Questions FS1 AS - A-Level Maths

Edexcel FS1 AS 2024 June Q2

13 marks Moderate -0.8

A manager keeps a record of accidents in a canteen.

Accidents occur randomly with an average of 2.7 per month. The manager decides to model the number of accidents with a Poisson distribution.

Give a reason why a Poisson distribution could be a suitable model in this situation.
Assuming that a Poisson model is suitable, find the probability of
1. at least 3 accidents in the next month,
2. no more than 10 accidents in a 3-month period,
3. at least 2 months with no accidents in an 8-month period. One day, two members of staff bump into each other in the canteen and each report the accident to the manager. The canteen manager is unsure whether to record this as one or two accidents. Given that the manager still wants to model the number of accidents per month with a Poisson distribution,
state
- a property of the Poisson distribution that the manager should consider when deciding how to record this situation
- whether the manager should record this as one or two accidents
The manager introduces some new procedures to try and reduce the average number of accidents per month. During the following 12 months the total number of accidents is 22 The manager claims that the accident rate has been reduced.
Use a $5 \%$ level of significance to carry out a suitable test to assess the manager's claim.
You should state your hypotheses clearly and the $p$-value used in your test.

Edexcel FS1 AS 2024 June Q3

6 marks Standard +0.8

The discrete random variable $X$ has probability distribution,

$x$	- 1	0	1	3	7
$\mathrm { P } ( X = x )$	$p$	$r$	$p$	0.3	$r$

where $p$ and $r$ are probabilities.
Given that $\mathrm { E } ( X ) = 1.95$ find the exact value of $\mathrm { E } ( \sqrt { X + 1 } )$ giving your answer in the form $a + b \sqrt { 2 }$ where $a$ and $b$ are rational.
(6)

Edexcel FS1 AS 2024 June Q4

15 marks Standard +0.3

Robin shoots 8 arrows at a target each day for 100 days.

The number of times he hits the target each day is summarised in the table below.

Number of hits	0	1	2	3	4	5	6	7	8
Frequency	1	10	30	34	17	4	2	0	2

Misha believes that these data can be modelled by a binomial distribution.

State, in context, two assumptions that are implied by the use of this model.
Find an estimate for the proportion of arrows Robin shoots that hit the target. Misha calculates expected frequencies, to 2 decimal places, as follows.
Number of hits 0 1 2 3 4 5 6 7 8
Expected frequency 2.81 12.67 $r$ 28.05 19.73 $s$ 2.50 0.40 0.03
Find the value of $r$ and the value of $s$ Misha correctly used a suitable test to assess her belief.
1. Explain why she used a test with 3 degrees of freedom.
2. Complete the test using a $5 \%$ level of significance. You should clearly state your hypotheses, test statistic, critical value and conclusion.

Edexcel FS1 AS Specimen Q1

8 marks Standard +0.3

A university foreign language department carried out a survey of prospective students to find out which of three languages they were most interested in studying.

A random sample of 150 prospective students gave the following results.

\cline { 3 - 5 } \multicolumn{2}{c\|}{}	Language
\cline { 3 - 5 } \multicolumn{2}{c\|}{}	French	Spanish	M andarin
\multirow{2}{*}{Gender}	M ale	23	22	20
\cline { 2 - 5 }	Female	38	32	15

A test is carried out at the $1 \%$ level of significance to determine whether or not there is an association between gender and choice of language.

State the null hypothesis for this test.
Show that the expected frequency for females choosing Spanish is 30.6
Calculate the test statistic for this test, stating the expected frequencies you have used.
State whether or not the null hypothesis is rejected. Justify your answer.
Explain whether or not the null hypothesis would be rejected if the test was carried out at the $10 \%$ level of significance. \section*{Q uestion 1 continued} \section*{Q uestion 1 continued} \section*{Q uestion 1 continued}

Edexcel FS1 AS Specimen Q2

11 marks Standard +0.8

The discrete random variable $X$ has probability distribution given by

$x$	- 1	0	1	2	3
$P ( X = x )$	$c$	$a$	$a$	$b$	$c$

The random variable $Y = 2 - 5 X$ Given that $\mathrm { E } ( \mathrm { Y } ) = - 4$ and $\mathrm { P } ( \mathrm { Y } \geqslant - 3 ) = 0.45$

find the probability distribution of X . Given also that $\mathrm { E } \left( \mathrm { Y } ^ { 2 } \right) = 75$
find the exact value of $\operatorname { Var } ( \mathrm { X } )$
Find $\mathrm { P } ( \mathrm { Y } > \mathrm { X } )$ \section*{Q uestion 2 continued}

Edexcel FS1 AS Specimen Q3

10 marks Standard +0.3

Two car hire companies hire cars independently of each other.

Car Hire A hires cars at a rate of 2.6 cars per hour.
Car Hire B hires cars at a rate of 1.2 cars per hour.

In a 1 hour period, find the probability that each company hires exactly 2 cars.
In a 1 hour period, find the probability that the total number of cars hired by the two companies is 3
In a 2 hour period, find the probability that the total number of cars hired by the two companies is less than 9 On average, 1 in 250 new cars produced at a factory has a defect.
In a random sample of 600 new cars produced at the factory,
1. find the mean of the number of cars with a defect,
2. find the variance of the number of cars with a defect.
1. Use a Poisson approximation to find the probability that no more than 4 of the cars in the sample have a defect.
2. Give a reason to support the use of a Poisson approximation. \section*{Q uestion 3 continued}

Edexcel FS1 AS Specimen Q4

11 marks Standard +0.3

The discrete random variable $X$ follows a Poisson distribution with mean 1.4
1. Write down the value of
  1. $\mathrm { P } ( \mathrm { X } = 1 )$
  2. $\mathrm { P } ( \mathrm { X } \leqslant 4 )$
The manager of a bank recorded the number of mortgages approved each week over a 40 week period.
Number of mortgages approved 0 1 2 3 4 5 6
Frequency 10 16 7 4 2 0 1
Show that the mean number of mortgages approved over the 40 week period is 1.4 The bank manager believes that the Poisson distribution may be a good model for the number of mortgages approved each week. She uses a Poisson distribution with a mean of 1.4 to calculate expected frequencies as follows.
Number of mortgages approved 0 1 2 3 4 5 or more
Expected frequency 9.86 r 9.67 4.51 1.58 s
Find the value of r and the value of s giving your answers to 2 decimal places. The bank manager will test, at the $5 \%$ level of significance, whether or not the data can be modelled by a Poisson distribution.
Calculate the test statistic and state the conclusion for this test. State clearly the degrees of freedom and the hypotheses used in the test. \section*{Q uestion 4 continued} \section*{Q uestion 4 continued}

OCR FS1 AS 2017 December Q1

8 marks Moderate -0.3

1 Bill and Gill send letters to potential sponsors of a show. On past experience, they know that $5 \%$ of letters receive a favourable reply.

Bill sends a letter to each of 40 potential sponsors. Assuming that the number $N$ of favourable responses can be modelled by a binomial distribution, find the mean and variance of $N$.
Gill sends one letter at a time to potential sponsors. $L$ is the number of letters she sends, up to and including the first letter that receives a favourable response.
1. State two assumptions needed for $L$ to be well modelled by a geometric distribution.
2. Using the assumptions in part (ii)(a), find the smallest number of letters that Gill has to send in order to have at least a $90 \%$ chance of receiving at least one favourable reply.

OCR FS1 AS 2017 December Q2

7 marks Moderate -0.3

2 Each letter of the words NEW COURSE is written on a card (including one blank card, representing the space between the words), so that there are 10 cards altogether.

All 10 cards are arranged in a random order in a straight line. Find the probability that the two cards containing an E are next to each other.
4 cards are chosen at random. Find the probability that at least three consonants ( $\mathrm { N } , \mathrm { W } , \mathrm { C } , \mathrm { R } , \mathrm { S }$ ) are on the cards chosen.

OCR FS1 AS 2017 December Q3

7 marks Standard +0.3

3 Over a long period Jenny counts the number of trolleys used at her local supermarket between 10 am and 10.20 am each day. She finds that the mean number of trolleys used between these times on a weekday is 40.00. You should assume that the use of trolleys occurs randomly, independently of one another, and at a constant average rate.

Calculate the probability that, on a randomly chosen weekday, the number of trolleys used between these times is between 32 and 50 inclusive.
Write down an expression for the probability that, on a randomly chosen weekday, exactly 5 trolleys are used during a time period of $t$ minutes between 10 am and 10.20 am. Jenny carries out this process for seven consecutive days. She finds that the mean number of trolleys used between 10 am and 10.20 am is 35.14 and the variance is 91.55 .
Explain why this suggests that the distribution of the number of trolleys used between these times on these seven consecutive days is not well modelled by a Poisson distribution.
Give a reason why it might not be appropriate to apply the Poisson model to the total number of trolleys used between these times on seven consecutive days.

OCR FS1 AS 2017 December Q4

10 marks Standard +0.3

4 The discrete random variable $X$ has the distribution $\mathrm { U } ( n )$.

Use the results $\sum _ { r = 1 } ^ { n } r ^ { 2 } = \frac { 1 } { 6 } n ( n + 1 ) ( 2 n + 1 )$ and $\mathrm { E } ( X ) = \frac { n + 1 } { 2 }$ to show that $\operatorname { Var } ( X ) = \frac { 1 } { 12 } \left( n ^ { 2 } - 1 \right)$. It is given that $\mathrm { E } ( X ) = 13$.
Find the value of $n$.
Find $\mathrm { P } ( X < 7.5 )$. It is given that $\mathrm { E } ( a X + b ) = 10$ and $\operatorname { Var } ( a X + b ) = 117$, where $a$ and $b$ are positive.
Calculate the value of $a$ and the value of $b$.

OCR FS1 AS 2017 December Q5

8 marks Moderate -0.5

5 A shop manager recorded the maximum daytime temperature $T ^ { \circ } \mathrm { C }$ and the number $C$ of ice creams sold on 9 summer days. The results are given in the table and illustrated in the scatter diagram.

$T$	17	21	25	26	27	27	29	30	30
$C$	21	16	20	38	32	37	35	39	42

\includegraphics[max width=\textwidth, alt={}]{64d7ed6d-fadd-4c59-afb0-97d1788ba369-3_661_1189_1320_431}

$$n = 9 , \Sigma t = 232 , \Sigma c = 280 , \Sigma t ^ { 2 } = 6130 , \Sigma c ^ { 2 } = 9444 , \Sigma t c = 7489$$

State, with a reason, whether one of the variables $C$ or $T$ is likely to be dependent upon the other.
Calculate Pearson's product-moment correlation coefficient $r$ for the data.
State with a reason what the value of $r$ would have been if the temperature had been measured in ${ } ^ { \circ } \mathrm { F }$ rather than ${ } ^ { \circ } \mathrm { C }$.
Calculate the equation of the least squares regression line of $c$ on $t$.
The regression line is drawn on the copy of the scatter diagram in the Printed Answer Booklet. Use this diagram to explain what is meant by "least squares".

OCR FS1 AS 2017 December Q6

9 marks Standard +0.3

6 Arlosh, Sarah and Desi are investigating the ratings given to six different films by two critics.

Arlosh calculates Spearman's rank correlation coefficient $r _ { s }$ for the critics' ratings. He calculates that $\Sigma d ^ { 2 } = 72$. Show that this value must be incorrect.
Arlosh checks his working with Sarah, whose answer $r _ { s } = \frac { 29 } { 35 }$ is correct. Find the correct value of $\Sigma d ^ { 2 }$.
Carry out an appropriate two-tailed significance test of the value of $r _ { s }$ at the $5 \%$ significance level, stating your hypotheses clearly. Each critic gives a score out of 100 to each film. Desi uses these scores to calculate Pearson's product-moment correlation coefficient. She carries out a two-tailed significance test of this value at the $5 \%$ significance level.
Explain with a reason whether you would expect the conclusion of Desi's test to be the same as the result of the test in part (iii).

OCR FS1 AS 2017 December Q7

11 marks Standard +0.3

7 Josh is investigating whether sticking pins into a map at random, while blindfolded, provides a random sample of regions of the map. Josh divides the map into 49 squares of equal size and asks each of 98 friends to stick a pin into the map at random, while blindfolded. He then notes the number of pins in each square. To analyse the results he groups the squares as shown in the diagram.

D	D	D	D	D	D	D
D	C	C	C	C	C	D
D	C	B	B	B	C	D
D	C	B	A	B	C	D
D	C	B	B	B	C	D
D	C	C	C	C	C	D
D	D	D	D	D	D	D

The results are summarised in the table.

Region	A	B	C	D
Number of squares	1	8	16	24
Number of pins	6	21	33	38

Test at the 10\% significance level whether the use of pins in this way provides a random sample of regions of the map.
What can be deduced from considering the different contributions to the test statistic? \section*{OCR} \section*{Oxford Cambridge and RSA}

OCR FS1 AS 2018 March Q1

7 marks Easy -1.2

1 A learner driver keeps taking the driving test until she passes. The number of attempts taken, up to and including the pass, is denoted by $X$.

State two assumptions needed for $X$ to be well modelled by a geometric distribution. Assume now that $X \sim \operatorname { Geo } ( 0.4 )$.
Find $\mathrm { P } ( X < 6 )$.
Find $\mathrm { E } ( X )$.
Find $\operatorname { Var } ( X )$.

OCR FS1 AS 2018 March Q2

6 marks Standard +0.3

2 The number of calls received by a customer service department in 30 minutes is denoted by $W$. It is known that $\mathrm { E } ( W ) = 6.5$.

It is given that $W$ has a Poisson distribution.
1. Write down the standard deviation of $W$.
2. Find the probability that the total number of calls received in a randomly chosen period of 2 hours is less than 30 .
3. It is given instead that $W$ has a uniform distribution on $[ 1 , N ]$. Calculate the value of $\mathrm { P } ( W > 3 )$.

OCR FS1 AS 2018 March Q3

8 marks Standard +0.8

3 A pack of 40 cards consists of 10 cards in each of four colours: red, yellow, blue and green. The pack is dealt at random into four "hands", each of 10 cards. The hands are labelled North, South, East and West.

Find the probability that West has exactly 3 red cards.
Find the probability that West has exactly 3 red cards, given that East and West have between them a total of exactly 5 red cards.
South has 5 red cards and 5 blue cards. These cards are placed in a row in a random order. Find the probability that the colour of each card is different from the colour of the preceding card.

OCR FS1 AS 2018 March Q4

9 marks Moderate -0.3

4 A spinner has edges numbered $1,2,3,4$ and 5 . When the spinner is spun, the number of the edge on which it lands is the score. The probability distribution of the score, $N$, is given in the table.

Score, $N$	1	2	3	4	5
Probability	0.3	0.2	0.2	$x$	$y$

It is known that $\mathrm { E } ( N ) = 2.55$.

Find $\operatorname { Var } ( N )$.
Find $\mathrm { E } ( 3 N + 2 )$.
Find $\operatorname { Var } ( 3 N + 2 )$.

OCR FS1 AS 2018 March Q5

4 marks Easy -1.8

5 The speed $v \mathrm {~ms} ^ { - 1 }$ of a car at time $t$ seconds after it starts to accelerate was measured at 1 -second intervals. The results are shown in the following diagram. \includegraphics[max width=\textwidth, alt={}, center]{d5843350-52f9-4fed-adf4-86ceb958033f-3_661_1186_1078_443}

State whether $t$ or $v$ or neither is a controlled variable. The value of the product moment correlation coefficient $r$ for the data is 0.987 correct to 3 significant figures.
The speed of the car is converted to miles per hour and the time to minutes. State the value of $r$ for the converted data.
State the value of Spearman's rank correlation coefficient $r _ { s }$ for the data.
What information does $r$ give about the data that is not given by $r _ { s }$ ?

OCR FS1 AS 2018 March Q6

7 marks Challenging +1.2

6 The discrete random variable $R$ has the distribution $\operatorname { Po } ( \lambda )$.
Use an algebraic method to find the range of values of $\lambda$ for which the single most likely value of $R$ is 7. [7]

OCR FS1 AS 2018 March Q7

11 marks Standard +0.3

7 The numbers of students taking A levels in three subjects at a school were classified by the year in which they entered the school as follows.

\cline { 2 - 5 } \multicolumn{1}{c|}{}

Subject

Mathematics

English

Physics

\multirow{3}{*}{

Year of

Entry

}

Year 7

17

16

7

\cline { 2 - 5 }

Year 12

13

2

5

The Head of the school carries out a significance test at the $10 \%$ level to test whether subjects taken are independent of year of entry.

Show that in carrying out the test it is necessary to combine columns.
Suggest a reason why it is more sensible to combine the columns for Mathematics and Physics than the columns for Physics and English.
Carry out the test.
State which cell gives the largest contribution to the test statistic.
Interpret your answer to part (iv).

OCR FS1 AS 2018 March Q8

8 marks Challenging +1.2

8 In a competition, entrants have to give ranks from 1 to 7 to each of seven resorts. The correct ranks for the resorts are decided by an expert.

One competitor chooses his ranks randomly. By considering all the possible rankings, find the probability that the value of Spearman's rank correlation coefficient $r _ { s }$ between the competitor's ranks and the expert's ranks is at least $\frac { 27 } { 28 }$.
Another competitor ranks the seven resorts. A significance test is carried out to test whether there is evidence that this competitor is merely guessing the rank order of the seven resorts. The critical region is $r _ { s } \geqslant \frac { 27 } { 28 }$. State the significance level of the test. \section*{END OF QUESTION PAPER}

OCR FS1 AS 2021 June Q1

8 marks Moderate -0.8

1 The probability distribution for the discrete random variable $W$ is given in the table.

$w$	1	2	3	4
$\mathrm { P } ( W = w )$	0.25	0.36	$x$	$x ^ { 2 }$

Show that $\operatorname { Var } ( W ) = 0.8571$.
Find $\operatorname { Var } ( 3 W + 6 )$.

OCR FS1 AS 2021 June Q2

6 marks Moderate -0.8

2 In the manufacture of fibre optical cable (FOC), flaws occur randomly. Whether any point on a cable is flawed is independent of whether any other point is flawed. The number of flaws in 100 m of FOC of standard diameter is denoted by $X$.

State a further assumption needed for $X$ to be well modelled by a Poisson distribution. Assume now that $X$ can be well modelled by the distribution $\operatorname { Po } ( 0.7 )$.
Find the probability that in 300 m of FOC of standard diameter there are exactly 3 flaws. The number of flaws in 100 m of FOC of a larger diameter has the distribution $\mathrm { Po } ( 1.6 )$.

Find the probability that in 200 m of FOC of standard diameter and 100 m of FOC of the larger diameter the total number of flaws is at least 4 . Judith believes that mathematical ability and chess-playing ability are related. She asks 20 randomly chosen chess players, with known British Chess Federation (BCF) ratings $X$, to take a mathematics aptitude test, with scores $Y$. The results are summarised as follows. $$n = 20 , \Sigma x = 3600 , \Sigma x ^ { 2 } = 660500 , \Sigma y = 1440 , \Sigma y ^ { 2 } = 105280 , \Sigma x y = 260990$$

Calculate the value of Pearson's product-moment correlation coefficient $r$.
State an assumption needed to be able to carry out a significance test on the value of $r$.
Assume now that the assumption in part (b) is valid. Test at the $5 \%$ significance level whether there is evidence that chess players with higher BCF ratings are better at mathematics.
There are two different grading systems for chess players, the BCF system and the international ELO system. The two sets of ratings are related by $$\text { ELO rating } = 8 \times \text { BCF rating } + 650$$ Magnus says that the experiment should have used ELO ratings instead of BCF ratings. Comment on Magnus's suggestion.
Calculate the value of Pearson's product-moment correlation coefficient $r$.
State an assumption needed to be able to carry out a significance test on the value of $r$.
Assume now that the assumption in part (b) is valid. Test at the $5 \%$ significance level whether there is evidence that chess players with higher BCF ratings are better at mathematics.

There are two different grading systems for chess players, the BCF system and the international ELO system. The two sets of ratings are related by $$\mathrm { ELO } \text { rating } = 8 \times \mathrm { BCF } \text { rating } + 650 .$$ Magnus says that the experiment should have used ELO ratings instead of BCF ratings. Comment on Magnus's suggestion. An environmentalist measures the mean concentration, $c$ milligrams per litre, of a particular chemical in a group of rivers, and the mean mass, $m$ pounds, of fish of a certain species found in those rivers. The results are given in the table.

Question

Answer

Marks

AO

Guidance

1

(a)

\(\begin{aligned}

0.25 + 0.36 + x + x ^ { 2 } = 1

x ^ { 2 } + x - 0.39 = 0

x = 0.3 \text { (or } - 1.3 \text { ) }

x \text { cannot be negative }

\mathrm { E } ( W ) = 2.23

\mathrm { E } \left( W ^ { 2 } \right) = \Sigma w ^ { 2 } \mathrm { p } ( w ) \quad [ = 5.83 ]

\text { Subtract } [ \mathrm { E } ( W ) ] ^ { 2 } \text { to get } \mathbf { 0 . 8 5 7 1 } \end{aligned}\)

\(\begin{gathered} \text { M1 }

\text { A1 }

\text { B1ft }

\text { B1 }

\text { M1 }

\text { A1 }

{ [ 7 ] } \end{gathered}\)

3.1a

1.1b

2.3

1.1b

1.1

2.1

Equation using $\Sigma p = 1$

Correct simplified quadratic Correctly obtain $x = 0.3$

Explicitly reject other solution

2.23 or exact equivalent only Use $\Sigma w ^ { 2 } \mathrm { p } ( w )$

Correctly obtain given answer, www

Can be implied

Method needed ft on their quadratic Allow for $\mathrm { E } ( W ) ^ { 2 } = 4.9729$

Need 2.23 or 4.9729 and 5.83 or full numerical $\Sigma w ^ { 2 } \mathrm { p } ( w )$

1

(b)

$9 \times 0.8571 = 7.7139$

B1

[1]

1.1b

Allow 7.71 or 7.714

2

(a)

Flaws must occur at constant average rate (uniform rate)

B1

[1]

1.2

Context (e.g. "flaws") needed

Extra answers, e.g. "singly": B0

Not "constant rate" or "average constant rate".

2

(b)

$\operatorname { Po(2.1)~or~ } e ^ { - \lambda } \frac { \lambda ^ { 3 } } { 3 ! }$

M1

A1

[2]

1.1

1.1b

Po(2.1) stated or implied, or formula with $\lambda = 2.1$ stated Awrt 0.189

2

(c)

Po(3)

$1 - \mathrm { P } ( \leq 3 )$

M1

A1

[3]

1.1

1.1b

$\operatorname { Po } ( 2 \times 0.7 + 1.6 )$ stated or implied

Allow $1 - \mathrm { P } ( \leq 4 ) = 0.1847$, or from wrong $\lambda$

Awrt 0.353

Or all combinations $\leq 3$

$1 -$ above, not just $= 3$

Question

Answer

Marks

AO

Guidance

3

(a)

0.4(00)

B2

[2]

1.1

1.1b

SC: if B0, give SC B1 for two of $S _ { x x } = 12500 , S _ { y y } = 1600 , S _ { x y } = 1790$ and $S _ { x y } / \sqrt { } \left( S _ { x x } S _ { y y } \right)$

Also allow SC B1 for equivalent methods using Covariance \

SDs

3

(b)

Data needs to have a bivariate normal distribution

B1

[1]

1.2

Needs "bivariate normal" or clear equivalent. Not just "both normally distributed"

Allow "scatter diagram forms ellipse"

3

(c)

$\mathrm { H } _ { 0 }$ : higher maths scores are not associated with higher BCF grading; $\mathrm { H } _ { 1 }$ : positively associated

CV 0.3783

$0.400 > 0.3783$ so reject $\mathrm { H } _ { 0 }$

Significant evidence that higher maths scores are associated with higher BCF grading

B1

M1ft

A1ft

[4]

2.5

1.1b

2.2b

3.5a

Needs context and clearly onetailed $O R \rho$ used and defined Not "evidence that ..."

Allow 0.378

Reject/do not reject $\mathrm { H } _ { 0 }$

Contextualised, not too definite Needn't say "positive" if $\mathrm { H } _ { 1 } \mathrm { OK }$

SC 2-tail: B0; 0.4438, or 0.3783 B1; then M1A0

$\mathrm { H } _ { 0 } : \rho = 0 , \mathrm { H } _ { 1 } : \rho > 0$ where $\rho$ is population pmcc (not $r$ )

FT on their $r$, but not CV

Not "scores are associated

...". FT on their $r$ only

3

(d)

It makes no difference as this is a linear transformation

B1

[1]

2.2a

Need both "unchanged" oe and reason, need "linear" or exact equivalent

"oe" includes "their 0.4"

4

(a)

Neither

B1

[1]

2.5

OE

Not "neither is independent of the other"

4

(b)

$c = 2.848 - 0.1567 m$

B1

[3]

1.1

Correct $a$, awrt 2.85

Correct $b$, awrt 0.157

Letters correct from correct method

(If both wrongly rounded, e.g. $c = 2.84 - 0.156 m$, give B2)

$\mathrm { SC } : m$ on $c$ :

$m = 15.65 - 4.832 c$ : B2

$y = 15.65 - 4.832 x$ : B1

$c = 15.65 - 4.832 m : \mathrm { B } 1$

If B0B0, give B1 for correct letters from valid working

Question

Answer

Marks

AO

Guidance

4

(c)

$a$ unchanged, $b$ multiplied by 2.2 (allow " $a$ unchanged, $b$ increases", etc)

B1 [1]

2.2a

oe, e.g. $c = 2.848 - 0.345 m$; $m = 7.114 - 2.196 c$

SC: $m$ on $c$ in (b): Both divided by 2.2 B1

4

(d)

Draw approximate line of best fit

Draw at least one vertical from line to point

Say that "Best fit" line minimises the sum of squares of these distances

M1

A1

[3]

1.1

2.4

Needs M2 and "minimises" and "sums of squares" oe

SC: Horizontal(s):

full marks (indept of (b))

OCR FS1 AS 2021 June Q1

6 marks Standard +0.3

1 On any day, the number of orders received in one randomly chosen hour by an online supplier can be modelled by the distribution $\mathrm { Po } ( 120 )$.

Find the probability that at least 28 orders are received in a randomly chosen 10 -minute period.
Find the probability that in a randomly chosen 10-minute period on one day and a randomly chosen 10-minute period on the next day a total of at least 56 orders are received.
State a necessary assumption for the validity of your calculation in part (b).

\(x\)	- 1	0	1	3	7
\(\mathrm { P } ( X = x )\)	\(p\)	\(r\)	\(p\)	0.3	\(r\)

\(x\)	- 1	0	1	2	3
\(P ( X = x )\)	\(c\)	\(a\)	\(a\)	\(b\)	\(c\)

\(w\)	1	2	3	4
\(\mathrm { P } ( W = w )\)	0.25	0.36	\(x\)	\(x ^ { 2 }\)

Questions FS1 AS (68 questions)

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Edexcel FS1 AS 2024 June Q2

Edexcel FS1 AS 2024 June Q3

Edexcel FS1 AS 2024 June Q4

Edexcel FS1 AS Specimen Q1

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Edexcel FS1 AS Specimen Q3

Edexcel FS1 AS Specimen Q4

OCR FS1 AS 2017 December Q1

OCR FS1 AS 2017 December Q2

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OCR FS1 AS 2017 December Q7

OCR FS1 AS 2018 March Q1

OCR FS1 AS 2018 March Q2

OCR FS1 AS 2018 March Q3

OCR FS1 AS 2018 March Q4

OCR FS1 AS 2018 March Q5

OCR FS1 AS 2018 March Q6

OCR FS1 AS 2018 March Q7

OCR FS1 AS 2018 March Q8

OCR FS1 AS 2021 June Q1

OCR FS1 AS 2021 June Q2

OCR FS1 AS 2021 June Q1

Number of hits	0	1	2	3	4	5	6	7	8
Expected frequency	2.81	12.67	\(r\)	28.05	19.73	\(s\)	2.50	0.40	0.03

Number of mortgages approved	0	1	2	3	4	5 or more
Expected frequency	9.86	r	9.67	4.51	1.58	s

\(T\)	17	21	25	26	27	27	29	30	30
\(C\)	21	16	20	38	32	37	35	39	42