A Level Mathematics Summer AssignmentThis summer work is compulsory. Your maths teacher will ask to see your work (and method) in your first maths lesson.

Purpose

This work gives you the opportunity to practice the skills that will be required to start AS Level Mathematics successfully and identify any areas where you may need to spend additional time. We want to ensure you do not feel overwhelmed when you begin your Sixth Form studies, however it is only through an excellent attitude to learning and work ethic can students succeed in A level maths so use this summer work as an example of the effort you plan to put into the course.

Support

These two books might be helpful: “Head Start to AS Maths” by Richard Parsons. “Collins Maths - Bridging GCSE and A Level: Student Book” by Mark Rowland.

These websites may be useful

http://www.cimt.plymouth.ac.uk/projects/mepres/step-up/default.htmThis website provides interactive resources, questions and answers on many GCSE topics.

www.mathcentre.ac.ukTo use this website follow the following steps:On the left hand side click on “Topic”, this will bring up a new page and you need to click on Algebra.This will bring you to a list of topics, you need to choose the topic you are finding difficult.Once your topic has been selected you will then see a list of resources to use. The two most suitable ones are ‘iPOD Video’ and ‘Teach Yourself’

We hope that you will use this introduction to give you a good start to your AS work and that it will help you enjoy and benefit from the course.

Enjoy your summer break.

Name:

Instructions:

Complete all the questions to the best of your ability.Take your time to do it right. This is not a test, you don’t have to complete it all in one goYou may use a calculator

Geometry Algebra Statistics

6 3 4

11 5 4

6 2 5

3 4 6

4 7 3

4 4 4

5 3 3

6 2 4

3 6 6

4 3 3

6 4 7

7 6 6

3 3 4

4 4 4

5 5 3

5 4

Geometry

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

11)

12)

13)

14)

15)

Algebra

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

11)

12)

13)

14)

15)

16)

Statistics

1)

(a) Max wants to take a random sample of students from his year group.(i) Explain what is meant by a random sample.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

(ii) Describe a method Max could use to take his random sample.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(2 marks)

(b) The table below shows the numbers of students in 5 year groups at a school.

Year Number of students

9 23910 25711 24812 19013 206

Lisa takes a stratified sample of 100 students by year group.

Work out the number of students from Year 9 she has in her sample.

..............................................................................................................................................(2 marks)

2)

The scatter graph shows information about 8 people. It shows each person's height and the circumference of their head.

The table gives this information for 2 other people.

(a) On the scatter graph, plot the information from the table.

(1 mark)

(b) Describe the correlation.

...........................................................

(1 mark)

(c) Draw a line of best fit on your scatter graph.

(1 mark)

(d) Estimate the circumference of the head of a person who is 156 cm tall.

........................................................... cm

(1 mark)3)

Lyndsey records the number of miles (m) she drives each day for 120 days.

Some information about the results is given in the table.

(a) Complete the cumulative frequency table.

(1 mark)

(b) On the grid, draw a cumulative frequency graph.

(2 marks)

(c) Work out an estimate for the number of days on which Lyndsey drives more than 36 miles.

...........................................................days

(2 marks)

4)Harry grows tomatoes.This year he put his tomato plants into two groups, group A and group B.

Harry gave fertiliser to the tomato plants in group A.He did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group A.The cumulative frequency graph shows some information about these weights.

(a) Use the graph to find an estimate for the median weight.

. . . . . . . . . . . . . . . . . . . . . . g

(1 mark)

The 60 tomatoes from group A had a minimum weight of 153 grams and a maximum weight of 186 grams.

(b) Use this information and the cumulative frequency graph to draw a box plot for the 60 tomatoes from group A.

(3 marks)

Harry did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group B.He drew this box plot for his results.

(c) Compare the distribution of the weights of the tomatoes from group A with the distribution of the weights of the tomatoes from group B.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(2 marks)

5)

The table below shows information about the times, in minutes, a group of students took to answer 10 maths questions.

Least Lower quartile Median Upper

quartile Greatest

Time in minutes 14 18 20 25 30

On the grid below, draw a box plot to show the information in the table.

(3 marks)

6)

The table shows some information about the weights of oranges.

Weight (w grams) Frequency

0 < w ≤ 2020 < w ≤ 30 1530 < w ≤ 5050 < w≤ 60 1360 < w≤ 75 15

75 < w ≤ 100 10

(a) Use the histogram to complete the table.

(2 marks)

(b) Use the table to complete the histogram.

(2 marks)

7) The table shows some information about the length of time some birds were on a bird table.

Draw a histogram for the information in the table.

(3 marks)

8)Faisel weighed 50 pumpkins.

The grouped frequency table gives some information about the weights of the pumpkins.

Weight (w kilograms) Frequency

0 < w ≤ 4 114 < w ≤ 8 23

8 < w ≤ 12 1412 < w ≤ 16 2

Work out an estimate for the mean weight.

(4 marks)

9) The table shows information about the number of years 41 teachers have each taught at a school.

(a) Write down the class interval that contains the median.

...........................................................

(2 marks)

(b) Calculate an estimate for the mean number of years. You must show all your working.

...........................................................

(4 marks)10)There are 15 bags of apples on a market stall. The mean number of apples in each bag is 9

The table below shows the numbers of apples in 14 of the bags.

Numberof apples Frequency

7 28 39 3

10 411 2

Calculate the number of apples in the 15th bag.

(3 marks)

11)

Josh plays a game with two sets of cards.

Josh takes at random one card from each set. He adds the numbers on the two cards to get the total score.

(a) Complete the table to show all the possible total scores.

(1 mark)

(b) What is the probability that Josh's total score will be greater than 12?

...........................................................

(2 marks)

Josh's year group are raising money for a sponsored skydive.

60 students are each going to play Josh's card game once. Each student pays 50p to play the game.

Josh pays £1.50 to any player getting a total of 8

(c) Show that Josh can expect to make a profit of £21 from his game.

(4 marks)12)

= odd numbers less than 30 A = 3, 9, 15, 21, 27 B = 5, 15, 25

Complete the Venn diagram to represent this information.

(4 marks)

13) Here is a Venn diagram.

(a) Write down the numbers that are in set

(i) A ∪ B

...........................................................

(ii) A ∩ B

...........................................................

(2 marks)

One of the numbers in the diagram is chosen at random.

(b) Find the probability that the number is in set A'

...........................................................

(2 marks)

14)

Seb has a biased dice. When the dice is thrown once, the probability that it will land on 6 is . Seb is going to throw the dice twice.

(a) Complete the probability tree diagram.

(2 marks)

(b) Work out the probability that the dice will land on 6 on the first throw and will not land on 6 on the second throw.

...........................................................

(2 marks)

15.

Alan has two spinners, spinner A and spinner B. Each spinner can land on only red or white.

The probability that spinner A will land on red is 0.25 The probability that spinner B will land on red is 0.6

The probability tree diagram shows this information.

Alan spins spinner A once and he spins spinner B once. He does this a number of times.

The number of times both spinners land on red is 24

Work out an estimate for the number of times both spinners land on white.

(3 marks)

16)

Carolyn has 20 biscuits in a tin.

She has

12 plain biscuits5 chocolate biscuits3 ginger biscuits

Carolyn takes at random two biscuits from the tin.

Work out the probability that the two biscuits were not the same type.

(4 marks)