Edexcel Higher Tier Predicted Paper 3 - 2018 · 2018. 6. 10. · Edexcel Higher Tier Predicted...

www.drfrostmaths.com

Edexcel Higher Tier Predicted Paper 3 - 2018

This is a compilation of questions based on all topics (within reason) that have not yet

appeared on either of the papers. This worksheet was automatically generated by the

DrFrostMaths Homework Platform: students can practice this set of questions interactively by

going to www.drfrostmaths.com/homework, logging on, Practise → Past Papers/Worksheets

(or Library → Past/Past Papers for teachers), and using the ‘Revision’ tab. Numerical solutions

are at the back of this paper.

Question 1

[Edexcel IGCSE Jan2013-3H Q12]

Make ℎ the subject of the formula 𝐴 = 2𝜋𝑟(𝑟 + ℎ)

ℎ = ..........................

Question 2

[Edexcel GCSE(9-1) Mock Set 2 Spring 2017 1H Q16]

Make 𝑡 the subject of the formula

𝑘 =2(𝑡 + 3)

𝑡 − 3

𝑡 = ..........................

http://www.drfrostmaths.com/homework


Question 3

[Edexcel GCSE Nov2005-6H Q15]

The sketch graph shows a curve with equation 𝑦 = 𝑝𝑞𝑥

The curve passes through the points (1,5) and (4,320) .

Calculate the value of 𝑝 and the value of 𝑞 .

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


Question 4


By completing the square, find the coordinates of the turning point of the curve with equation

𝑦 = 𝑥2 + 10𝑥 + 18 You must show all your working.

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

Question 5

Find the coordinates of the minimum point of the graph with equation

𝑦 = 3𝑥2 − 3𝑥 + 1

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


Question 6

[Edexcel GCSE March2012-3H Q20]

Each equation in the table represents one of the graphs A to F.

Write the letter of each graph in the correct place in the table.

Equation Graph

𝑦 = 4 𝑠𝑖𝑛 𝑥° .................. 𝑦 = 4 𝑐𝑜𝑠 𝑥° ..................

𝑦 = 𝑥2 − 4𝑥 + 5 .................. 𝑦 = 4 × 2𝑥 .................. 𝑦 = 𝑥3 + 4 ..................

𝑦 =4

𝑥 ..................


Question 7

[Edexcel IGCSE June2011-3H Q3c]

Expand and simplify (𝑦 − 7)(𝑦 + 3)

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

Question 8

[Edexcel GCSE(9-1) June 2017 1H Q10]

Show that (𝑥 + 1)(𝑥 + 2)(𝑥 + 3) can be written in the form 𝑎𝑥3 + 𝑏𝑥2 + 𝑐𝑥 + 𝑑 where 𝑎 ,

𝑏 , 𝑐 and 𝑑 are positive integers.

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

Question 9

[Edexcel IGCSE Jan2015-4H Q12c]

Factorise 𝑥2 + 𝑥 − 30

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

Question 10

[Edexcel IGCSE May2016(R)-4H Q14b]

Factorise 3𝑥2 − 8𝑥 − 3

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


Question 11

[Edexcel IGCSE Nov-2010-4H Q22]

Simplify fully

1 +𝑥2 + 𝑥 − 6

(𝑥 + 4)(𝑥 − 2)

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

Question 12

[Edexcel GCSE June2003-5H Q20c]

Simplify fully

𝑛2 − 1

𝑛 + 1×

2

𝑛 − 2

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

Question 13

[Edexcel IGCSE May2016-3H Q2a]

𝑎 = −5 𝑏 = −2

Work out the value of 2𝑎2 + 6𝑏

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


Question 14

[Edexcel IGCSE Nov2010-3H Q21a]

𝑓(𝑥) = 2𝑥 + 1

Express the inverse function 𝑓−1 in the form 𝑓−1(𝑥) = ...

𝑓−1(𝑥) = ..........................

Question 15

[Edexcel IGCSE June2010-4H Q20di]

𝑔(𝑥) =𝑥

𝑥 − 1

Express the inverse function 𝑔−1 in the form 𝑔−1(𝑥) = ...

𝑔−1(𝑥) = ..........................

Question 16

[Edexcel Specimen Papers Set 1, Paper 2H Q18]

𝑓(𝑥) = 3𝑥2 − 2𝑥 − 8

Express 𝑓(𝑥 + 2) in the form 𝑎𝑥2 + 𝑏𝑥

𝑓(𝑥 + 2) = ..........................


Question 17

[Edexcel GCSE(9-1) Mock Set 1 Autumn 2016 3H Q13c]

The equation 𝑥3 + 5𝑥 − 4 = 0 can be arranged to give 𝑥 =4

𝑥2+5

(c) Starting with 𝑥0 = 0 , use the iteration formula 𝑥𝑛+1 =4

𝑥𝑛2+5 twice to find an estimate for

the solution of 𝑥3 + 5𝑥 − 4 = 0

𝑥1 = ..........................

𝑥2 = ..........................

Question 18

[Edexcel IGCSE Jan2017-2F Q6e]

Here is a sequence of shapes drawn on a square grid.

The width of Shape number 1 is 3 squares.

The width of Shape number 2 is 4 squares.

The width of Shape number n is 𝑊 squares.

Write down a formula for 𝑊 in terms of 𝑛.

𝑊 = ..........................


Question 19


Here are the first five terms of a sequence.

4 11 22 37 56

Find an expression, in terms of 𝑛, for the 𝑛 th term of this sequence.

𝑛 th term = ..........................

Question 20

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 1F Q24, 1H Q5]

Solve the simultaneous equations

3𝑥 − 2𝑦 = −5

2𝑥 − 4𝑦 = 2

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

Question 21

[Edexcel IGCSE June2011-3H Q22]

Solve the simultaneous equations

𝑦 = 2𝑥 − 3

𝑥2 + 𝑦2 = 2

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


Question 22

[Edexcel IGCSE May2012-3H Q9b Edited]

Solve

2𝑦 + 1

3=𝑦 − 2

4

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

Question 23

[Edexcel GCSE June2007-6H Q20]

Solve the equation

𝑥

2𝑥 − 3+

4

𝑥 + 1= 1

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


Question 24

[Edexcel GCSE Nov2016-1F Q22b, Nov2016-1H Q6b]

The table shows some information about the ages of 60 teachers.

Draw a frequency polygon for the information in the table.


Question 25

[Edexcel IGCSE May2012-3H Q12b]

The cumulative frequency graph gives information about the lengths, in minutes, of 80

telephone calls.

Find an estimate for the interquartile range of the lengths of the 80 calls.

.......................... minutes


Question 26

[Edexcel IGCSE June2010-3H Q6d Edited]

The table shows information about the volume of water, in m3, used by each of 80

families in one year.

On the grid, draw a cumulative frequency graph for the table.


Question 27

[Edexcel IGCSE Jan2017-1F Q23b, Jan2017-3H Q6]

The table gives information about the distances, in kilometres, Darren travelled to deliver 100

parcels.

Work out an estimate for the mean distance Darren travelled to deliver these parcels.

.......................... km

Question 28

[Edexcel GCSE June2003-4I Q14a, June2003-6H Q3a]

A garage keeps records of the costs of repairs to its customers’ cars.

The table gives information about the costs of all repairs which were less than £250 in

one week.

Find the class interval in which the median lies.

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


Question 29

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 1H Q8a]

20 men, 10 women and 10 children are in a competition.

The mean score for the women is 15.6.

The mean score for the children is 9.2.

Kevin says that the mean score for all 40 people is 11.2.

Work out the mean score for the men.

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

Question 30

[Edexcel GCSE(9-1) Mock Set 1 Autumn 2016 - 2H Q18]

There are 95 girls and 87 boys in Year 13 at a school.

One girl is going to be chosen for the role of Head Girl.

A different girl is going to be chosen for the role of Deputy Head Girl.

One boy is going to be chosen for the role of Head Boy.

A different boy is going to be chosen for the role of Deputy Head Boy.

Work out how many different ways this can be done.

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


Question 31

[Edexcel Specimen Papers Set 2, Paper 2H Q12b]

There are 12 boys and 10 girls in David’s class.

David is going to pick three different students from his class and write their names in a

list in order.

The order will be

How many different lists can David write?

.......................... ways

Question 32

[Edexcel GCSE(9-1) June 2017 1F Q23, June 2017 1H Q3]

Work out 54.6 × 4.3

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


Question 33

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 3F Q19a, 3H Q1a]

Write 168 as a product of its prime factors.

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

Question 34

[Edexcel IGCSE Jan2012-3H Q17 Edited]

Convert 0.17̇ to a fraction, giving your answer in its simplest form.

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

Question 35

[Edexcel GCSE June2011-4H Q16]

In a sale the normal price of a book is reduced by 10%.

The sale price of the book is £4.86

Calculate the normal price of the book.

£ ..........................


Question 36

[Edexcel IGCSE Jan2016(R)-3H Q17c]

𝜉 = {1,2,3,4,5,6,7,8,9,10,11,12,13} 𝐴 = {3,7,11,13}

𝐵 = {3,6,9,12,13} 𝐶 = {2,3,5,6,7,8}

List the members of the set (𝐴 ∪ 𝐶)′ ∩ 𝐵

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

Question 37

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 3F Q26b]

Write 0.0704 in standard form.

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


Question 38


𝑦 = 16 × 108𝑘 where 𝑘 is an integer.

Find an expression, in terms of 𝑘 , for 𝑦5

4 Give your answer in standard form.

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

Question 39


The diagram shows a large tin of pet food in the shape of a cylinder.

The large tin has a radius of 6.5 cm and a height of 11.5 cm.

A pet food company wants to make a new size of tin.

The new tin will have a radius of 5.8 cm.

It will have the same volume as the large tin.

Calculate the height of the new tin.

Give your answer correct to one decimal place.

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


Question 40

[Edexcel IGCSE May2014-3H Q13]

The diagram shows a square ABCD drawn inside a circle, centre O.

A, B, C and D are points on the circle.

The lengths of the sides of the square are 10 cm.

AC is a diameter of the circle.

Calculate the circumference of the circle. Give your answer correct to 3 significant

figures.

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


Question 41

[Edexcel GCSE Jun2015-1F Q27, Jun2015-1H Q10]

The diagram shows the floor plan of Mary’s conservatory.

Mary is going to cover the floor with tiles.

The tiles are sold in packs.

One pack of tiles will cover 2m2.

A pack of tiles normally costs £24.80.

Mary gets a discount of 25% off the cost of the tiles.

Mary has £100.

Does Mary have enough money to buy all the tiles she needs?

You must show all your working.

[ ] Yes

[ ] No


Question 42

[Edexcel IGCSE Nov2009-3H Q18]

In the diagram, a sector of a circle of radius 12 cm is shaded.

The area of the sector is 112 𝜋 𝑐𝑚 2 .

Calculate the value of 𝑥 .

𝑥 = .......................... °

Question 43


The diagram shows a sector OAPB of a circle, centre O.

AB is a chord of the circle.

OA = OB = 5.4 cm.

Angle AOB = 72°

Calculate the area of the shaded segment APB.

Give your answer correct to 3 significant figures.

.......................... 𝑐𝑚2


Question 44

[Edexcel IGCSE Jan2017(R)-3H Q1]

The area of the floor of a room is 12 m2.

Change 12 m2 into cm2.

.......................... 𝑐𝑚2

Question 45

[Edexcel GCSE Nov2014-2H Q13a]

The diagram shows a swimming pool in the shape of a prism.

The swimming pool is empty.

The swimming pool is filled with water at a constant rate of 50 litres per minute.

Work out how long it will take for the swimming pool to be completely full of water.

Give your answer in hours.

(1 m3 = 1000 litres)

.......................... hours


Question 46

[Edexcel Specimen Papers Set 1, Paper 2H Q20b]

The graph shows information about the velocity, 𝑣 m/s, of a parachutist 𝑡 seconds after

leaving a plane.

Work out an estimate for the distance fallen by the parachutist in the first 12 seconds

after leaving the plane.

Use 3 strips of equal width.

.......................... m


Question 47


𝐴𝐵𝐶 is a right-angled triangle.

Calculate the length of AB.


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

Question 48

[Edexcel IGCSE June2010-3H Q14c]

Triangle ABC is right-angled at B.

AB = 20 cm, correct to 1 significant figure.

BC = 8.3 cm, correct to 2 significant figures.

Calculate the lower bound for the value of 𝑡𝑎𝑛 𝑥° .

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


Question 49



Give your answer correct to 1 decimal place.

𝑥 = .......................... °

Question 50


The area of triangle 𝐴𝐵𝐶 is 42 cm 2

Find the length of 𝐴𝐵 .


𝐴𝐵 = .......................... cm


Question 51


𝐴𝐵𝐶 is a triangle.𝐷 is a point on 𝐴𝐶 .

Angle 𝐵𝐴𝐷 = 45°

Angle 𝐴𝐷𝐵 = 80° 𝐴𝐵 = 7.4 cm𝐷𝐶 = 5.8 cm

Work out the length of 𝐵𝐶 .


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

Question 52


The area of triangle ABC is 6√2 m2.



𝑥 = .......................... metres


Question 53

[Edexcel IGCSE Nov-2010-4H Q21aiii]

PQRS is a trapezium with PQ parallel to SR.

𝑆𝑅→ = 𝐚 𝑃𝑄

→ = 3𝐚 𝑃𝑆

→ = 𝐛

𝑇 is the point on 𝑆𝑄 such that 𝑆𝑇 =1

4𝑆𝑄 .

Find 𝑃𝑇→

in terms of 𝐚 and 𝐛 .

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


Question 54


The diagram shows the positions of a yacht Y, a ship S and a beacon B.

The bearing of B from Y is 228°

The bearing of S from Y is 118°

Given also that BY = SY, find the bearing of S from B.

.......................... °


Question 55

[Edexcel IGCSE May2015-2F Q17a, May2015-4H Q6a]

𝐿𝑀𝑁 is parallel to 𝑃𝑄𝑅. 𝑄𝑀 = 𝑄𝑅 .

Angle 𝑅𝑀𝑁 = 𝑥°

Angle 𝑀𝑄𝑅 = 𝑦°

Write down an expression for 𝑦 in terms of 𝑥.

𝑦 = ..........................


Question 56

[Edexcel IGCSE May2012-3H Q13 Edited]

The diagram shows two congruent regular pentagons and part of a regular 𝑛 -sided polygon

A.

Two sides of each of the regular pentagons and two sides of A meet at the point P.

Calculate the value of 𝑛 .

𝑛 = .......................... sides


Question 57

[Edexcel IGCSE May2013-3H Q20a Edited]

The diagram shows a rectangle.

The length of the rectangle is 𝑥 cm.

The length of a diagonal of the rectangle is 8 cm.

The perimeter of the rectangle is 20 cm.

Show that 𝑥2 + 𝑎𝑥 + 𝑏 = 0 where 𝑎 and 𝑏 are integers to be found.

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


Question 58


Solve 3𝑥2 + 2𝑥 − 7 = 0 Give your solutions correct to 3 significant figures.

Show your working clearly.

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

Question 59

[Edexcel GCSE June2010-4H Q19b]

Solve 𝑥2 − 7𝑥 + 10 = 0

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


Question 60

[Edexcel IGCSE Nov2009-4H Q13b]

Quadrilateral P is mathematically similar to quadrilateral Q.

Calculate the value of .

𝑦 = .......................... cm

Question 61

[Edexcel GCSE June2003-4I Q19b, June2003-6H Q8b]

BE is parallel to CD.

AE=6 cm, ED=4 cm, AB=4.5 cm, BE=4.8 cm.

Calculate the perimeter of the trapezium EBCD.

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


Question 62


ABCDE and AWXYZ are two mathematically similar pentagons.

AE = 4 cm WX = 6 cm DE = 5 cm YZ = 8 cm

The area of pentagon AWXYZ is 52.48 cm2

Calculate the area of the shaded region.

.......................... 𝑐𝑚2


Question 63

[Edexcel IGCSE Jan2017-1H Q16b]

The diagram shows two mathematically similar pots, 𝐴 and 𝐵 .

𝐴 has a volume of 264𝑐𝑚3 𝐵 has a volume of 891𝑐𝑚3

𝐵 has a surface area of 459𝑐𝑚2

Work out the surface area of pot 𝐴 .

.......................... 𝑐𝑚2

Question 64

[Edexcel IGCSE Jan2014(R)-4H Q9b]

On a map, 4 centimetres represents a real distance of 1 kilometre.

On the map, the distance between two points is 14 cm.

Work out the scale of the map in the form 1: 𝑛

................ : ................


Answers

Question 1

ℎ =𝐴−2𝜋𝑟2

2𝜋𝑟

Question 2

𝑡 =6+3𝑘

𝑘−2

Question 3

𝑝 = 1.25 , 𝑞 = 4

Question 4

(−5,−7)

Question 5

(1

2,1

4)

Question 6

E, B, F, C, D, A

Question 7

𝑦2 − 4𝑦 − 21

Question 8

𝑎 = 1 , 𝑏 = 6 , 𝑐 = 11 , 𝑑 = 6

Question 9

(𝑥 − 5)(𝑥 + 6)

Question 10

(3𝑥 + 1)(𝑥 − 3)

Question 11

2𝑥+7

𝑥+4

Question 12

2(𝑛−1)

𝑛−2

Question 13

38

Question 14

𝑓−1(𝑥) =𝑥−1

2

Question 15

𝑔−1(𝑥) =𝑥

𝑥−1

Question 16

𝑓(𝑥 + 2) = 3𝑥2 + 10𝑥

Question 17

𝑥1 = 0.8 and 𝑥2 = 0.71

Question 18

𝑊 = 𝑛 + 2

Question 19

𝑛 th term = 2𝑛2 + 𝑛 + 1

Question 20

𝑥 = −3 , 𝑦 = −2

Question 21

𝑥 = 1 , 𝑦 = −1 or 𝑥 =7

5 , 𝑦 = −

1

5

Question 22

𝑦 = −2


Question 23

𝑥 = 1 or 𝑥 = 9

Question 24

Question 25

any value in the range 4.5 minutes to 6

minutes

Question 26

Question 27

9.4 km

Question 28

150 < 𝐶 ≤ 200

Question 29

10

Question 30

66814260

Question 31

2400 ways

Question 32

234.78

Question 33

23 × 3 × 7

Question 34

8

45

Question 35

£ 5.40

Question 36

9 , 12

Question 37

7.04 × 10−2

Question 38

3.2 × 1010𝑘+1

Question 39

any value in the range 14.4 cm to 14.5 cm

Question 40

any value in the range 44.25 cm to 44.45

cm

Question 41

Yes

Question 42

𝑥 = 280 °


Question 43

any value in the range 4.45 𝑐𝑚2 to 4.46

𝑐𝑚2

Question 44

120000 𝑐𝑚2

Question 45

65 hours

Question 46

452 m

Question 47

5.86 cm

Question 48

0.33

Question 49

𝑥 = 104.5 °

Question 50

any value in the range 𝐴𝐵 = 12.28 cm to

𝐴𝐵 = 12.3 cm

Question 51

8.52 cm

Question 52

𝑥 = 2.63 metres

Question 53

3

4𝑎 +

3

4𝑏

Question 54

083 °

Question 55

𝑦 = 180 − 2𝑥

Question 56

𝑛 = 10 sides

Question 57

𝑎 = −10 , 𝑏 = 18

Question 58

𝑥 = 1.23 or 𝑥 = −1.90

Question 59

𝑥 = 2 or 𝑥 = 5

Question 60

𝑦 = 16 cm

Question 61

19.8 cm

Question 62

31.98 𝑐𝑚2

Question 63

204 𝑐𝑚2

Question 64

1: 25000

Edexcel Higher Tier Predicted Paper 3 - 2018 · 2018. 6. 10. · Edexcel Higher Tier Predicted...

Documents

Transcript of Edexcel Higher Tier Predicted Paper 3 - 2018 · 2018. 6. 10. · Edexcel Higher Tier Predicted...