Download Junior Cert 2009 Foundation Level Q 1

Junior Cert 2011 Foundation Level Project Maths, Answers
1
(a) 100,
b) 1197
2
(a) 16,
(b) 4 (c) 16.3 / 3.7 is approx 16/4 = 4
(d) calculator says 4.405405405…. or 4 and 15/37.
3
(a) 2 * €25.50 = € 51, 3 * € 15 = €45, 51 + 45 = € 96
Note that 2*25.5+3*15 on a scientific calculator (like the Casio fx 83) will give the
right answer as it will do the multiplying first and the adding afterwards.
4
(i) B = {5, 2, 7, 3} AuB = {1, 5, 7, 4, 2, 3} Remember that the order of the
elements inside the {} curly brackets doesn’t matter.
5
(a) 7, 9, 11, 13, 15
(b) See Below (c) 12.
6
(a) 16 + 20 + 2 = 38 ; (b) (x-2) = 7, x = 9.
7
(a) 3.65 * 100 = 365cm,
(b) 365 – 195 = 170
8
(a) 30 * 20 = 600 metres squared,
(b) area of flowerbed is 8*8= 64 metres
squared,
(c) 600 – 64 = 536 metres squared
9
(a) €700 – €500 = €200, percentage profit = 200/500 * 100 = 40%
(b) Find 1% = €8, so 20% = 20* 8 = €160 so price is €800 - €160 = €640.
10
(a) 100,
(b) 11, (c) 11/100 = 0.11
(d) 100 – 9 – 8 – 11 = 72, Probability = 72 / 100 = 0.72
Graph for Q5 (b)
11
Certain to happen B, probability = 1, e.g. sun rising tomorrow
Very unlikely to happen A, probability low but not zero, e.g. lotto win
50% Chance D, probability is 50/100 = 0.5, e.g. tossing a coin
12
(a) Add the numbers of houses and apartments for each year,
2006 60,000 + 19,000 = 79,000
2007 63,000 + 22,000 = 85,000
2008 48,000 + 20,000 = 68,000
2009 27,000 + 14,000 = 41,000
(b) 85,000 – 41,000 = 44,000
(c) 44/85 * 100/1 = 51.76470588% to 2decimal points 51.76%
(d)
first drop is 79,000 – 85,000 = 14,000
second drop is 85,000 – 68,000 = 17,000
third drop is 68,000 – 41,000 = 27,000
so third drop, 2009, is largest.
13
(a) read the number of each age on the vertical scale and get
1 + 4 + 4+ 6 + 1 + 4 = 20
(b) Mode is the most frequent result, so it is the age with the highest number
of students, hence it’s 15.
Range is the difference between the largest and smallest result 17 – 12 = 5
(c) younger than 15 means 12, 13 or 14 years old. Not 15 years old. 1+4+4=9
(d) number of students aged 17 = 4,
Total number of students = 20
so the probability that a student is 17 years is 4/20 = 0.2
(e)
14
(a)
The years on the horizontal axis are in a sequence.
It is much easier to compare two years on the bar chart (also called a
histogram), than to compare two years on the pie chart, and so, it’s
easier to spot a pattern.
It is easier to read the number of dog licences on the bar chart, it is not
clear to figure out the numbers from a pie chart.
(b) Marks are given because you show you understand what the picture shows,
so you could say that the jump between 2001 and 2002 is interesting, perhaps
more dog wardens were hired or the price went down. You could say that the drop
from 2003 to 2004 was interesting as it’s a bit of a drop, perhaps the price went up.
You could say 2006 was interesting as there seems to be a pattern of increasing
numbers from 2004 to 2009 except for the drop in 2006, perhaps the person recording
the data made a mistake.
15 (a) The photocopier didn’t catch the squares very well, but use a ruler and it’s a
3cm, 4cm, 5cm triangle.
(b) Pythagoras said (amongst some other things) that the square of the length of the
longest side of a right angled triangle ( hypotenuse) is equal to the sum of the squares
of the other two sides. In this case
5*5 =3*3 + 4*4
25 = 9 + 16
Draw squares on outside of the triangle using each of the triangle’s sides as one side
of the square. The big square should have the same area as the sum of the two others.
(c) Area of triangle = half the base * perpendicular height
½ * 4*3 = 6
16 (a) The half circle thing that looks like a protractor has 18 sectors, so we can guess
that as they look equal each is worth 10 degrees. Angle at A 40 degrees.
(b) 180 – 40 = 140
(c) angle B + angle C = straight line = 180 degrees
(d) A and C are opposite each other and so are the same size, both are 40 degrees.
17 (a) Type ‘sin’ ‘30’ ‘=’ into your calculator and read the answer. Press ‘SD’ to get
the answers into decimals so that it’s easier to compare the answers.
A
Sin A
Cos A
30
0.5000
0.8660
45
0.7071
0.7071
60
0.8660
0.5000
(b) 45 degrees
(c) 30 degrees
(d) 60 degrees
(e) cos A gets smaller
18 on back of this page
19
All triangles add up to 180
One angle greater than 90
Equilateral Triangle
Only two sides equal Isosceles
No angle greater than or = 90
So the other one is bigger than 90
A
y
B
y
C
y
D
y
E
y
y
y
y
y
y
y
Don’t forget that you can go to www.examinations.ie and look for the papers > left
side of page Examination Material Archive and fill in the form
Try www.projectmaths.ie
or best of all, go to www.youtube.com and search for ‘ triangles James Blunt’
And finally....... In the recent election there was a valid poll of 28,254 in Donegal NE.
The following were the scores reported in the Sunday Times 30th Oct page 10.
Candidate
Michael D Higgins
Martin Mc Guinness
David Norris
Gay Mitchell
Dana
Sean Gallagher
Mary Davis
%
Number of Voters
23.1
32.2
2.8
4.9
6.7
28.2
2.1
For example for Michael D Higgins
23.1/100 * 28,254 = 6,526.674 so we round to whole number 6,527 voters.
Check the number of voters add up correctly and that the total of the percentages adds
up to 100.