Questions — AQA S1 (156 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

AQA S1 2015 June Q2

2 The table summarises the diameters, \(d\) millimetres, of a random sample of 60 new cricket balls to be used in junior cricket.

AQA S1 2015 June Q3

3 A ferry sails once each day from port D to port A. The ferry departs from D on time or late but never early. However, the ferry can arrive at A early, on time or late. The probabilities for some combined events of departing from \(D\) and arriving at \(A\) are shown in the table below.

Complete the table.
Write down the probability that, on a particular day, the ferry:
1. both departs and arrives on time;
2. departs late.
Find the probability that, on a particular day, the ferry:
1. arrives late, given that it departed late;
2. does not arrive late, given that it departed on time.
On three particular days, the ferry departs from port D on time. Find the probability that, on these three days, the ferry arrives at port A early once, on time once and late once. Give your answer to three decimal places.
[0pt] [4 marks]
\begin{table}[h]
\captionsetup{labelformat=empty} \caption{Answer space for question 3}
\multirow{2}{*}{} Arrive at A
Early On time Late Total
\multirow{2}{*}{Depart from D} On time 0.16 0.56 0.08
Late
Total 0.22 0.65 1.00
\end{table}

AQA S1 2015 June Q4

4 Stephan is a roofing contractor who is often required to replace loose ridge tiles on house roofs. In order to help him to quote more accurately the prices for such jobs in the future, he records, for each of 11 recently repaired roofs, the number of ridge tiles replaced, \(x _ { i }\), and the time taken, \(y _ { i }\) hours. His results are shown in the table.

Roof \(( \boldsymbol { i } )\)	\(\mathbf { 1 }\)	\(\mathbf { 2 }\)	\(\mathbf { 3 }\)	\(\mathbf { 4 }\)	\(\mathbf { 5 }\)	\(\mathbf { 6 }\)	\(\mathbf { 7 }\)	\(\mathbf { 8 }\)	\(\mathbf { 9 }\)	\(\mathbf { 1 0 }\)	\(\mathbf { 1 1 }\)
\(\boldsymbol { x } _ { \boldsymbol { i } }\)	8	11	14	14	16	20	22	22	25	27	30
\(\boldsymbol { y } _ { \boldsymbol { i } }\)	5.0	5.2	6.3	7.2	8.0	8.8	10.6	11.0	11.8	12.1	13.0

The pairs of data values for roofs 1 to 7 are plotted on the scatter diagram shown on the opposite page. Plot the 4 pairs of data values for roofs 8 to 11 on the scatter diagram.
1. Calculate the equation of the least squares regression line of \(y _ { i }\) on \(x _ { i }\), and draw your line on the scatter diagram.
2. Interpret your values for the gradient and for the intercept of this regression line.
Estimate the time that it would take Stephan to replace 15 loose ridge tiles on a house roof.
Given that \(r _ { i }\) denotes the residual for the point representing roof \(i\) :
1. calculate the value of \(r _ { 6 }\);
2. state why the value of \(\sum _ { i = 1 } ^ { 11 } r _ { i }\) gives no useful information about the connection between the number of ridge tiles replaced and the time taken.
  [0pt] [1 mark]
  \section*{Answer space for question 4}
  \includegraphics[max width=\textwidth, alt={}]{6fbb8891-e6de-42fe-a195-ea643552fdcf-11_2385_1714_322_155}

AQA S1 2015 June Q5

Wooden lawn edging is supplied in 1.8 m length rolls. The actual length, \(X\) metres, of a roll may be modelled by a normal distribution with mean 1.81 and standard deviation 0.08 . Determine the probability that a randomly selected roll has length:
1. less than 1.90 m ;
2. greater than 1.85 m ;
3. between 1.81 m and 1.85 m .
Plastic lawn edging is supplied in 9 m length rolls. The actual length, \(Y\) metres, of a roll may be modelled by a normal distribution with mean \(\mu\) and standard deviation \(\sigma\). An analysis of a batch of rolls, selected at random, showed that $$\mathrm { P } ( Y < 9.25 ) = 0.88$$
1. Use this probability to find the value of \(z\) such that $$9.25 - \mu = z \times \sigma$$ where \(z\) is a value of \(Z \sim \mathrm {~N} ( 0,1 )\).
2. Given also that $$\mathrm { P } ( Y > 8.75 ) = 0.975$$ find values for \(\mu\) and \(\sigma\).

AQA S1 2015 June Q6

In a particular country, 35 per cent of the population is estimated to have at least one mobile phone. A sample of 40 people is selected from the population.
Use the distribution \(\mathrm { B } ( 40,0.35 )\) to estimate the probability that the number of people in the sample that have at least one mobile phone is:
1. at most 15 ;
2. more than 10 ;
3. more than 12 but fewer than 18 ;
4. exactly equal to the mean of the distribution.
In the same country, 70 per cent of households have a landline telephone connection. A sample of 50 households is selected from all households in the country.
Stating a necessary condition regarding this selection, estimate the probability that fewer than 30 households have a landline telephone connection.
[0pt] [4 marks]

AQA S1 2015 June Q7

The weight of a sack of mixed dog biscuits can be modelled by a normal distribution with a mean of 10.15 kg and a standard deviation of 0.3 kg . A pet shop purchases 12 such sacks that can be considered to be a random sample.
Calculate the probability that the mean weight of the 12 sacks is less than 10 kg .
The weight of dry cat food in a pouch can also be modelled by a normal distribution. The contents, \(x\) grams, of each of a random sample of 40 pouches were weighed. Subsequent analysis of these weights gave $$\bar { x } = 304.6 \quad \text { and } \quad s = 5.37$$
1. Construct a \(99 \%\) confidence interval for the mean weight of dry cat food in a pouch. Give the limits to one decimal place.
2. Comment, with justification, on each of the following two claims. Claim 1: The mean weight of dry cat food in a pouch is more than 300 grams.
  Claim 2: All pouches contain more than 300 grams of dry cat food.
  [0pt] [4 marks]
  \includegraphics[max width=\textwidth, alt={}]{6fbb8891-e6de-42fe-a195-ea643552fdcf-24_2288_1705_221_155}

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