Hence, state the length of \(A D\).
    AQA AS Paper 2 2021 June Q6
    3 marks Easy -1.2
    6 Find the solution to $$5 ^ { ( 2 x + 4 ) } = 9$$ giving your answer in the form \(a + \log _ { 5 } b\), where \(a\) and \(b\) are integers.
    AQA AS Paper 2 2021 June Q7
    8 marks Moderate -0.3
    7 The diagram below shows the graph of the curve that has equation \(y = x ^ { 2 } - 3 x + 2\) along with two shaded regions. \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-08_646_711_408_667} 7
    1. State the coordinates of the points \(A , B\) and \(C\).
      7
    2. Katy is asked by her teacher to find the total area of the two shaded regions.
      Katy uses her calculator to find \(\int _ { 0 } ^ { 2 } \left( x ^ { 2 } - 3 x + 2 \right) \mathrm { d } x\) and gets the answer \(\frac { 2 } { 3 }\) Katy's teacher says that her answer is incorrect.
      7 (b) (i) Show that the total area of the two shaded regions is 1
      Fully justify your answer.
      7 (b) (ii) Explain why Katy's method was not valid.
    AQA AS Paper 2 2021 June Q8
    4 marks Moderate -0.3
    8 It is given that \(y = 3 x - 5 x ^ { 2 }\) Use differentiation from first principles to find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) [0pt] [4 marks]
    LIH
    AQA AS Paper 2 2021 June Q9
    4 marks Standard +0.3
    9
    1. Express \(n ^ { 3 } - n\) as a product of three factors. 9
    2. Given that \(n\) is a positive integer, prove that \(n ^ { 3 } - n\) is a multiple of 6
    AQA AS Paper 2 2021 June Q10
    9 marks Moderate -0.3
    10 A square sheet of metal has edges 30 cm long. Four squares each with edge \(x \mathrm {~cm}\), where \(x < 15\), are removed from the corners of the sheet. The four rectangular sections are bent upwards to form an open-topped box, as shown in the diagrams. \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-12_392_460_630_347} \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-12_387_437_635_872} \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-12_282_380_703_1318} 10
    1. Show that the capacity, \(C \mathrm {~cm} ^ { 3 }\), of the box is given by $$C = 900 x - 120 x ^ { 2 } + 4 x ^ { 3 }$$ 10
    2. Find the maximum capacity of the box. Fully justify your answer.
    AQA AS Paper 2 2021 June Q11
    10 marks Standard +0.3
    11 A circle \(C\) has centre \(( 0,10 )\) and radius \(\sqrt { 20 }\) A line \(L\) has equation \(y = m x\) 11
      1. Show that the \(x\)-coordinate of any point of intersection of \(L\) and \(C\) satisfies the equation $$\left( 1 + m ^ { 2 } \right) x ^ { 2 } - 20 m x + 80 = 0$$ 11
        1. (ii) Find the values of \(m\) for which the equation in part (a)(i) has equal roots.
          11
      2. Two lines are drawn from the origin which are tangents to \(C\). Find the coordinates of the points of contact between the tangents and \(C\).
    AQA AS Paper 2 2021 June Q12
    1 marks Easy -1.8
    12 The table below shows the total monthly rainfall (in mm ) in England and Wales in a sample of six years. The sample of six years was taken from a data set covering every year from 1768 to 2018.
    JanFebMarAprMayJunJulAugSepOctNovDec
    1768109.2129.112.885.646.1148.7121.991.6136.8119.4142.5103.6
    181898.065.8134.7135.655.931.250.421.0115.675.8112.046.8
    186899.962.271.161.436.716.520.0106.790.295.661.4185.6
    191891.261.636.763.358.530.9110.062.9189.569.166.3122.5
    196885.847.659.568.878.794.0107.872.2148.199.069.684.2
    2018104.552.8115.191.451.916.539.676.767.075.8104.9116.0
    Deduce the sampling method most likely to have been used to collect this sample. Circle your answer.
    [0pt] [1 mark] Opportunity
    Simple Random
    Stratified
    Systematic
    AQA AS Paper 2 2021 June Q13
    1 marks Easy -1.3
    13 The diagram below shows the probability distribution for a discrete random variable \(Y\). \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-17_816_1338_356_351} Find \(\mathrm { P } ( 0 < Y \leq 3 )\).
    Circle your answer. \(0.40 \quad 0.42 \quad 0.58 \quad 0.66\)
    AQA AS Paper 2 2021 June Q14
    3 marks Moderate -0.8
    14 The random variable \(T\) follows a binomial distribution where $$T \sim \mathrm {~B} ( 16,0.3 )$$ The mean of \(T\) is denoted by \(\mu\).
    14
    1. \(\quad\) Find \(\mathrm { P } ( T \leq \mu )\).
      14
    2. Find the variance of \(T\). \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-19_2488_1716_219_153}
    AQA AS Paper 2 2021 June Q15
    3 marks Easy -1.8
    15
    The number of hours of sunshine and the daily maximum temperature were recorded over a 9-day period in June at an English seaside town. A scatter diagram representing the recorded data is shown below. \includegraphics[max width=\textwidth, alt={}, center]{f87d1b36-26db-4a0b-b9ec-d7d82a396aba-20_872_1511_488_264} One of the points on the scatter diagram is an error. 15
      1. Write down the letter that identifies this point.
        15
        1. (ii) Suggest one possible action that could be taken to deal with this error.
          15
      2. It is claimed that the scatter diagram proves that longer hours of sunshine cause
        higher maximum daily temperatures. Comment on the validity of this claim.
        [0pt] [1 mark]
    AQA AS Paper 2 2021 June Q16
    5 marks Easy -1.2
    16 An analysis was carried out using the Large Data Set to compare the \(\mathrm { CO } _ { 2 }\) emissions (in g/km) from 2002 and 2016. The summary statistics for the \(\mathrm { CO } _ { 2 }\) emissions, \(X\), for all cars registered as owned by either females or males is given in the table below.
    \cline { 2 - 3 } \multicolumn{1}{c|}{}\(\mathbf { 2 0 0 2 }\)\(\mathbf { 2 0 1 6 }\)
    \(\sum \boldsymbol { x }\)207901142103
    Sample size12151144
    16
    1. Find the reduction in the mean of the \(\mathrm { CO } _ { 2 }\) emissions in 2016 compared to the mean of the CO2 emissions in 2002.
      16
    2. It is claimed that the move to more electric and gas/petrol powered cars has caused the reduction in the mean \(\mathrm { CO } _ { 2 }\) emissions found in part (a). Using your knowledge of the Large Data Set, state whether you agree with this claim.
      Give a reason for your answer.
      16
    3. There are 3827 data values in the Large Data Set. It is claimed that the data in the table above must have been summarised incorrectly.
      16 (c) (i) Explain why this claim is being made. 16 (c) (ii) State whether this claim is correct.
      Give a reason for your answer.
    AQA AS Paper 2 2021 June Q17
    7 marks Moderate -0.8
    17 The number of toilets in each of a random sample of 200 properties from a town was recorded. Four types of properties were included: terraced, semi-detached, detached and apartment. The data is summarised in the table below.
    \multirow{2}{*}{}Number of toilets
    OneTwoThree
    Terraced20104
    Semi-Detached185016
    Detached12108
    Apartment22300
    One of the properties is selected at random. \(A\) is the event 'the property has exactly two toilets'. \(B\) is the event 'the property is detached'.
    17
      1. Find \(\mathrm { P } ( A )\). 17
        1. (ii) Find \(\mathrm { P } \left( A ^ { \prime } \cap B \right)\). 17
      2. (iii) Find \(\mathrm { P } ( A \cup B )\).
        17
      3. Determine whether events \(A\) and \(B\) are independent.
        Fully justify your answer.
        17
      4. Using the table, write down two events, other than event \(\boldsymbol { A }\) and event \(\boldsymbol { B }\), which are mutually exclusive. Event 1 \(\_\_\_\_\) \section*{Event 2}
    AQA AS Paper 2 2021 June Q18
    7 marks Moderate -0.3
    18 It is known from previous data that 14\% of the visitors to a particular cookery website are under 30 years of age. To encourage more visitors under 30 years of age a large advertising campaign took place to target this age group. To test whether the campaign was effective, a sample of 60 visitors to the website was selected. It was found that 15 of the visitors were under 30 years of age. 18
    1. Explain why a one-tailed hypothesis test should be used to decide whether the sample provides evidence that the campaign was effective. 18
    2. Carry out the hypothesis test at the \(5 \%\) level of significance to investigate whether the sample provides evidence that the proportion of visitors under 30 years of age has increased.
      18
    3. State one necessary assumption about the sample for the distribution used in part (b) to be valid.
      [0pt] [1 mark]
    AQA AS Paper 2 2022 June Q1
    1 marks Easy -2.0
    1 Find \(\int 12 x ^ { 3 } \mathrm {~d} x\) Circle your answer. \(36 x ^ { 2 } + c\) \(3 x ^ { 4 } + c\) \(3 x ^ { 2 } + c\) \(36 x ^ { 4 } + c\)
    AQA AS Paper 2 2022 June Q2
    1 marks Easy -1.8
    2 Given that $$\cos \left( \theta - 20 ^ { \circ } \right) = \cos 60 ^ { \circ }$$ which one of the following is a possible value for \(\theta\) ?
    Circle your answer.
    [0pt] [1 mark] \(40 ^ { \circ }\) \(140 ^ { \circ }\) \(280 ^ { \circ }\) \(320 ^ { \circ }\)
    AQA AS Paper 2 2022 June Q3
    5 marks Moderate -0.8
    3 A curve has equation \(y = k \sqrt { x }\) where \(k\) is a constant. Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at the point \(( 4,2 k )\) on the curve, giving your answer as an expression in terms of \(k\).