gcse past examination questions volume (1)

7/25/2019 GCSE Past Examination Questions Volume (1)

1/21

Nyan Tun

B.Eng (Hons) Aerospace

www.gmtmaths.com
http://www.gmtmaths.com/http://www.gmtmaths.com/http://www.gmtmaths.com/


2/21

Fractions

1. (a) Work out6

5

3

2

[Give your fraction in its simplest form.]

(b) Work out5

21

3

12

6 marks (2011 J/NC)2. Mr Mason asks 240 Year 11 students what they want to do next year.

15% of the students want to go to college.

4

3of the students want to stay at school.

The rest of the students do not know.Work out the number of students who do not know.

(4 marks, 2013 J/NC)

3. (a) Work out3

2

7

1 (b) Work out

3

1

5

3

(3 marks, 2014 J/NC)4. Mr Brown and his 2 children are going to London by train.

An adult ticket costs 24

A child ticket costs 12

Mr Brown has a Family Railcard.

Work out the total cost of the tickets when Mr Brown uses his Family Railcard.(4 Marks, 2014 J/NC)

5. Show that15

8

6

5

9

4

(2 marks, IGCSE 3H/Cal 2014 May)

6. Work out524

313

Give your answer as a mixed number in its simplest form.(3 marks, Maths B 2014Nov/NC)

7. Toms take home pay is $ 205 per week. He gives5

2of this to his mother. He saves 15 % of the remainder. How

much of his pay does he have left to spend?

8.9

5 of the students in a group are male.

6

5 of the female students in the group are right-handed.

(a) Work out the fraction of students in the group who are right-handed females.

(b) Find the smallest possible number of students in the group.

(5 marks, IG MA4H 2013 Jan/ Cal)9. Write down the reciprocal of 4

10. A machine tool is made from two parts.

One part has a length of4

31 inches.

The other part has a length of3

22 inches.

What is the total length, in inches, of the machine tool?

11. A school has 900 pupils. 460 of these pupils are girls.

5

2 of the boys like drama.5

3 of the girls like drama. Work out the total number of pupils in the school who like drama.


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Indices

Law of Indices

nmnm aaa

nmnm

n

m

aaaa

a

nmnm

aa )(

n

nn

b

a

b

a

n

n

aa

1

n

nn

a

b

b

a

nmaa nm

m

nn

m

aa

1

nn aa

1

10 a

1. Find the value of 3

2

27

2 mark (2011 June/NC)

2. Simplify 21

38 )9( yx

2 mark (2012 June/C)

3. (a) Simplify54

aa

(b) Simplify2

86

5

45

ef

fe

(c) Write down the value of 21

9 (4 marks, 2013 Mar NC)

4. Write these numbers in order of size. Start with the smallest number.

51

0.5 5 50

2 mark (2013 June/NC)

5. (a) Write down the reciprocal of 5

(b) Evaluate 32

(2marks, 2013 N/NC)

6. (a) Write down the value of 010 .

(b) Write down the value of 210 .

(2marks, 2014 J/NC)

7. (a) Work out the value ofn .

93 222 n (b) Work out the value of .x

1282 3 x (2marks, 2014 J/Cal)

8. Find the value of32

(2015 June/NC)

9. Simplify326

8

a

(2 marks, IGMB/P1, 2014 May/Cal)


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10. (a) Find the value of05

(b) Find the value of 31

27

(c) Find the value of3

2

(3 marks, 2012 Mar U2/NC)

11. Work out 32

64

(2 marks, 2015 June U2/NC)

12. Simplify 21

62 )9( yw

(2 marks)

13. Solve 4103 x

14. Estimate the value of 32

04

1

99.743.64.101 (4 marks, AQA U2/NC 2014J)

15. Write down the value of 23

4

16. Solve the following equations

(a) 3)81(

1

x

(b)5

125 x

17. Find the value of

i)0

8

ii) 21

64

iii)3

2

8

27

(4 marks)


5/21

Algebraic Expressions

1. Simplify452 )( kc


2. Simplify 21

38)9( yx


3. (a) Simplify52)(

m

(b) Write down the value of 010 .

2 marks (2012 June)

4. Simplify

(a)35

mm

(b) yxyx 2345

(2012 Nov/NC)

5. (a) Simplify 54 aa

(b) Simplify2

86

5

45

ef

fe

(c) Write down the value of 21

9

(4 marks, 2013 Mar NC)

6. (a) Simplify37

xx

(b) Simplify34)(m

(c) Simplify25

8

12

36

fa

af

(4 marks, 2013 N/C)

7. Simplify 83324 xxy

(2 marks, 2013 N/NC)8. Simplify

342 )3( yx


9. (a) Simplify23)(p

(b) Simplify3

8

t

t

(2 marks, 2014 J/C)

10. x = 3

Work out the value of2

4x

(1 mark, 2015J/NC)


6/21

11. (a) Simplify hghg 2456

(c) Simplify fully2

43

p

pp


12. (a) Simplify53 pp

(b) Simplify2

7

h

h

(c) Simplify32 )(x

(3 marks, 2011 Jan, U2/NC)

13. Simplify3

2

6

8

a

(2 marks, IGCSE Maths B/P1, 2014 May/Cal)

14. (a) Simplify42

655

yx

yx

(b) Simplify34 )2( n

(4 marks, IG MA4H 2013 Jan/ Cal)

15. Simplify yxyx 745

16. Simplify each of the following

(a) 23)( bab

(b)33)3()2( xx

(c)347 434 xxx


7/21

Expanding Brackets

1. Expand and simplify )3(4)52(3 xx

2. Expand and simplify )32(5)54(3 yy

3. (a) Expand )2( xx

(b) Expand and simplify )4)(3( xx 4 marks (2011 J/NC)

4. Expand and simplify )14)(53( xx

2 marks (2011 June/C)

5. Expand )52(3 y


6. Expand and simplify )4)(9( pp (2 marks, 2012 J/Cal)

7. (a) Expand )53(4 x

(b) Expand and simplify )5(3)4(2 xx

(c) Expand and simplify )6)(4( xx 5 marks (2012 Nov/NC)

8. (a) Expand )2(3 t

(b) Expand )52(3 xx

(c) Expand and simplify )10)(3( mm


9. Expand )5(2 mm (1 marks, 2014 J/NC)

10. (a) Expand )2(4 x

(b) Expand and simplify )3)(5( xx

(3 marks, 2013 N/NC)

11. Expand and simplify )5)(2( yy (2 marks, 2014 J/Cal)

12. Expand and simplify )3(2)2(5 yy

(2 marks, 2014 N/Cal)

13. Expand and simplify )8)(32( xx (2 marks, 2014 Nov/NC)

14. (a) Expand )5(7 x

(b) Expand )34(3 yy

(c) Expand and simplify )4)(2( tt

(2015 June/C)

15. Expand )53)(35( xx


8/21

Factorising

1. Factorise ee 53 2

2. Factorise completely22)( ddc

3. Factorise 32 2 ww

4. Factorise completely xyx 48 2


5. Factorise 1032 xx (2 marks, 2012 J/NC)

6. Factorise 492 x

(1 marks, 2012 J/Cal)

7. (a) (i) Factorise 27122 xx

(ii) Solve the equation 027122 xx

(b) Factorise 1002 y

(4 marks, 2013 Mar/NC)

8. (a) Factorise x96

(b) Factorise 162 y

(c) Factorise 102 2 pp (4 marks, 2013 J/CAL)

9. Factorise 94 2 x

(1 marks, 2013 N/Cal)

10. Factorise fully xyx 69 2


11. Factorise fully xyxy 63 2


12. (a) Factorise xx 72

(b) Factorise 16102 yy

(c) (i) Factorise 252 2 tt

(ii) tis a positive whole number. The expression 252 2 tt can never have a value that is a

prime number. Explain why.

(6 marks, 2014 N/C)

13. Factorise yy 22

(1 mark, 2015 J/NC)

14. Factories each of the following expressions.

(a) 23 26 xx

(b) 422 xx

(c) 143115 2 xx

(6 marks, WJEC13Jan)

15. Factorise:

(a) 3242 xx

(b) 42132 xx

(c)22 164 yx

(d) 15132 2 x

(e) 12146 2 xx

(f) 16142 2 xx

(g) 253 2 nn

(h) 325211 2 pp


9/21


10/21

10. Solve 24

37

f

3 marks (EdExcel 2014 Nov/NC)

11. Solve 53)3(7 kk 3 marks (EdExcel 2014 Nov/NC)

12. Solve xx 1445 (2 Marks, 2015 J/NC)

13. Redlands School sent x students to a revision day.

St. Samuel School sent twice as many students as Redlands School.Francis Long School sent 7 fewer students than Redlands School.

Each student paid 15 for the revision day.The students paid a total of 1155.

Workout how many students were sent by each school to the revision day?You must show all your working.

(2015 June/ C)

14. Solve xx 21163 Show clear algebraic working.


15. Solve 7)2(7 x

16. Asha and Lucy are selling pencils in a school shop.

They sell boxes of pencils and single pencils.

Asha sells 7 boxes of pencils and 22 single pencils.

Lucy sells 5 boxes of pencils and 2 single pencils.

Asha sells twice as many pencils as Lucy.

Work out how many pencils there are in a box.

(4 marks, 2015 J U3/C)

17. Stephanie is x years old.Tobi is twice as old as Stephanie.

Ulrika is 3 years younger than Tobi.

The sum of all their ages is 52 years.

(a) Show that 5235 x

(b) Work out the value ofx .

(5 marks, 2014 J U3/C)

18. Solve16

3

25

2

xx


19. Solve 13

2

x

x


20. Sarah drives her car from her home to the railway station, a distance of x kilometres.

She then gets the train and travels to London, 8 times the distance she travelled in her car.

If her total journey is 36 kilometres, calculate the length of the car journey.


11/21

Factors and Primes

1. Buses to Acton leave a bus station every 24 minutes.Buses to Barton leave the same bus station every 20 minutes.

A bus to Acton and a bus to Barton both leave the bus station at 9:00 am.When will a bus to Acton and a bus to Barton next leave the bus station at the same time?


2. Trams leave Piccadillyto Eccles every 9 minutesto Didsbury every 12 minutes

A tram to Eccles and a tram to Didsbury both leave Piccadilly at 9 am.At what time will a tram to Eccles and a tram to Didsbury next leave Piccadillyat the same time?

(3 marks, EdExcel 2013 Mar/ NC)

3. Write 525 as a product of its prime factors.3 marks (2013 June/NC)

4. Matt and Dan cycle around a cycle track.Each lap Matt cycles takes him 50 seconds.Each lap Dan cycles takes him 80 seconds.

Dan and Matt start cycling at the same time at the start line.Work out how many laps they will each have cycled when they are next at the start line together.


5. Rita is going to make some cheeseburgers for a party.

She buys some packets of cheese slices and some boxes of burgers.There are 20 cheese slices in each packet.There are 12 burgers in each box.Rita buys exactly the same number of cheese slices and burgers.

i) How many packets of cheese slices and how many boxes of burgers does she buy?

Rita wants to put one cheese slice and one burger into each bread roll.She wants to use all the cheese slices and all the burgers.

ii) How many bread rolls does Rita need?(4 marks, 2013 N/NC)

6. Ali is planning a party.

He wants to buy some cakes and some sausage rolls.The cakes are sold in boxes.There are 12 cakes in each box.Each box of cakes costs 2.50

The sausage rolls are sold in packs.There are 8 sausage rolls in each pack.Each pack of sausage rolls costs 1.20

Ali wants to buy more than 60 cakes and more than 60 sausage rolls.He wants to buy exactly the same number of cakes as sausage rolls.

What is the least amount of money Ali will have to pay?

(5 marks, 2014 J/Cal)7. (a) Express 180 as a product of its prime factors. (3)

Martin thinks of two numbers.He says,

The Highest Common Factor (HCF) of my two numbers is 6The Lowest Common Multiple (LCM) of my two numbers is a mult iple of 15

(b) Write down two possible numbers that Martin is thinking of.

. (Total 5 marks, 2014 Nov/NC)8. John buys some boxes of pencils and some packets of pens for people to use at a conference.

There are 40 pencils in a box.There are 15 pens in a packet.

John gives one pencil and one pen to each person at the conference.

He has no pencils left.He has no pens left.

How many boxes of pencils and how many packets of pen did John buy?(3 marks, 2015 J/NC)


12/21

9. (a) Express 48 as a product of its prime factors.

Buses to Exeter leave a bus station every 20 minutes. Buses to Plymouth leave the bus station every 16minutes. A bus to Exeter and a bus to Plymouth both leave the bus station at 8am.

(b) When will buses to Exeter and to Plymouth next leave the bus station at the same time?(Total 5 marks, 2011 June, U2/NC)

10. Caroline is making some table decorations.Each decoration is made from a candle and a holder.

Caroline buys some candles and some holders each in packs.There are 30 candles in a pack of candles.There are 18 holders in a pack of holders.

Caroline buys exactly the same number of candles and holders.(i) How many packs of candles and how many packs of holders does Caroline buy?

Caroline uses all her candles and all her holders.(ii) How many table decorations does Caroline make?

(5 marks, Maths B 2014Nov/NC)

11. Sally is going to buy some packs of blue paint and some packs of white paint.

Blue paint is sold in packs of 12 tubes.White paint is sold in packs of 15 tubes.

Sally is going to put all the tubes of paint she buys into boxes.She is going to put 1 tube of blue paint and 1 tube of white paint in each box.

Sally wants to buy the smallest number of packs of blue paint and the smallest number of packs of whitepaint.Work out the number of packs of blue paint and the number of packs of white paint she will buy.

(4 Marks, 2014 J U2/NC)

12. (a) Express 54 as a product of its prime factors.

(b) Find the Lowest Common Multiple (LCM) of 45 and 54(4 marks, 2012 N U2/NC)


13/21

Surds

Rules of Surds

1. (a) Rationalise the denominator of3

12

(b) Work out the value of 2)82(


2. 55 can be written in the formk5

(a) Find the value of k

(b) Work out the value of2)312(

(2015 June/NC)

3. Write 45 in the form 5k , where kis an integer.

4. Express 245 - 45 in the form m4 where m is a prime number.Show all your working.

(3 marks, IG MB/P1, 2014 May/Cal)

5. (a) Rationalise the denominator of5

15

2)31( can be written in the form 3ba , where a and b are integers.

(b) Work out the value of a and the value ofb .

(4 marks, 2012 Mar, U2/NC)

6. (a) aka 7)( , wheren

ak

Find the value ofn .

(b) Express22

1as a power of 2.

(4 marks, IG3H 2009 Nov)

7. (a) Expand and simplify )153)(152(

(b) Write 12

6

in the form n , where n is an integer.

(4 marks, 2015 J U2/NC)

8. akaa 17)4)(3( where a and kare positive integers.

Find the value of a and the value ofk.


9. Rationalise the denominator of7

14

Give your answer in its simplest form.(2 marks, Maths B 2014Nov/NC)

10. Rationalise the denominator of31

)56)(56(

Give your answer in its simplest form.

(3 Marks, 2012 N U2/NC)


14/21

11. All measurement in triangles are in centimetre.

ABC is a right angle triangle.

kis a positive integer.

Find the value of k.

12. Rationalise and simplify-----

(a)2

21

(b)32

122

(c)36

2

13. Simplify

(a) )533)(352(

(b)2

222

(c)32

34

12

4

(d)5

12

4

2

(e)12

3

32

1

14. Solve 4103 x

15. Rationalise the denominator of the following.

(a) 48

9

(b)35

325


15/21


16/21

Decimals

12. Express the recurring decimal

182.0 as a fraction in its simplest form.(3 marks, 2012 J/ NC)

13. Work out 1.83 47(3 marks, EdExcel 2013 Mar NC)

14. Given that 1793185 = 331705

Write down the value of

(a) 1.793 185

(b) 331705 1.85(2 marks, 2013 J/ NC)

15. Using the information that

6.7 52 = 348.4

Find the value of

(a) 6.7 520

(b) 67 0.52

(c) 3484 5.2

(3 marks, EdExcel 2014 Nov NC)

16. Steve wants to put a hedge along one side of his garden.He needs to buy 27 plants for the hedge.Each plant costs 5.54Steve has 150 to spend on plants for the hedge.

Does Steve have enough money to buy all the plants he needs?(4 marks, EdExcel 2014 Nov NC)

17.

540.0x

Prove algebraically that x can be written as22

1

(2015 J/NC)

18. Express

52.0 as a fraction in its simplest form.(3 marks, 2012 Mar U2/NC)

19. Richards car uses 1 litre of petrol every 8 miles.Petrol costs 1.30 per litre.Richard drives 240 miles.

Work out the total cost of the petrol the car uses.(3 marks, 2012 N U2/NC)

20. Using the information that 170.2 4.6 = 37

write down the value of

(a) 1702 4.6

(b) 170.2 460

(c) 3.7 4.6

(3 Marks, 2012 N U2/NC)


17/21

Quadratic Equations/ Formula

1. Solve 0243 2 xx

Give your solutions correct to 3 significant figures.(3 marks, 2012 J/CAL)

2. ABCD is a square with a side length of x4 .

M is the midpoint of DC.

N is the point onAD where ND = .x

BMN is a right-angled triangle.

Find an expression, in terms of .x , for the area of triangle BMN.

Give your expression in its simplest form.(4 marks, 2013 J/NC)

3. Solve 1222 xx (2 marks, 2013 J/CAL)

4. The diagram shows a trapezium.

All the measurements are in centimetres.

The area of the trapezium is 351 cm2.

(a) Show that 03512 2 xx

(b) Work out the value of .x (5 marks, 2013 N/CAL)

5. Solve 3122 xxx (2 marks, 2014 J/NC)

6. Solve 0153 2 xx Give your solutions correct to 3 significant figures.

(3 marks, 2014 N/C)

7. ABCD is a rectangle.

AB = 10 cm BC = 8 cm.

P, Q, R and S are points on the sides of the rectangle.

BP = CQ = DR =AS = x cm.

Show that the area,A cm2, of the quadrilateral PQRS is given by the formula 80182 2 xxA

(3 marks, EdExcel IG3H/Cal)

8. The diagram shows a triangle inside a rectangle.

All measurements are given in centimetres.

Show that the total area, in cm2,

of the shaded regions is 3018 x

(4 marks, 2012 Mar U2/NC)


18/21

9. Solve 01522 xx (3 marks, 2015 J U3/C)

10. Solve the equation 0234 2 xx Give your solutions to 3 significant figures.


11. Solve 0425 2 xx Give your solutions correct to 3 significant figures. Show your working clearly.

(3 marks, IG4H 2013 Jan/ Cal)

12. The expression 682 xx can be written in the form qpx 2)( for all values ofx .

(a) Find the value of p and the value ofq .

The graph of 682 xxy has a minimum point.(b) Write down the coordinates of this point.

(4 marks, 2015 J U3/C)

13. The diagram shows a right-angled triangle with sides of length 5 cm ,

cmx )3( and cmx )32( .

(a) Show that 02563 2 xx

(b) Solve the equation 02563 2

xx (Give your answerscorrect to 2 decimal places)

(c) Calculate the area of triangle.

(6 Marks)

14. A rectangle has a length of cmx )4( cm and a width of cmx )72( .

(a) If the area of a similar rectangle is 63, show that 0912 2 xx and calculate the valueofx .

(b) If the perimeter is 36cm, what is the value of x ?

15. Solve this quadratic equation;0852 xx (Give your answers correct to 3 S.F)


19/21

Straight Line Graph

1. On the grid, draw the graph of 23 xy for values of x from1 to 3.

(3 marks, 2012 J/Cal)

2. Complete the table of values for 52 xy

On the grid, draw the graph of 52 xy for values ofx from x =2 to x = 2

(4 marks, EdExcel 2013 Mar NC)


20/21

3. On the grid, draw the graph of 52

1 xy for values ofx from2 to 4.

(3 marks, 2013J/NC)

4. On the grid, draw the graph of 23 xy for values of x from2 to 2



21/21

5. On the grid, draw the graph of 32 xy for values of x from2 to 3

(4 marks, 2014 Nov)

6. On the grid, draw the graph of 32 xy for values of x from -2 to 3.

(3 marks, Maths B 2014Nov/NC)

gcse past examination questions volume (1)

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