Questions AS Paper 2 (308 questions)

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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 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 Mechanics 1 PURE Pure 1 S1 S2 S3 S4 Stats 1 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 SPS SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics 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
Edexcel AS Paper 2 Specimen Q6
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8f3dbcb4-3260-4493-a230-12577b4ed691-12_520_1072_616_388} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A car moves along a straight horizontal road. At time \(t = 0\), the velocity of the car is \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The car then accelerates with constant acceleration \(a \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for \(T\) seconds. The car travels a distance \(D\) metres during these \(T\) seconds. Figure 1 shows the velocity-time graph for the motion of the car for \(0 \leqslant t \leqslant T\).
Using the graph, show that \(D = U T + 1 / 2 a T ^ { 2 }\).
(No credit will be given for answers which use any of the kinematics (suvat) formulae listed under Mechanics in the AS Mathematics section of the formulae booklet.)
Edexcel AS Paper 2 Specimen Q7
  1. A car is moving along a straight horizontal road with constant acceleration. There are three points \(A , B\) and \(C\), in that order, on the road, where \(A B = 22 \mathrm {~m}\) and \(B C = 104 \mathrm {~m}\). The car takes 2 s to travel from \(A\) to \(B\) and 4 s to travel from \(B\) to \(C\).
Find
  1. the acceleration of the car,
  2. the speed of the car at the instant it passes \(A\).
Edexcel AS Paper 2 Specimen Q8
  1. A bird leaves its nest at time \(t = 0\) for a short flight along a straight line.
The bird then returns to its nest.
The bird is modelled as a particle moving in a straight horizontal line.
The distance, \(s\) metres, of the bird from its nest at time \(t\) seconds is given by $$s = \frac { 1 } { 10 } \left( t ^ { 4 } - 20 t ^ { 3 } + 100 t ^ { 2 } \right) , \quad \text { where } 0 \leqslant t \leqslant 10$$
  1. Explain the restriction, \(0 \leqslant t \leqslant 10\)
  2. Find the distance of the bird from the nest when the bird first comes to instantaneous rest.
Edexcel AS Paper 2 Specimen Q9
9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8f3dbcb4-3260-4493-a230-12577b4ed691-18_694_1262_223_406} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A small ball \(A\) of mass 2.5 kg is held at rest on a rough horizontal table.
The ball is attached to one end of a string.
The string passes over a pulley \(P\) which is fixed at the edge of the table. The other end of the string is attached to a small ball \(B\) of mass 1.5 kg hanging freely, vertically below \(P\) and with \(B\) at a height of 1 m above the horizontal floor. The system is release from rest, with the string taut, as shown in Figure 2.
The resistance to the motion of \(A\) from the rough table is modelled as having constant magnitude 12.7 N . Ball \(B\) reaches the floor before ball \(A\) reaches the pulley. The balls are modelled as particles, the string is modelled as being light and inextensible, the pulley is modelled as being small and smooth and the acceleration due to gravity, \(g\), is modelled as being \(9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
    1. Write down an equation of motion for \(A\).
    2. Write down an equation of motion for \(B\).
  2. Hence find the acceleration of \(B\).
  3. Using the model, find the time it takes, from release, for \(B\) to reach the floor.
  4. Suggest two improvements that could be made in the model.
Edexcel AS Paper 2 Specimen Q1
  1. A company manager is investigating the time taken, \(t\) minutes, to complete an aptitude test. The human resources manager produced the table below of coded times, \(x\) minutes, for a random sample of 30 applicants.
Coded time ( \(x\) minutes)Frequency (f)Coded time midpoint (y minutes)
\(0 \leq x < 5\)32.5
\(5 \leq x < 10\)157.5
\(10 \leq x < 15\)212.5
\(15 \leq x < 25\)920
\(25 \leq x < 35\)130
(You may use \(\sum f y = 355\) and \(\sum f y ^ { 2 } = 5675\) )
  1. Use linear interpolation to estimate the median of the coded times.
  2. Estimate the standard deviation of the coded times. The company manager is told by the human resources manager that he subtracted 15 from each of the times and then divided by 2 , to calculate the coded times.
  3. Calculate an estimate for the median and the standard deviation of \(t\).
    (3) The following year, the company has 25 positions available. The company manager decides not to offer a position to any applicant who takes 35 minutes or more to complete the aptitude test. The company has 60 applicants.
  4. Comment on whether or not the company manager's decision will result in the company being able to fill the 25 positions available from these 60 applicants. Give a reason for your answer.
Edexcel AS Paper 2 Specimen Q2
2. The discrete random variable \(X \sim \mathrm {~B} ( 30,0.28 )\)
  1. Find \(\mathrm { P } ( 5 \leq X < 12 )\). Past records from a large supermarket show that \(25 \%\) of people who buy eggs, buy organic eggs. On one particular day a random sample of 40 people is taken from those that had bought eggs and 16 people are found to have bought organic eggs.
  2. Test, at the \(1 \%\) significance level, whether or not the proportion \(p\) of people who bought organic eggs that day had increased. State your hypotheses clearly.
  3. State the conclusion you would have reached if a \(5 \%\) significance level had been used for this test. \section*{(Total for Question 2 is 8 marks)}
Edexcel AS Paper 2 Specimen Q3
  1. Pete is investigating the relationship between daily rainfall, \(w \mathrm {~mm}\), and daily mean pressure, \(p\) hPa , in Perth during 2015. He used the large data set to take a sample of size 12.
He obtained the following results.
\(p\)100710121013100910191010101010101013101110141022
\(w\)102.063.063.038.438.035.034.232.030.428.028.015
Pete drew the following scatter diagram for the values of \(w\) and \(p\) and calculated the quartiles.
Q 1Q 2Q 3
\(p\)10101011.51013.5
\(w\)29.234.650.7
\includegraphics[max width=\textwidth, alt={}]{b29b0411-8401-420b-9227-befe25c245d8-04_818_1081_989_477}
An outlier is a value which is more than 1.5 times the interquartile range above Q3 or more than 1.5 times the interquartile range below Q1.
  1. Show that the 3 points circled on the scatter diagram above are outliers.
    (2)
  2. Describe the effect of removing the 3 outliers on the correlation between daily rainfall and daily mean pressure in this sample.
    (1) John has also been studying the large data set and believes that the sample Pete has taken is not random.
  3. From your knowledge of the large data set, explain why Pete's sample is unlikely to be a random sample. John finds that the equation of the regression line of \(w\) on \(p\), using all the data in the large data set, is $$w = 1023 - 0.223 p$$
  4. Give an interpretation of the figure - 0.223 in this regression line. John decided to use the regression line to estimate the daily rainfall for a day in December when the daily mean pressure is 1011 hPa .
  5. Using your knowledge of the large data set, comment on the reliability of John's estimate.
    (Total for Question 3 is 6 marks)
Edexcel AS Paper 2 Specimen Q4
4. Alyona, Dawn and Sergei are sometimes late for school. The events \(A , D\) and \(S\) are as follows:
A Alyona is late for school
D Dawn is late for school
S Sergei is late for school The Venn diagram below shows the three events \(A , D\) and \(S\) and the probabilities associated with each region of \(D\). The constants \(p , q\) and \(r\) each represent probabilities associated with the three separate regions outside \(D\).
\includegraphics[max width=\textwidth, alt={}, center]{b29b0411-8401-420b-9227-befe25c245d8-06_624_1068_845_479}
  1. Write down 2 of the events \(A , D\) and \(S\) that are mutually exclusive. Give a reason for your answer. The probability that Sergei is late for school is 0.2 . The events \(A\) and \(D\) are independent.
  2. Find the value of \(r\).
    (4) Dawn and Sergei's teacher believes that when Sergei is late for school, Dawn tends to be late for school.
  3. State whether or not \(D\) and \(S\) are independent, giving a reason for your answer.
    (1)
  4. Comment on the teacher's belief in the light of your answer to part (c).
    (1)
    (Total for Question 4 is 7 marks) \section*{Pearson Edexcel Level 3} \section*{GCE Mathematics} \section*{Paper 2: Mechanics}
    Specimen paper
    Time: \(\mathbf { 3 5 }\) minutes
    		Paper Reference(s)
    \(\mathbf { 8 M A 0 } / \mathbf { 0 2 }\)
    You must have:
    Mathematical Formulae and Statistical Tables, calculator
    Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for algebraic manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. \section*{Instructions}
    • Use black ink or ball-point pen.
    • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
    • Fill in the boxes at the top of this page with your name, centre number and candidate number.
    • Answer all the questions in Section B.
    • Answer the questions in the spaces provided - there may be more space than you need.
    • You should show sufficient working to make your methods clear. Answers without working may not gain full credit.
    • Inexact answers should be given to three significant figures unless otherwise stated.
    \section*{Information}
    • A booklet 'Mathematical Formulae and Statistical Tables' is provided.
    • There are 4 questions in this section. The total mark for Part B of this paper is 30.
    • The marks for each question are shown in brackets - use this as a guide as to how much time to spend on each question.
    \section*{Advice}
    • Read each question carefully before you start to answer it.
    • Try to answer every question.
    • Check your answers if you have time at the end.
    • If you change your mind about an answer, cross it out and put your new answer and any working underneath.