Year 11 – Higher Maths
Table of Contents
Intro .............................................................................................................................................. 2
What you need to know test ......................................................................................................... 2
Answers to what you need to know test ....................................................................................... 3
Starter .......................................................................................................................................... 3
How to find “Limits of Accuracy” ................................................................................................... 3
Example 1 ................................................................................................................................. 4
Example 2 ................................................................................................................................. 4
Example 3 ................................................................................................................................. 4
Main work (Incorporating homework) ........................................................................................... 5
Answers (to some questions to help you check your work) ....................................................... 6
Intro
Today’s work is from Chapter 20 – “Number and Limits of Accuracy”.
As an introduction the quality of any from a high end Mercedes to a 99p gel pen is determined
by how accurately the individual parts fit together. For this reason if a part needs to be
manufactured to be 8cm long then it is desirable to know how close to 8cm the part will actually
be when finished. For example an 8cm pen insert may actually be anything from 7.5 – 8.5cm
long when finished meaning that the outside of the pen would need to be at least 8.5cm long for
the insert to fit.
THIS IS A VERY IMPORTANT LESSON AND MUST BE FULLY COMPLETED
TO THE BEST OF YOUR ABILITY
For extra help email me on bpcross@sky,com or try this page
http://www.bbc.co.uk/schools/gcsebitesize/maths/shapes/measureshirev3.shtml
What you need to know test
1 Round off 13 605 to:
a the nearest 10.
b the nearest 100.
c the nearest 1000.
2 Round off 14.592 04 to:
a 1 decimal place
b 1 significant figure
c 2 decimal places
d 2 significant figures
e 3 decimal places
f 3 significant figures
3 Find the area of a square of side length 4.75 cm.
4 Find the volume of a cube of side length 8.1 cm.
5 Find the side length of a square with an area of 256 cm 2.
6 Find the surface area of a cube of volume 1000 cm 3.
Answers to what you need to know test
1 a 13 610
b 13 600
c 14 000
2 a 14.6
b 10
c 14.59
3 22.5625 cm2 4 531.441 cm3
d 15
5
e 14.592
16 cm
f 14.6
6
600 cm2
Starter
Using the number 6513.9604, please round off to the nearest
a) 1000
b) 100
c) 10
d) 1
e) 1 dp
f) 2 dp
g) 3 dp
h) 1 sf
i) 2 sf
j) 3 sf
k) 4 sf
How to find “Limits of Accuracy”
Now consider the number 43,000 which was the attendance for the recent derby
match to the nearest thousand.
The question is how many people could actually have been at the game?
If the attendance was rounded to the nearest thousand then there could have been
43,100 since this figure is still 43,000 when rounded to nearest thousand, it could
equally have been 42,900 or 42,800 or 43,200... But what are the largest and
smallest values the attendance could have been? These figures give us the Limits
of Accuracy of the rounded 43,000 attendance.
The actual answers are 42,500 for the smallest figure (since 42,500 rounds up to
43,000 but 42,499 rounds down to 42,000) and 43,499 for the largest (for similar
reasons).
So for 43,000 rounded to nearest thousand the limits of accuracy is written like this
Which reads as 42,500 is less than or equal to 43,000 which is less than or equal
to 43,499
Or simply 43,000 is between the values of 42,500 and 43,499 inclusive.
Important point: This example used whole numbers only since you can’t have half a
person for non whole number examples (which is the majority of our work) there is a
slight difference.
Example 1
Take the recent snow fall which was 23cm where I live in Warrington. Now this figure
was to the nearest whole cm so... what could it have actually been?
The smallest value is 22.5cm (easy enough)
But the largest value is 23.4999999999999999999999...cm since 23.5cm would
have been rounded to 24cm.
However the answer 23.4999999999999999999999 is a bit long winded to write so
we simply say less than 23.5 (
) rather than less than or equal to (
)
So the Limits of Accuracy of 23 to the nearest whole are...
Example 2
Write down the limits of accuracy for 18kg which is given to 2 sf (2 significant figures)
Answer
Smallest possible value = 17.5
Largest possible value = 18.499999999...
answer is:
Example 3
Write down the limits of accuracy for 3.24m which is given to 2 dp (2 decimal places)
Answer
Smallest possible value = 3.235
Largest possible value = 3.24499999999...
answer is:
Main work (Incorporating homework)
1). Give the limits of accuracy of these numbers.
a) 4.43 b) 0.54 c) 3.264 d) 46 e) 3.04
f) 150 (given to the nearest 10) g) 6800 (given to the nearest 100)
h) 21.0 i) 65 j) 0.07 k) 3 l) 3.0
m) 3.00 n) 45.00 o) 79 p) 3400 (given to 2 sig.fig.)
q) 3400 (given to 3 sig.fig.) r) 4.98 s) 4567
2) In the following questions the numbers given are all to the nearest whole number.
Work out the answer and then the lower and upper bounds of the answers.
a) 65 + 78 b) 4 + 3 c) 7 + 32 d) 97 + 88
e) 98 - 46 f) 92 - 79 g) 9 - 2 h) 45 - 9
i) 3 x 60 j) 92 x 3 k) 50 x 21 l) 49 x 12
m)
5 n)
9 o)
20 p)
3) In the following questions the numbers given are all to 2 significant figures.
Work out the answer and then the lower and upper bounds of the answers.
a) 65 + 470 b) 45 + 370 c) 780 + 320 d) 490 + 88
e) 7.9 - 4.6 f) 24 - 7.9 g) 980 - 29 h) 9.0 - 6.7
i) 3.0 x 6.4 j) 2.9 x 3.0 k) 5.0 x 2.9 l) 4.6 x 6.4
m) 78
4) In the following questions the numbers given are all to 1 decimal place.
Work out the answer and then the lower and upper bounds of the answers.
a) 2.5 + 4.7 b) 0.4 + 0.3 c) 0.8 + 3.2 d) 4.7 + 8.8
e) 7.8 - 4.6 f) 14.2 - 7.9 g) 3.1 - 2.3 h) 9.5 - 6.0
i) 3.0 x 6.8 j) 2.2 x 3.1 k) 5.0 x 2.1 l) 4.7 x 1.5
Answers (to some questions to help you check your work)
Note all answers here are without
and the actual number in the middle
so the answer you should have to question 1 a should be...
1
a) 4.425 4.435 b) 0.535 0.545 c) 3.2635 3.2645 d) 45.5 46.5 e) 3.035 3.045
2
a) 143 142 144 b) 7 6 8 c) 39 38 40 d) 185 184 186 e) 52 51 53
3
a) 535 529.5 540.5 b) 415 409.5 420.5 c) 1100 1090 1110 d) 578 572.5 583.5 e) 3.3
3.2 3.4
4
a) 7.2 7.1 7.3 b) 0.7 0.6 0.8 c) 4.0 3.9 4.1 d) 13.5 13.4 13.6 e) 3.2 3.1 3.3
5
a) 7.43 7.42 7.44 b) 0.41 0.40 0.42 c) 4.04 4.03 4.05 d) 13.8 13.79 13.81 e) 3.37
3.36 3.38