Message from the St Brendan’s Mathematics department

We hope that you are well.

Due to covid-19 and the subsequent lockdown it is possible that you may feel underprepared for the rigours of A level mathematics. If so, you would not be alone. Fear not, one of the positive consequences of the pandemic is that there is an unprecedented number of resources to help you prepare.

Whilst the resources in this first section are not part of the required transition tasks it is highly recommended that you make use of them. You can use them before, during and after attempting the transition tasks. We recommend as a starting point to look at the first set of resources to make sure your knowledge is up to date. Then you can start looking at some of the other resources to help practise your mathematical skills. Keep coming back here and take charge of your learning – this is the first step in becoming a successful A level student.

GCSE to AS/A level Mathematics transition resources : This link takes you to resources designed to help you to make the transition from GCSE to AS and A level Mathematics. Make sure you watch the guidance video before trying the tasks. We suggest that you try to look at 3 sections each week from now until you start in September.

These Bridging Tests are produced by the organisation that provides our online A-level resources - you will use their resources a lot if your study A-level Maths at St Brendan’s - and cover a wide range of the topics that are important for the transition from GCSE to Year 12. There are twelve tests, with associated answers. They can be challenging but if you persevere with them will improve your skills in answering questions in an unfamiliar context.

Problem Solving

Whatever you go on to do next, problem solving will be one of the key take-aways from your maths A Level. Here are some starting points.

Advice: Give these tasks a go on your own first before looking for the solutions; at least 20 minutes of struggle before you watch an explanation! This is not 20min wasted! You could even wait a day, mulling the problem over in your mind as you do other stuff. Sometimes the solution will come to you in your sleep. That is not a joke. You need to be prepared for extended thinking on one question, attacking it from various angles. GCSE doesn't necessarily prepare you well for this. The process of attacking a problem from multiple angles is an absolutely invaluable skill - practise it!

Task 1: The Josephus Problem https://www.youtube.com/watch?v=uCsD3ZGzMgE Watch the first bit, have a go at solving it, then listen to the methodology of solving the problem as much as finding what the answer is!

Task 2: The Cat and Mouse Problem https://www.youtube.com/watch?v=vF_-ob9vseM

Extended Task: As ever, a Brilliant Course

All the tasks above are optional additional tasks that can help ensure you are prepared for the A-level mathematics course. The next 4 tasks below (5 for further maths) and the form on the next page make up the required transition task for A-level mathematics and should be completed before you start the course and handed in on your first lesson.

Name:

Handing in: Please bring to your first lesson.

Use this form to detail any which of the above tasks or any from the ‘Headstart’ sheet you have completed this summer (continue on a separate sheet if necessary):

Week commencing

Task(s) completed (from the resources listed above or from the Headstart sheet)

What did you learn or get better at?

6th July

13th July

20th July

27th July

3rd August

10th August

17th August

24th August

31st August

St Brendan’s Sixth Form College – A-level Mathematics Transition Task

All students that wish to study A-level mathematics at St Brendan’s will need to have the appropriate algebra skills to tackle the course. If you have a grade 6, you will be required to take an algebra assessment at enrolment. This will comprise of algebraic skills you have learned at GCSE and to assist your preparation for this, the first task below is practice questions for this initial assessment. You should bring this completed task with fully worked solutions with you to enrolment if you are taking the test, otherwise bring to your first lesson.

You must show all working to gain full marks. Answer all these questions

1. Give answers as fractions in simplest form:

(a)

34 +

13 (b) 2

12 - 1

56 (c) 2

23 x 1

14 (d) 5

13 ¿ 2

14

2. Simplify:

(a) 32×34

(b) (2¿¿3)5¿

(c) ( 23 )

2

(d) ( 19 )

− 2

3. Factorise:

(a) 15ab+6bc (b) a (b+c )– d (b+c) (c) x2+5x+6

(d) 36a2–16b2 (e) 6a2+5a−6

4. Solve the following equations:

(a) 5 x+8=18

(b)

4 x+13

=15(c) x2=¿

4916

(d)

x−24 ¿2

(e)

x5 +7=16

(f)

3x−7 ¿−¿

12

5. Solve the simultaneous equations:

(a) 3 x+ y=10 (b) 5 x – 2 y –8=0

5 x – 2 y=13 2 x+3 y=11– 2 x

6. Solve the following quadratic equations:

(a) x2– 2x –15=0 (b) x2+10 x+23=2 (c) 4 x2 –34=2

7. Rearrange to make y the subject in the following formulae:

Subject: The mathematics A-level course consists of pure mathematics, statistics and mechanics. A good level of algebraic technique is necessary for success on this course.

Task 1 - Preparation for initial assessment: Please complete the following questions using full worked solutions. The answers have been provided so that you can check your progress. The test will be non-calculator.

(a) 2 y+3=x

(b)

5xy−4 x ¿3

(c) 2 y2−1=x

Solutions:

1. (a)

34

+13

=912

+412

=1312

(=1112

)(b)

212−156

=13−56

=1−26

=46

=23 (c)

223×114

=83

×54

=103

=313 (d)

513

÷214

=163

÷94

=163

×49

=6427

(=21027

)

2. (a) 32 x 34 = 36 (b) (23)5 = 215 (c) ( 23 )

2= 49 (d)

( 19 )− 2

=92=81

3. (a) 15ab + 6bc = 3b(5a + 2c) (b) a(b + c) – d(b + c) = (b + c)(a – d)

(c) x2 + 5x + 6 = (x + 2)(x + 3) (d) 36 a2 – 16 b2 = 4(9a2 - 4b2) = 4(3a+2b)(3a – 2b)

(e) 6a2 + 5a – 6 = (3a – 2)(2a + 3)

4. (a)

5 x+8=185 x=10x=2 (b)

4 x+13

=15

4 x+1=454 x=44x=11 (c)

x2=4916

x=±74

(d)

x−24

=2

x−2=8x=10 (e)

x5

+7=16

x5

=9

x=45 (f)

3x−7

=−12

x−73

=−2

x−7=−6x=1

6. (a) x2 – 2x – 15 = 0 (b) x2 + 10x + 21 = 0 (c) 4x2 = 36

(x - 5)(x+3) = 0 (x + 3)(x + 7) = 0 x2= 9

x = 5, -3 x = -3, -7 x = ± 3

7. (a) y= x−3

2 (b)

5 x=3 y−12 x17 x=3 y

y=173x

(c)

2 y2=x+1

y2=x+12

y=±√x+12

R I M W H T M Y P N I Y S P ED A C R I C F Q O B I H U A TX P L M O I T I V N P Y O R ON U I U L F S E E R R P E A TR L R P C S S Q K I O O N L PB O M P E I U N N S O T A L MD I O R O A D T A X F H T E YS R P T L L E N A R G E L L SH X Q I S G Y X E B T S U M AE T T A E V I N P P T I M E KA Y G R E S A B O O R S I V KV A R I A B L E X M N E S L CR E C I P R O C A L I E P O JD N A P X E I N D E X A N S HR S E S I R O T C A F A L T A

Word Example / Definition

Task 2 - Glossary: Use the word search below to see how many key mathematical terms you can find! When you find a word, write a definition or give an example of the term. Some of the words you will already know but you may need to do a little research on the others… There are at least 24 words in total and they can be found forwards, backwards, diagonally and vertically; see how many you can find!

Word Example / Definition

Task 3 - Resource use: All mathematics students at the college will have access to the ‘Integral’ website. This website acts as an online textbook where students can find notes and exercises on all A-level topics along with a variety of other interactive resources. One type of resource is the walkthrough and in this task we would like you to access the walkthrough and practice some questions based on this walkthrough.

You can find the walkthrough at:

https://integralmaths.org/walkthroughs.php

We would like you to complete the ‘Equations of circles’ walkthrough.

After you have completed this walkthrough try the ‘Circle equations’ skills pack:

https://integralmaths.org/skill_packs.php

Then attempt the following questions below.

Task 4 - Challenge: In November, all students will have an opportunity to take part in the UKMT Senior Maths Challenge. You have the opportunity to achieve a Gold, Silver or Bronze certificate which can be used to support a university or job application. Here are a few example questions, see how you get on and be sure to let your maths teacher know in September whether you would like to take part in the challenge!

More information can be found at:

https://www.ukmt.org.uk/individual-competitions/senior-challenge/

Note that this challenge is non-calculator!

(a) A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

(b) Find the exact values of x, y and a satisfying the following system of equations:

(Hints – you are looking for an answer which is exact i.e. it contains surds. You may find the difference of 2 squares formula useful.)

(c) ABC is an isosceles right angled triangle. Each diagram has a different shape inscribed within it.

Which shaded area is the largest?

Task 5 – Further Maths: If you plan on taking Further Maths (or would like an extra challenge!) try the three problems below: