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Sets of
Numbers/Venn
Diagrams
Probability
Logic
100
100
200
Statistics
Geometry
100
100
100
200
200
200
200
300
300
300
300
300
400
400
400
400
400
500
500
500
500
500
U = {2, 3, 4 ,5, 6, 7, 8, 9, 10}
A, B, and C are subsets of U;
A = {factors of 20}
B = {prime numbers}

C = {3, 4, 5, 6}
List the elements of
a) A
b) A
B


B’
c) (A B) C 

Place the values in the appropriate
space on the Venn Diagram if U =
{Real Numbers}, P = {Positive
Numbers}, and Q = {Rational
Numbers}
-3, 2.3 x
10-3,
P
sin 60°,1.2 x
106,
Q
U
π,  27
3
In a group of 30 students, 18 take the
Mathematical Studies course and 14 take
a Biology course. 7 students don’t take
Mathematical Studies or Biology.
A) Make a Venn Diagram that displays
the above information.
b) Find the number who study both
Mathematical Studies and Biology
c)the probability that a student chosen at
random studies Biology given that the
student does not study Mathematical
Studies.
There are 24 students in a class. 14
study Biology and 8 study Chemistry.
6 don’t study either of those two
subjects.
A) How many students study Biology
and Chemistry?
B) If a student is chosen at random,
find the probability that the student
studies Chemistry or Biology but not
both.
U = {2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {multiples of 3} B = {2, 5, 6, 7, 9}
C = {4, 5, 6, 8}
(A, B, and C are subsets of U)
a) Draw a Venn Diagram to illustrate these
sets.
b i) List the elements of A’  B .
ii) Find n(B U C’)
ci ) An element of U is chosen at random.
Find the probability it is an element of A or
C.
ii) An element of B is chosen at random.
Find the probability it is not an element of A
A number is chosen at random
from the list below:
2 3 6 8 9 11 12 13
Find the probability that:
a) the number is prime,
b) the number is greater than 7,
given it is less than 10.
Two unbiased 6 sided dice are
thrown and the scores are added.
a) Draw a diagram of the sample
space
b) Find the probability that the
total is 9 or more, given neither
die shows a 1
Two people independently write
down a digit from 0 to 9 at
random. Find the probability
that:
a) both people write a ‘5’.
b) neither person writes a ‘5’
c) one person writes a ‘5’ and
the other does not
In her purse a woman has the
following bills:
$5 $10 $20 $50
She selects two bills at
random.
a) List the sample space.
b) Find the probability that
she has less than $50 in her
hand.
In a box there are 2 red cards, 4 green cards, and 3
blue cards. A card is chosen at random at not replaced,
then a second card is chosen at random.
A) Explain the entry 1/8 in the tree diagram.
B) Copy and complete the tree diagram.
C) Find the probability that:
i) both cards are blue
ii) the two cards are the same color
iii) one card is green and the other is blue.
D) (i) Find the probability that the second card is blue.
(ii) Hence find the probability that the first card was
blue, given that the second card is blue.
1/8
2/9
R
G
B
R
G
B
Complete this truth table
for p  q
p
q
q
p  q
P: the integer N is less than 20
q: the integer N is less than 12
r: the integer N is greater than 20.
True or false?
(a) p  q
(b)
( c)
q  r
p  r
Complete the truth table
for ( p  q )  p
A, B, and C are all different ages. Three
propositions are:
p: A is older than B
q: B is younger than C
r: A is older than C
(a) Write in simple English the meaning
of
(b) If A is 16, B is 18 and C is 15 years
old, which of the following propositions
are true?
(i)
p
(ii)
pr
(iii)
q  p
Three propositions are: r: it is raining s: it is
not snowing w: it is windy
(a) Write the following as simple English
sentences:
(i) r  w
(ii)
s  r
(iii) rw
(b) Write in symbol form: (i) if it is not windy,
then it is raining
(ii) it is snowing or raining
(c) In simple English, give the converse of
sw
The weights w grams of letters
leaving an office were measured.
The grouped data are below:
Weight
0 <= w < 30
frequency
24
30<= w < 60
60 <= w < 90
90 <= w < 120
15
8
5
120 <= w < 150
2
Find the five number summary of this data
This stem and leaf graph shows the
ages of people at a meeting:
Stem (tens)
Leaf (units)
1
6,8
2
2,4,5,7,7
3
1,5,6,8,8,9
4
3,5,9,9
5
2,3,7,8
6
1,3,5
7
0
(a) Find the median age
(b) Find the range of the ages
The weights (in kilograms) of a
group of 9 children were:
44 51 38 36 62 55 32 43 47
(a) Find:
(i) the range of the weights
(ii) the standard deviation of the
weights
(iii) the interquartile range of the
weights
At a certain school students sit two end of year
mathematics exams, Paper 1 (with 40 marks)
and Paper 2 (with 60 marks). The table below
shows the scores of six students:
Paper 21
1 (x)
Paper 36
2 (y)
33
17
28
25
14
49
24
48
43
22
(a)
What is the line of best fit for this set of data?
(b)
What is the correlation coefficient?
(c)
What does the correlation coefficient tell you about the data?
A company which manufactures light bulbs
surveyed the lifetimes, t hours of 60 bulbs. The
results are shown in the table below.
Time, t
Frequency
0 < t <= 500
2
500< t <= 1000
5
1000 < t <= 1500
10
1500 < t <= 2000
20
2000 < t <= 2500
14
2500 < t <= 3000
8
3000 < t <= 3500
1
(a)
Construct a cumulative frequency graph illustrating the information. Use a scale of 1 cm to 200
hours on the x-axis, and 1 cm to 5 bulbs on the y-axis.
(b)
From your graph estimate
(i) the median lifetime
(ii) the 70th percentile
Given the following triangle:
(a) Calculate length CD
(b) Calculate length DB
C
10 cm
8 cm
50°
A
D
B
C
A
D
B
In the right prism illustrated above,
AB = 10cm, AC = 13cm, and BD = 20
cm.
(a) Calculate the vertical height of the
solid.
(b) Calculate the volume of the solid.
In the diagram AD = 15 cm, BD = 11
cm and CD = 6 cm Find:
(a) the length AC
(b) the length AB D
A
B
C
The diagram shows a quadrilateral piece
of fenced land, ABCD. Fence AB and AD
are perpendicular. AB = 55m, AD = 45m,
CD = 65m and angle BDC = 50°
C
B
A
50°
D
(a)
Calculate the length of line BD.
(b)
Calculate the length of fence BC.
(c)
It is necessary to re-fence the land with
fencing that cost $7.49 per metre
length. What will be the cost of this
correct to the nearest dollar?
In quadrilateral PQRS: PQ = 12 cm, angle SPQ
= 90°, SR = 18 cm, QR = 17 cm and angle PQS
= 38°.
(a) show that QS = 15.23 cm correct to 2
decimal places.
(b) calulate angle QRS.
R
(c) find the area of triangle QRS.
S
P
38°
Q