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ANSWERS Marks shown in brackets for each question (2)
A* A B C D E
88 75 60 45 25 15
3 Legend used in answers
Green Box - Working out Red Box and - Answer
Authors Note Every possible effort has been made to ensure that everything in this paper is accurate and the author cannot accept responsibility for any errors. Apart from any fair dealing for the purposes of research or private study as permitted under the Copyright, Designs and Patents Act 1988, this paper may only be reproduced, stored or transmitted in any form or by any means with the prior permission in writing of the author, or in the case of reprographic reproduction in accordance with the terms and licence by the CLA. Enquiries concerning reproduction outside these terms should be sent to the author. The right of David Weeks to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
2. Joe made Spaghetti Bolognese for dinner. Some of the ingredients he used are shown. Some of the amounts are missing. Calculate and write the missing amounts in the table
For 6 people For 9 people
mushrooms 150 gram
minced beef 900 grams
spaghetti 1125 grams
chopped tomatoes 500 grams
3. Stuart went to Australia He exchanged some money at £1.00 for 1.52 Australian dollar a) What is £25 in Australian dollars.
3053 =− xx The value for x is between 3 and 4 Use trial and improvement to find the value for x to one decimal place. Show all your working. Use the table to help you.
13. A line has the equation 12 −= xy What is the gradient of the line that is perpendicular to this line
...............................
14. a) What is 0.0053 in standard form.
........................................
b) What is 610563.7 × as an ordinary number
........................................
c) Light travels at a speed of 8103 × metres per second Assuming that there are 365 days in a year calculate how far light travels in a year. Give your answer in standard form in kilometres
Km... ........................................
(1)
(1)
(1)
(4)
9.4608 x 1012
Convert 1 year into seconds: 365 x 24 x 60 x 60 = 31536000 seconds = 3.1536 x 107 Distance travel in 1 year = 3.1536 x 107 x 3 x 108 metres = 9.4608 x 1015 metres = 9.4608 x 1012 km
– ½
Take gradient of the line ( 2 ), flip it over ( ½ ) and change the sign
Diagram NOT drawn accurately ABC is a triangle. BC = 11 cm AC = 5 cm Angle ACB = 80° Calculate the area of the triangle. Give your answer correct to 3 significant figures.
......................... cm2
17. Lewis Hamilton drove 378 kilometres in 2 hours 15 minutes. Calculate his average speed in km/h.
.................................km/h
(3)
(2)
Area ∆∆∆∆ = ½ a b Sin C or ½ × a × b × Sin C = ½ × 11 × 5 × sin 80 = 27.08
27.1
Side b
Side a
b
½
1 Sin x 5 x 8 = 27.08
0
a
Label the sides of the triangle using the letters g iven. Side a is opposite angle A, Side b is opposite angle B a nd side c is opposite angle C
Side c
Angle A
C
. 5 x 0 1
Convert 2hr 15min into a decimal Speed = distance ÷ time = 378 ÷ 2.25
Not drawn accurately CD is parallel to BE AB = 10cm, BC = 4cm, AE=8cm a) Calculate the length of ED
………………….cm
19. The diameter of a hula hoop is 0.85 m Diagram not drawn accurately a) Calculate the circumference of the Hula Hoop Give your answer to 2 decimal places.
................................m
(2)
(2)
diameter = 0.85 Circumference = ππππd
ππππ x 0.85
2.67
These are similar triangles and we need to work out the scaling factor. To make ∆∆∆∆ larger, this is 1.4 (14÷ 10) AD = 8 x 1.4 = 11.2 ED = AD – AE =11.2 – 8 = 3.2 cm
3.2
14 8 10 AD
Or ratio of 10:4 is same as 8:ED 10:4 = 2.5 so 8:ED = 2.5 or ED = 8÷ 2.5 = 3.2
The van has a sign that says “maximum load 1200 kg. Each bag of carrots weighs 30 kg. Gaynor needs to keep within the safety weight limits of her van and she assumes that 1200kg is correct to the nearest 100kg and 30kg is correct to 1 significant figure a) What is the lower bound for the load of the van
................................
b) What is the upper bound for a bag of carrots.
................................ c) Hence calculate the greatest number of bags of potatoes that Gaynor can safely put into her van if her assumptions are correct.
…………………
(1)
(1)
(3)
1150
What is lowest value of 1200 before it changes to 1100?
35 What is highest value of 30 before it
changes to 40?
32
To find the greatest number of bags we can carry safely, find the smallest weight (lower bound) that the van could ca rry and divide that by the largest weight (upper bound) of each bag
Greatest number bags = Van lower bound Bag uppe r bound
A cuboid ABCDEFGH is shown with AB = 4 cm. BC = 5 cm. CE = 9 cm. a) Calculate the length of CG. Give your answer correct to 3 significant figures.
...................................... cm
b) Calculate the size of the angle between CG and the face BCEH. Give your answer correct to 1 decimal place.
........................................°
(3)
(2)
Sine GHC = GH = 4 CG √ 122
11.0
Work out the length of CH using Pythagoras on the base triangle CHE CH2 = CE2 + HE2 = 81 + 25 = 106 Work out the length of CG using Pythagoras on the vertical triangle CHG CG2 = CH2 + HG2 = 106 + 16 = 122