A Level

Revision Starters

Year 1 (AS) Material

Question 2

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A company assembles drills using components from two sources.

Goodbuy supplies 85% of the components and Amart supplies the rest.

It is known that 3% of the components supplied by Goodbuy are faulty and 6% of those supplied by Amart are faulty.

An assembled drill is selected at random.

Find the probability that it is not faulty.

Question 2

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(0.85 X 0.97) + (0.15 X 0.94) = 0.9655

Question 2

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The discrete random variable X has probability distribution given by

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Question 2

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Question 2

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A car of mass 1000 kg is pulling a caravan of mass 1500 kg along a horizontal road. The driving force of the car is 3500 N, and resistances to motion acting on the car and the caravan are 200 N and 350 N respectively.

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1. Find the acceleration of the car and the caravan.

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(ii) Find the tension in the tow-bar coupling the car to the caravan.

Question 2

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Using F = ma on the whole system,

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3500 + T – T – 200 – 350 = 2500a

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2950 = 2500a

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a = 1.18 ms^-2

Using F = ma on the car,

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3500 – T – 200 = 1000 x 1.18

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3300 - T = 1180

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T = 2120 N

OR Using F = ma on the caravan,

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T – 350 = 1500 x 1.18

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T – 350 = 1770

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T = 2120 N

For example:

Which is always true since square numbers are bigger or equal to 0, a square number + 3 will always be bigger than 0.

Question 2

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In a shopping survey a random sample of 104 teenagers were asked how many hours, to the nearest hour, they spent shopping in the last month. The results are summarised in the table on the right.

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Use linear interpolation to estimate the median and interquartile range.

Question 3

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The following table summarises the times, t minutes to the nearest minute, recorded for a group of students to complete an exam.

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Estimate the mean and standard deviation of these data.

Question 1

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Interquartile range = 15.3 – 6.25 = 9.05

Question 3

The variable x was measured to the nearest whole number. Forty observations are given in the table below.

A histogram was drawn and the bar representing the 10 – 15 class has a width of 2 cm and a height of 5 cm.

For the 16 – 18 class find i) the width, ii) the height of the bar representing this class.

Question 3

1. Width of bar = 3 ÷ 3 = 1 cm
2. Height of bar = 9 ÷ 1.5 = 6 cm

Question 2

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A researcher is hired by a cleaning company to survey the opinions of employees on a proposed pension scheme.

The company employs 55 managers and 495 cleaners.

To collect data the researcher decides to give a questionnaire to the first 50 cleaners to leave at the end of the day.

1. Give 2 reasons why this method is likely to produce biased results.
2. Explain briefly how the researcher could select a sample of 50 employees using (i) a systematic sample, (ii) a stratified sample.

Question 3

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1. a speed-time graph, ii) an acceleration-time graph.

Crosses y axis at y = 7

Question 2

A long distance lorry driver recorded the distance travelled, m miles, and the amount of fuel used, f litres, each day.

The equation of the regression line of f on m is f = 0.735 + 0.395m

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1. Interpret the value 0.395 in this context.

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• Estimate the distance travelled by the driver one day, given that the driver used 48 litres of fuel.

Question 3

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Find the total distance travelled in the

journey modelled by the velocity time graph

on the right.

Question 1

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Triangle ABC has area 10cm². AB = 6cm, BC = 8cm and angle ABC is obtuse.

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Find the size of angle ABC and the length of AC.

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Question 2

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f = 0.735 + 0.395m

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1. For every 1 mile driven, 0.395 litres of fuel are used.

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• 48 = 0.735 + 0.395m m = 119.658….. Approximately 120 miles.

Question 3

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Area under velocity time graph = distance.

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Total distance = 72 + 12 + 16 = 100 m

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Question 1

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Question 2

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Past records from a large supermarket show that 20% of people who buy chocolate bars buy the family size bar.

On one particular day a random sample of 30 people was taken from those that had bought chocolate bars and 2 of them were found to have bought a family size bar.

Test, at the 5% significance level, whether or not the proportion p of people who bought a family size bar of chocolate that day had decreased. State your hypotheses clearly.

Question 2

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Question 3

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Solve the equation to find x.

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Question 2

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P(A) = 0.54

P(B) = 0.33

Question 3

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Question 2

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It is known from past records that 1 in 5 bowls produced in a pottery have minor defects.

To monitor production a random sample of 25 bowls was taken and the number of such bowls with defects was recorded.

Using a 5% level of significance, find critical regions for a two-tailed test of the hypothesis that 1 in 5 bowls have defects.

The probability of rejecting, in either tail, should be as close to 2.5% as possible.

Question 3

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Solve the equation to find x.

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Question 1

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Solve the equation to find x.

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Question 2

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Question 3

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Question 1

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