Paper 2 Predictions - Corbettmaths · PDF filePaper 2 Predictions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser ... Check your answers seem right. 5

Paper 2 Predictions

Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser

You will need a calculator

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 2016

Question Topic Video number

1 Currency 214a

2 Angles in Parallel Lines 25

3 Pythagoras 257

4 Speed, Distance, Time 299

5 Best Buys 210

6 LCM, HCF 223, 224

7 Ratio 270, 271

8 nth Term 288, 289

9 Drawing Linear Graphs 186

10 y = mx + c 191

11 Trial and Improvement 116

12 Drawing Pie Charts 163, 164

13 Scatter Graphs 165, 166

14 Frequency Polygons 155, 156

15 Stem-and-Leaf 169, 170

16 Estimated Mean 55

17 Trigonometry 329, 330, 331

18 Similar Shapes 292, 293a, 293b

19 Compound Interest 236

20 Reverse Percentages 240

21 Simultaneous Equations (Grade B) 295

22 Cumulative Frequency 153, 154

23 Congruent Triangles 67

24 Sine Rule 333

25 Cosine Rule 335, 336

26 Area of a Triangle (1/2abSinC) 337

27 Limits of Accuracy 183, 184

28 Parallel Lines 196

29 Perpendicular Lines 197

30 Inequalities (regions) 182


1. A coat in London costs £60.The same coat in Dublin costs €105.60.The exchange rate is £1 = €1.65.

In which city is the coat cheaper and by how much?

(3)

2. AB is parallel to CD.

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Work out the size of angle y.Give reasons for your answer.

.........................°(4)

Question Topic Video number

31 Factorising Quadratics 118, 119, 120

32 Quadratic Formula 267

33 Stratified Sampling 281

34 Histograms 157, 158, 159

35 Algebraic Proof 365

36 Simultaneous Equations (Grade A*) 298

37 Transformations of Graphs 323

38 Algebraic Fractions 21, 22, 23, 24

39 Volume 359-361


3.

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ABC is a right-angled triangle.AC = 6cm.AB = 20cm.

Calculate the length of BC.Give your answer correct to 1 decimal place.

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

4. A car travels 240 kilometres in 3 hours 20 minutes.

Calculate the average speed, in km/h, of the car.

.........................km/h(3)


5. A supermarket sells Baked Beans in two different size cans.

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Which size can is the best value for money?You must show all your working.

(4)

6. Helen thinks of two numbers.The Highest Common Factor (HCF) of her two numbers is 5The Lowest Common Multiple (LCM) of her two numbers is a multiple of 12

Write down two possible numbers that Helen could be thinking of.

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


7. At a rugby match, the ratio of children to adults is 2 : 3There are 6000 children in the crowd.Each adult ticket costs £8Each child ticket costs a quarter of the adult ticket.

Work out the total money made from ticket sales.

£......................... (4)

8. The first 5 terms in a number sequence are

10 7 4 1 -2 ... ...

(a) Work out the nth term of the sequence.

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

(b) Find the 50th term of the sequence.

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


9. On the grid, draw y = 4x − 5 for values of x from −2 to 2.

�(4)


10. A straight line L is shown on the grid.

�

Work out the equation of line L

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

11. The equation

x³ + 4x = 170

has a solution between 5 and 6.

Use trial and improvement to find this solution.Give your answer correct to 1 decimal places.You must show all your working.

x = ...............................(4)


12. The table gives information about the holiday destination of 18 students in a class.

�

Draw an accurate pie chart to show this information.

�

(4)


13. The table shows the time spent revising and the test scores of ten students.

�

The first seven points have been plotted on this scatter diagram.

�(a) Complete the scatter diagram.

(1)(b) Describe the relationship shown in the scatter diagram.

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

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

(c) Draw a line of best fit on your scatter diagram.(1)

(d) Another student has spent 4.5 hours revising. Use your line of best fit to estimate their test result.

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


14. 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)


15. Helen plays darts.

Here are her scores.

55 23 48 29 41 47 36

35 40 35 44 34 35

(a) Draw an ordered stem and leaf diagram to show her scores.

(3)

(b) Write down the mode.

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

(c) Work out the range.

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


16. Timothy asked 30 people how long it takes them to get to school.

The table shows some information about his results.

�

Work out an estimate for the mean time taken.

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

17.

�

Calculate the size of angle BAC.

....................⁰(3)


18. Shown below are two mathematically similar cuboids.

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The volume of cuboid B is 1728cm³

Find the volume of cuboid A.

..........................cm³(2)

19. Fiona leaves £1600 in the bank for four years.It earns compound interest of 4% each year.

Calculate the total amount Fiona has in the bank at the end of the four years.

£.........................(3)


20. Lauren is given a 12% pay rise.Her new salary is £24,080

What was Lauren’s salary before the pay rise?

£.........................(3)

21. Solve the simultaneous equations

3x + 5y = 12x − 3y = 7

Do not use trial and improvement

x = ......................... y = ..........................(4)


22. The ages of 100 teachers were recorded.The table below shows this information.

�

(a) Complete the cumulative frequency column in the table.(1)

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(b) Draw a cumulative frequency graph for this information.(2)


23. ABCD is a parallelogram.

�

Prove that triangles ABD and BCD are congruent.

(4)

24.

�

In triangle ABC the length of AC is 15cm.Angle ABC = 112°Angle BAC = 33°

Work out the length of BC.

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


25.

�

Calculate the length of BC.

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

26.

�

The area of the triangle shown is 25cm².

Calculate the perimeter of the triangle.

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


27. Declan ran a distance of 200m in a time of 26.2 seconds.

The distance of 200m was measured to the nearest 10 metres.The time of 26.2 was measured to the nearest tenth of a second.

(a) Work out the upper bound for Declan’s average speed.

.........................m/s(2)

(b) Work out the lower bound for Declan’s average speed.

.........................m/s(2)

28. Write down the equation of the line that is parallel to x + 2y = 4 and passes through the point (0, 5)

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

29. The point A is (5, −2) and the point B is (11, 1).

Find the equation of the line perpendicular to AB passing through the origin.

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


30.

�

The region labelled R satisfies three inequalities.

State the three inequalities

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

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

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


31. (a) Factorise y² − 12y − 64

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

(b) Factorise 2y² + 7y − 15

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

(c) Factorise fully 2y² − 50

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

(d) Factorise y² − 13y + 36

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


32. Solve the quadratic equation 7x² − 25x + 2 = 0

Give your answers to two decimal places.

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

32. Declan works in a confectioners.He is asked to test a sample of 40 chocolates stratified by type of chocolate.The table shows the number of each type of chocolate in the shop.

�

Calculate the number of dark chocolates required for his stratified sample.

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


33. The lengths of 200 fish in a pond, l centimetres, are recorded below.

�

Draw a histogram for this data.

�

(3)


34. Prove that the sum of three consecutive even numbers is always a multiple of 6

(3)

35. Solve the equations

x² + y² = 455x − 3y = 21

Give your answers to 1 decimal place.

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


36. Here is the graph of y = f(x)The point P(4, 1) is a point on the graph.

�

What are the coordinates of the new position of P when the graph y = f(x) istransformed to the graph of

(a) y = −f(x)

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

(b) y = f(x) + 4

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

(c) y = f(2x)

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

(d) y = f(x + 5)

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


37. Solve

�

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


38. A square based pyramid 1 is divided into two parts:a square based pyramid 2 and a frustum 3, as shown.

�

Pyramid 1 has a base of side length 8cm.Pyramid 2 has a base of side length 4cm.The perpendicular height of pyramid 1 is 10cm.

Calculate the volume of frustum 3.

........................cm³(4)


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Paper 2 Predictions - Corbettmaths · PDF filePaper 2 Predictions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser ... Check your answers seem right. 5