Paper 3 Unseen Topics - Corbettmaths | Videos, … 3 − Unseen Topics This is a collection of questions based on the topics that are so far UNSEEN or are usually more prominent Make

Paper 3 − Unseen Topics

This is a collection of questions based on the topics that are so far UNSEEN or are usually more prominent

Make sure you revise all topics as it is very likely topics from Paper 1 and 2 will appear in Paper 3.

Guidance

1. Read each question carefully before you begin answering it.2. Don’t spend too long on one question.3. Attempt every question.4. Check your answers seem right.5. Always show your workings

Revision for this test

© CORBETTMATHS 2017

Question Topic Video number

1 Best Buys 210

2 Currency 214a

3 Conversion Graphs 151, 152

4 LCM, HCF 218, 219

5 Percentages of Amounts 234, 235

6 Percentage Change 233

7 Ratio 270, 271

8 Two-way Tables 319

9 Pie Charts 163, 164

10 Frequency Polygons 155, 156

11 Stem-and-Leaf 169, 170

12 Estimated Mean 55

13 Box Plots 149

14 Collecting like Terms 9

15 Expanding 2 Brackets 14

16 Factorising 117

17 Factorising Two Brackets 118, 119, 120

18 nth term (linear) 288

19 Substitution 20

20 Equation (forming and solving) 114, 115

21 Solving Inequalities 177, 178, 179

22 Inequalities (Regions) 182

23 Drawing Linear Graphs 186

24 y = mx + c 191, 189, 194

25 Simultaneous Equations 295

26 Solving Quadratics 266

27 Angles in Parallel Lines 25, 39

28 Bearings 26, 27

29 Angles in Polygons 32



30 Constructions/Loci 72 to 80

31 Area of a Trapezium 48

32 Circumference 60

33 Area of a Circle 40

34 Arc Length 58

35 Volume of a Cylinder 357

36 Trigonometry 329-331

37 Volume of a Prism 356

38 Surface Area of a Prism 311

39 Translations 325

40 Rotations 275

41 Enlargements 104 to 108

42 Circle Theorems 64, 65

43 Travel Graphs 171

44 Density 384

45 Pressure 385

46 Limits of Accuracy 183, 184

47 Surds 305 to 308

48 Product Rule for Counting 383

49 Capture Recapture 391

50 Venn Diagrams 380

51 Area Under a Curve 389

52 Functions 369, 370

53 Trigonometric Graphs 338, 339

54 Quadratic Formula 267

55 Completing the Square 10, 371

56 Transformations of Graphs 323

57 Iteration 373

58 Circle Theorems Proofs 66

59 Sine Rule 333


1. Two shops sell the same type of perfume.A 100ml bottle of perfume normally costs £40.

�

Rebecca says that both offers give the same value for money.Is she correct? Show your working.

(5)

2. Terry goes to the Post Office to exchange money.

�Terry changes $651 and €161.20 into pounds sterling.The Post Office deducts their commission and gives Terry £528.

What is the percentage commission?

.........................%(4)

60 3D Trigonometry and Pythagoras 259, 332



3. (a) Use the fact 5 miles = 8 kilometres to draw a conversion graph on the grid.

�(2)

Use your graph to convert

(b) 8 miles to kilometres

.........................km(1)

(c) 6 kilometres to miles

.........................miles(1)


4. Find the Lowest Common Multiple (LCM) of 60 and 75.

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

5. The table gives information about the number of people voting for each party at an election.

�

There are 52852 people who can voteThe target was that 88% of people would vote.

Was the target met?

(3)

6. A clothes shop normally sells their goods at 80% above cost price.In a sale, the shop reduces the prices by 25%.

What percentage profit does the shop make on clothes sold in the sale?

.........................%(3)


7. A piece of carpet is 240cm long.Mr Jones cuts it into three pieces in the ratio 1 : 2 : 5

Work out the length of the longest piece of carpet.

................................(3)

8. 100 people study one language at a college.

Some people study French.Some people study Spanish.The rest of the people study German.

54 of the people are male.20 of the 29 people who study Spanish are female.31 people study German.15 females study French.

Work out the number of males who study German.

.........................(4)


9. The table gives information about the number of students in years 7 to 10.

�

Draw an accurate pie chart to show this information.

�

(4)


10. The frequency table gives information about the weight of some rugby players.

�

(a) Draw a frequency polygon to represent this data.(2)

�(b) Write down the modal class interval.

.........................(1)

One player is chosen at random.

(c) Work out the probability that this player is more than 90kg.

.........................(1)


11. The weights of books on a shelf are recorded in a stem and leaf diagram.

�

(a) Write down the median.

......................(1)

(b) Work out the total weight of books on the shelf.

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

A book weighing 1.8kg is added to the shelf.

Peter says the median will remain the same.

(c) Is Peter correct? Explain your answer.

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


12. Sally is raising money for charity for a fun run.The table below has been given to her from the website.

Sally says the average donation is £10.By calculating the estimated mean, decide if you agree with Sally.

(4)

13. Mrs Davis sets her class a quiz, which has a maximum score of 50.The distribution of the scores are shown in a box plot below.

�(a) Write down the median score.

.........................(1)

(b) Write down the highest score.

.........................(1)


(c) Find the interquartile range.

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

Martin scored 35 marks.(d) What percentage of the class scored a lower mark than Martin?

.........................%(1)

The interquartile range is a better measure of the spread of a distribution than the range.

Explain why.

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

................................................................................................................................(1)

14. Simplify

4(3y² + w − 7) − 2(11 − y² + 3w)

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

15. Expand and simplify (5w − 6)(2w + 7)

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


16. Factorise completely

�

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

17. (a) Factorise x² + 14x − 51

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

(b) Factorise 3y² + 10y − 8

.....................................(3)

18. A sequence of numbers is shown below.

1 5 9 13 17 ... ...

(a) Find an expression for the nth term of the sequence.

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

(b) Explain why 95 will not be a term in this sequence.

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

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


19. The amount of medicine, s ml, to give to a child can be worked out using the formula.

�

s is the amount of medicine, in ml.a is the adult dose, in ml.m is the age of the child, in months.

A child is 20 months old.An adult’s dose is 45ml.

Work out the amount of medicine the child should be given.

.........................ml(3)

20. Shown below is an isosceles triangle. Each side is measured in centimetres.

�

Calculate the perimeter of the triangle.

......................cm(2)


21. x is an integer.

Write down all the solutions of the inequality 3 < 2x + 1 < 13

......................................................(3)

22. On the grid, clearly label the region which satisfies all three inequalities below

x ≤ 2 y < 2x − 2 x + y + 2 > 0

�

(4)


23. On the grid, draw the graph of 3x − 2y = 6

�(4)


24. The point A (1, 1) and the point B (5, −1) lie on the line L.

Find the equation of the line L.

.........................(4)

25. Solve the simultaneous equations

x = …………………….. y = ..........................(3)

26. Solve y² + 9y + 2 = 8y + 58

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


27. CE and FI are parallel lines.Angle EDH = 50°Angle DGF = 100°

�

Show, giving reasons, that triangle DGH is isosceles.

(4)

28. The bearing of A from B is 074°Work out the bearing of B from A

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

29. Shown below are two identical regular polygons and an equilateral triangle.

�

Calculate the number of sides each regular polygon has.

.........................(3)


30.

�

A yacht leaves the port, P, on a course that is an equal distance from PB and PL.

Using ruler and compasses only, construct the course on the diagram.You must show your construction arcs.

(2)

31.

�

The area of the trapezium is 34cm².

Work out the value of x.

....................cm(2)


32. The circumference of a circle measures 19.5cm.

Work out the area of the circle

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

33. Shown below is a circular photo surrounded by a frame.

�

The photo has radius 12cm.The frame has width 4cm.

Work out area of the frame.This area is shaded in the diagram.

.........................cm²(3)


34.

�

The perimeter of the sector is 1m.Find the length of y, the radius of the circle.

.........................cm(4)

35.

�

The volume of the cuboid and the cylinder are equal.

Find h in terms of x.Give your answer in its simplest form.

......................... cm³(3)


36. Two right-angled triangles are shown below.PQ is 10cm.QR is 3cm.Angle QRS is 65⁰

�

Calculate the size of angle PQS

....................⁰(5)

37. Shown below is a triangular prism.

�

Find the volume of the triangular prism.

.........................cm³(3)


38. Shown below is a cylinder.

�

Calculate the curved surface area.Give your answer to 1 decimal place.

.........................cm²(2)

39.

�

Describe fully the single transformation that maps shape A onto shape B.

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

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


40.

�

Rotate shape A 90° anti-clockwise about centre (5, −1)

(3)

41.

�Enlarge the triangle by scale factor −½, using centre of enlargement (2, 0)

(3)


42. PDQ is a tangent at D.O is the centre of the circle.DEF is an isosceles triangle.

�

(a) Work out the value of a.

.........................°(2)

(b) Work out the value of b.

.........................°(3)


43. A remote control car drives in a straight line. It starts from rest and travels with constant acceleration for 15 seconds reaching a velocity of 10m/s.It then travels at a constant speed for 5 seconds. It then slows down with constant deceleration of 0.5m/s2.

(a) Draw a velocity time graph

(b) Using your velocity-time graph, work out the total distance travelled.

……………..m(2)


44. Material A has a density of 5.8g/cm³.Material B has a density of 4.1g/cm³.

377g of Material A and 1.64kg of Material B form Material C.

Work out the density of Material C.

………………..g/cm³(4)

45. The pressure of a tyre is 32 pounds per square inch.

Given 1pound=0.4536kilograms 1inch=2.54centimetres

Workoutthepressureingramspersquarecentimetre.

………………..(4)


46. The curved surface area of a cone is given by the formula

�

where A is the curved surface arear is the radius of the base of the coneand l is the slant height

Given A = 220 cm² correct to 3 significant figures,and r = 8 cm correct to 1 significant figure.

Calculate the upper bound for l.

....................cm(3)

47. The midpoints of the sides of a square of side 10cm are joined to form another square. This process is then repeated to create the shaded square.

�

Find the area of the shaded square.

.........................cm²(4)


48. Jim picks a five digit odd number. The second digit is less than 5. The fourth digit is a cube number The first digit is a prime number. How many different numbers could he pick?

.............................(3)

49. A group of scientists want to estimate the number of squirrels in a wood. They catch and ring 40 squirrels. They return the 40 squirrels to the wood. They then catch 50 squirrels and 7 are ringed.

Estimate the number of squirrels in the wood.

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

50. The Venn diagram shows information about the pets owned by 40 students

ξ = 40 studentsC = students who own a catD = students who own a dog

A student is chosen at random.They own a cat.Work out the probability that they own a dog.

............................(5)


51.

Above is the velocity-time graph of a particle over 12 seconds.

Estimate the distance travelled over the first 8 seconds

…………………………………m(3)

52. The function f is such that

Find

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


53. Shown is part of the curve y = cos x

�

(a) Write down the coordinates of the point A.

(.......... , ..........)(1)

(b) Write down the coordinates of the point B.

(.......... , ..........)(1)

54. Solve the equation x² − 2x − 9 = 0

Give your answers to two decimal places.

x = ..................... or x = .....................(3)

55. Write x² + 4x + 13 in the form (x + a)² + b, where a and b are constants.

..............................(3)


56. This is a sketch of the curve with equation y = f(x)

�

The vertex of the curve is at the point (-6, 1)

Write down the coordinates of the vertex of the curve with equation

(a) y = f(x + 3)

(............... , ...............)(1)

(b) y = f(−x)

(............... , ...............)(1)

(c) y = -f(x)

(............... , ...............)(1)


57. (a) Show the equation 3x³ + 7x = 5 has a solution between 0 and 1

(2)

(b) Show that 3x³ + 7x = 5 can be rearranged to give

(2)

(c) Starting with use the iteration formula

three times to find an estimate for the solution to 3x³ + 7x = 5

(3)


58.

�Prove that the angle at the centre is twice the angle at the circumference.

(4)

59.

�

Find the size of y.

.........................°(3)


60. A tree is located in the corner of a rectangular field.

�

The field is 15 metres long and 12 metres wide.The tree is 5 metres tall.

Calculate angle CAE.

.........................°(4)


Documents

Paper 3 Unseen Topics - Corbettmaths | Videos, … 3 − Unseen Topics This is a collection of questions based on the topics that are so far UNSEEN or are usually more prominent Make