further maths - city and islington college … · further maths bridging assignment (gcse to a...

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CITY AND ISLINGTON SIXTH FORM COLLEGE

FURTHER MATHS BRIDGING ASSIGNMENT (GCSE TO A LEVEL)

Section A – GCSE Grade 9 QuestionsThis is made up of grade 9 GCSE Higher Tier questions. Further Maths students are expected to be comfortable with all of the GCSE material.

Write your answers out on paper showing all working out clearly and bring it to your first lesson.

Please check and mark your answers using the numerical solutions (use a graphing programme such as https://www.desmos.com/calculator to check your sketches). If you are incorrect try the question again!

You may have to review some of the work, try the following online resources to help:

https://www.examsolutions.net/gcse-maths/

https://www.mathsgenie.co.uk/gcse.html (look for the grade 7/8/9 material)

https://www.youtube.com/user/HEGARTYMATHS

Section B – Problem SolvingIn mathematics it is an important skill to use knowledge you have to solve unfamiliar questions. Try these question and bring your solutions to be discussed in class. When you write out your answers include as much explanation as possible so that someone else with no knowledge of maths cold understand your solution.

If you would like to do some extra preparation or you just like a challenge, then check out these online courses:

https://www.accessheonline.ac.uk/courses/mathematics-short-e-course/

https://www.futurelearn.com/courses/precalculus

https://www.futurelearn.com/courses/maths-puzzles

https://www.futurelearn.com/courses/flexagons

https://www.futurelearn.com/courses/recreational-math

https://www.futurelearn.com/courses/advanced-precalculus

Let your teacher know if you have completed any of these courses!

BRIDGING ASSIGNMENT 2020

Section A – GCSE Grade 9 Questions

2

SECTION A – GCSE GRADE 9 QUESTIONS

1 n is an integer.

Prove algebraically that the sum of 12

n(n+1) and 12

(n+1)(n+ 2) is always a square number.

(Total for Question 1 is 2 marks)

___________________________________________________________________________

2

OABC is a parallelogram.

and

X is the midpoint of the line AC. OCD is a straight line so that OC : CD = k : 1

Given that

find the value of k.

(Total for Question 2 is 4 marks) ___________________________________________________________________________ 3 Solve algebraically the simultaneous equations

x2 + y2 = 25

y – 3x = 13

(Total for Question 4 is 5 marks) ___________________________________________________________________________

4 Given that n can be any integer such that n > 1, prove that n2 – n is never an odd number.


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https://www.examsolutions.net/gcse-maths/



https://www.youtube.com/user/HEGARTYMATHS



https://www.futurelearn.com/courses/precalculus

https://www.futurelearn.com/courses/maths-puzzles

https://www.futurelearn.com/courses/flexagons

https://www.futurelearn.com/courses/recreational-math

https://www.futurelearn.com/courses/advanced-precalculus


candi.ac.uk




2


1 n is an integer.


n(n+1) and 12



___________________________________________________________________________

2


and


Given that



x2 + y2 = 25

y – 3x = 13




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A B

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OA OC

X ACOCD OC CD k

XD1

2

k

k

2

2


1 n is an integer.


n(n+1) and 12



___________________________________________________________________________

2


and


Given that



x2 + y2 = 25

y – 3x = 13




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X ACOCD OC CD k

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k

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3

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1 n is an integer.


n(n+1) and 12



___________________________________________________________________________

2


and


Given that



x2 + y2 = 25

y – 3x = 13




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4

5

ABCD is a rectangle.

A, E and B are points on the straight line L with equation x + 2y = 12 A and D are points on the straight line M.

AE = EB

Find an equation for M.


6 Sketch the graph of

y = 2x2 – 8x – 5 showing the coordinates of the turning point and the exact coordinates of any intercepts with the coordinate axes.


7 Sketch the graph of y = tan x° for 0 £ x £ 360


___________________________________________________________________________

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ABCD

A E B x y A D

AE EB

4

5



AE = EB








___________________________________________________________________________

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8 Here is a sketch of a curve.

The equation of the curve is y = x2 + ax + b where a and b are integers.

The points (0, −5) and (5, 0) lie on the curve.

Find the coordinates of the turning point of the curve.


9 The equation of a curve is y = ax A is the point where the curve intersects the y-axis.

(a) State the coordinates of A.

(1) The equation of circle C is x2 + y2 = 16

The circle C is translated by the vector

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⎛⎝⎜

⎞⎠⎟

to give circle B.

(b) Draw a sketch of circle B.

Label with coordinates the centre of circle B and any points of intersection with the x-axis.

(3)


10 S is a geometric sequence.

(a) Given that ( x −1), 1 and ( x +1) are the first three terms of S, find the value of x. You must show all your working.

(3)

(b) Show that the 5th term of S is 7 + 5 2

(2)


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y x ax b a b

8

7

4

5



AE = EB








___________________________________________________________________________

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D O

ABCD

A E B x y A D

AE EB

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⎞⎠⎟

to give circle B.



(3)




(3)


(2)


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to give circle B.



(3)




(3)


(2)


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___________________________________________________________________________ 11

OAC is a sector of a circle, centre O, radius 10 m.

BA is the tangent to the circle at point A. BC is the tangent to the circle at point C.

Angle AOC = 120°

Calculate the area of the shaded region. Give your answer correct to 3 significant figures.


___________________________________________________________________________

12 2− x + 2

x − 3− x − 6

x + 3 can be written as a single fraction in the form

ax + bx2 − 9

where a and b are integers.

Work out the value of a and the value of b.


13 Work out the exact value of x.


___________________________________________________________________________

14 When a biased coin is thrown 4 times, the probability of getting 4 heads is

1681

Work out the probability of getting 4 tails when the coin is thrown 4 times.


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BA ABC C

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___________________________________________________________________________ 11



Angle AOC = 120°



___________________________________________________________________________

12 2− x + 2

x − 3− x − 6


ax + bx2 − 9






___________________________________________________________________________


1681



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B

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OAC O

BA ABC C

AOC

12

6

___________________________________________________________________________ 11



Angle AOC = 120°



___________________________________________________________________________

12 2− x + 2

x − 3− x − 6


ax + bx2 − 9






___________________________________________________________________________


1681



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OAC O

BA ABC C

AOC

13

6

___________________________________________________________________________ 11



Angle AOC = 120°



___________________________________________________________________________

12 2− x + 2

x − 3− x − 6


ax + bx2 − 9






___________________________________________________________________________


1681



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15 The diagram shows a parallelogram.

The area of the parallelogram is greater than 15 cm2 (a) Show that 2x2 – 21x + 40 < 0

(3)

(b) Find the range of possible values of x.

(3)


16 The straight line L has equation 3x + 2y = 17

The point A has coordinates (0, 2) The straight line M is perpendicular to L and passes through A. Line L crosses the y-axis at the point B. Lines L and M intersect at the point C. Work out the area of triangle ABC. You must show all your working.


17 ABC and ADC are triangles.

The area of triangle ADC is 56 m2

Work out the length of AB. Give your answer correct to 1 decimal place.


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(3)


(3)









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(3)


(3)









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Section B – Problem Solving

9

SECTION B – PROBLEM SOLVING

1

9


2

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3

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4

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6

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9

Section C – Numerical Soloutions

10

SECTION C – NUMERICAL SOLUTIONS

1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

1

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

2

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

3

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

4

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

5

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

6

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

7

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

8

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

9

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

10

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

11

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

12

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

13

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

14

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

15

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

16

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

17

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

18

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

19

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

20

10


1. Proof

2. k =

3. x = −3, y = 4, x = –

, y = –

4. proof

5. y = 2x + 36

6. sketch

7. sketch

8. (2, –9)

9. sketch

10. 7 + 5÷2

11. Area = 68.5

12. a = 4, b = –42

13. x = 1.45

14.

15. 2.5 < x < 8

16. Area ABC = 9.75

17. 14.38

18. a = 7, b = –1

19.

20. proof

21.

21

further maths - city and islington college … · further maths bridging assignment (gcse to a...

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