Dulwich College year 9 Mathematics Specimen paper B Online Quiz

1. Use your calculator to work out the value of:

\[\sqrt{\frac{3+\sqrt{2} }{4}}\]

(a) Write down all of the digits shown on your calculator:

1.050501495 1.118033989 0.866025404 2.236067978 2.10100299

(b) Write your answer to (a) rounded to 1 decimal place:

1.1 1 1.5 0.9 None of the Above

(c) Write your answer to (a) rounded to 4 significant figures:

1.051 1.041 1.15 1.055 1.04

2. (a) 140 students sat a Mathematics examination. 7 forgot their calculators. Calculate the percentage of students who forgot their calculators.

5% 7% 4% 8% None of the Above

(b) A teacher has purchased some calculators from a shop for £12 each and decides to sell these calculators to those forgetful students. For each calculator sold the teacher decides to make a 25% profit. Calculate how much each student pays for a calculator.

£15 £13 £12 £9 None of the Above

(c) In fact, one-fifth of the students failed to turn up to the examination. Calculate how many should have turned up in total given that 140 sat the examination.

175 28 112 35 None of the Above

3. Simplify the following:

(a) 3ab — 4a + 6b — ab — 3a — 10b

2ab-7a-4b 2ab-a+4b 4ab-7ab-4b 2ab+7ab-4b None of the Above

(b) 4(3x — 2)

12x-8 12x-4 12x-2 12x+8 None of the Above

(c) 3 — (4x — 2) — 6x

5-10x 1-10x 5-2x 5+10x All of the Above except 'd'

(d) (x — 2)(x + 7)

x2+5x-14 x2+9x-14 x2+5x+14 2x2+5x-14 2x+5x-14

(e) \[\frac{56ab^{3}}{8a^{3}b^{2}}\]

7b/a2 7ba 7ba2 7b 7b/a

4. The diagram below shows two parallel lines and a triangle with two equal sides as indicated. Calculate the values of x and y.

x =40º x =35º x =50º x =30º x =45º

y=

y = 70º y = 100º y = 60º y = 80º y = 65º

5. The current world record for the men’s 100 metre sprint is 9.58 seconds.

Writing your answers to 3 significant figures, calculate the average speed of the world record holder in:

(a) metres per second,

10.4m/s 9.5m/s 10m/s 10.3m/s All of the Above

(b) kilometres per hour,

37.6km/h 32.5km/h 34.6km/h 32.4km/h 35.6km/h

(c) miles per hour (note that one kilometre is roughly 0.621 miles).

23.3miles/h 20.2miles/h 21.5miles/h 20.0miles/h 22.1miles/h

6. (a) State the largest number less than 25 which is:

(i) a prime number,

23 29 19 21 All of the Above except 'b'

(ii) a square number,

16 9 4 25 All of the Above except 'd'

(iii) a triangular number,

21 24 25 27 23

(b) For the sequence of numbers:

3, 7, 11, 15, ...

calculate:

(i) the 6th term in the sequence,

23 25 24 22 None of the Above

(ii) the \[n^{th}\] term in the sequence,

4n -1 7n -7 n-4 n+3 4n - 3

(iii) the term of the sequence which has a value of 3999.

1000 572 3000 1500 None of the Above

7.

In the diagram shown above you are told that the angle marked y is twice as big as the angle marked x and the angle marked z is three times as big as that marked x.

Calculate the size of the angles marked x, y and z.

x =15º x =10º x =25º x =20º x =30º

y=

y = 30º y = 20º y = 10º y = 15º y = 25º

z=

z = 45º z = 35º z=30º z=40º z=60º

8.

Given that the above grid is made of squares with sides of 1 cm, calculate the area of:

(a) triangle A,

Answers: \[cm^{2}\]

(b) triangle B.

Answer:\[cm^{2}\]

9. The diagram below shows two right angled triangles. Calculate x and y.

Answer: x = cm

y = cm

8.
2, 2, 2, 3, 4, 5

For the data above calculate:

(a) the median,

2.5 1.5 3 4.5 5

Two more values, x and y, are added to the data list. The range of the new data list is 6 and its new mean is 3.75.

(b) Calculate the values of x and y.

x = 8 or 4, y = 4 or 8 x = 6 or 3, y = 2 or 4 x = 5 or 2, y = 6 or 2 x = 9 or 4, y = 4 or 6 None of the Above

11. (a) Complete the tables of values for the following straight lines:

(i) y = 2x — 2

x	-2	0	4
y			6

(ii) y = l — x

x	-2	0	4
y			-3

(b) Plot the lines y = 2x — 2 and y = 1 — x on the grid below.

(c) Write down the coordinates of where the two lines cross.

Answer:

9. Solve the following equations:

(a) 3s — 5 = 4 — 2x

9/5 4/5 8/5 5/9 6/5

(b) \[\frac{x}{3}\] —1 = 7

24 20 25 18 22

(c) (2x —1)(3x + 2) = 6\[x^{2}\] — x + 2

2 3 4 5 6

10. Factorise fully:

(a) 40\[x^{2}\] + 10

10(4x² +1) 20(2x² +1) 4(4x² +10) 10(4x² +40) 10(40x² + 1)

(b) 35abc — 45\[a^{2}\]\[c^{3}\]

5ac(7b-9ac²) 5a²c(7b-9c²) 5a(7ab-9ac²) 5c(7b-9ac²) 5a²c²(7b-9ac²)

11.

On the grid above draw the result of:

(a) translating shape T by the vector \[\left(\frac{-3}{-4}\right)\] labelling your answer A,

(b) rotating shape T 90° clockwise about (0,0) labelling your answer B,

(c) reflecting shape T in the line y = x labelling your answer C,

(d) enlarging shape T by a scale factor of 3 with centre of enlargement (3, 3) labelling your answer D.

12. (a) Calculate the size of an exterior angle of a regular pentagon.

72 64 80 76 60

(b) Calculate how many sides a regular polygon has if its interior angle is equal to the exterior angle of an equilateral triangle.

6 4 2 8 1

13. The faces of a cube are painted so that any two faces which have an edge in common are painted different colours. Find the smallest number of colours needed to paint the cube.

3 2 4 5 1

14. A bag contains n balls which are red, green or blue. The probability of picking a red ball at random from the bag is \[\frac{1}{6}\] and of picking a green ball is \[\frac{3}{10}\] . Calculate the smallest possible value of n.

30 20 25 40 35

15. A pafindromir number is one which reads the same forwards as backwards.

For example, 1551 is palindromic, as is 12321.

(a) Find the next palindromic number after 1551.

1661 1166 1616 1611 None of the Above

(b) Find the next palindromic number after 12321.

12421 12241 12141 12341 12320

(c) Calculate the sum of all of the palindromic numbers between 100 and 200.

1460 1640 1604 1046 1260

16. A cylindrical paint tin has a radius of 16 cm and a height of 30 cm.

(a) Calculate the circumference of the base, giving your answer to 1 decimal place.

100.5 96.5 102.5 98.5 94.5

(b) Calculate the volume of the cylinder, giving your answer to the nearest whole number.

24127 22417 24217 24712 27241

(c) Calculate the number of litres of paint that this tin contains, giving your answer to 1 decimal place.

24.1 22.1 26.1 28.1 30.1

(d) Each litre of paint covers 10 m2. Calculate the area of wall this can of paint covers, giving your answer in m2 and to the nearest whole number.

241 124 142 240 214

17. Calculate the sum of the angles shown in each of the diagrams:

(a)

900 180 820 920 800

(b)

1440 1540 1240 1640 1360

18. Α new way to combine two numbers, written Δ, is deﬁned as:

x Δ y = \[x^{2}\] + \[y^{2}\]

For example, 3 Δ 5 = 34 because 32 + 52 = 9 + 25 = 34.

(a)Calculate:

(i) 2 Δ 3,

13 14 12 15 11

(ii) (-2) Δ (-3),

13 14 15 12 11

(iii) 3 Δ (4 Δ 2).

4009 4000 3999 4006 4010

(b) Solve:

(i) 3 Δ x=10,

+1 or -1 0 0.5 0.05 None of the above

(ii) x Δ x = 242.

+11 or -11 +12 or -12 +10 or -10 +13 or -13 +14 or -14

19. The 5 digit number la78r is divided by 7 and gives the 4 digit result 25b1. Calculate the unknown digits a, b and c.

a = 7 b = 4 c = 7 a = 5 b = 3 c = 9 a = 6 b = 3 c = 5 a = 4 b = 7 c = 9 a = 6 b = 2 c = 7

b=

c=

20. Work out the dimension of a rectangle with an area of 242 cm2 if its length and breadth are both whole numbers of centimetres, one of which is an even number and the other a prime number.

22 by 11 20 by 10 24 by 12 20 by 11 22 by 12

by cm

21. The diagram below shows a rectangle containing three circles each with radius 2.5 cm. The rectangle has a width of 13 cm and a height of x cm.

Calculate the value of x.

8 7 6 5 9