Primary Mathematics

1
Primary Mathematics Challenge
A selection of questions 2007
2
Sample semi-final question
Look at the continuous sequence of squares below
53rd square
What colour will the fifty-third square be?
Answer - red
Answer sequence
3
Sample semi-final question
The sum of two numbers is 15 Their difference is
three. What is their product?
54
9 6 15 is their sum or total 9
- 6 3 is their difference 9 x
6 54 is their product (multiplied
together)
Answer sequence
4
Sample semi-final question
Jack draws the shape below
16
3
7
6
How many rectangles can be found in the drawing?
Answer sequence
5
Sample semi-final question
In a box of dominoes there are seven double
tiles
What is the total number of spots on the seven
doubles tiles altogether?
42
Answer sequence
6
Sample semi-final question
The perimeter of this rectangle (oblong) is 48
cm. The rectangle is three times as long as it
is wide
18 cm long 6 cm wide
How long and how wide is the rectangle?
The width and length shown in blue are 24 cm long
altogether
The width is a quarter of 24 cm and the length
three-quarters of 24 cm
Answer sequence
7
Sample semi-final question
Shirt 12.99
Sports shoes 16.49
Cap 9.50
Tom buys a cap, Amy buys shoes and Jack buys a
shirt. Each child pays with a 20 note.
How much change does each child receive?
Jack 7.01
Amy 3.51
Tom 10.50
Subtract each price from 20.
Answer sequence
8
Sample semi-final question
Joe thinks of two 2-digit numbers both less than
seventy-five. Both numbers have 6, 3 and 5 as
factors. One number is half the size of the other.
30
60
What are the two numbers?
Answer sequence
9
Sample semi-final question
To score a total of 10 on two standard dice you
would need to throw a 6 and a 4 or two fives.
If you had three dice what are the combinations
of scores you could throw to make a total of 10?
2
2
6
3
3
4
These may be thrown in any order
1
5
4
2
4
4
3
1
6
5
3
2
Answer sequence
10
Sample semi-final question
The graph shows the percentage scored by 7
children in a test
Jade
A. Chelsey
Paul
Lee
B. 35 (½ of 70)
Amy
Jack
C. Tom and Jade
Tom
Chelsey
0
10
20
30
40
50
60
80
90
100
70
A. Who scored exactly 30 less than Amy?
B. What did Paul score in his last test if this
score was double his last score?
C. Which two children scored exactly 55between
them?
Answer sequence
11
Sample semi-final question
The radius of the yellow circle is 12 cm and x is
the centre of the circle
288 cm2
x
What is the area of the red rectangle (oblong)?
The width of the rectangle equals the radius of
the circle 12 cm
The length of the rectangle is twice the radius
of the circle 24 cm
The area of the rectangle is 12 cm x 24 cm
288 cm2
Answer sequence
12
Sample semi-final question
The circumference of a bicycle wheel is 140 cm
How far in metres does the wheel travel in thirty
revolutions?
42 m
The wheel travels 140 cm x 30 4200 cm
4200 cm is the same distance as 42 metres
Answer sequence
13
Sample semi-final question
Chloe makes a square with four sticks
She then uses some more sticks to make another
square on the side
6
She continues the pattern in the same way adding
more squares. She uses 19 sticks altogether
How many squares are there in her completed
sequence?
4
7
10
13
16
19
Answer sequence
14
Sample semi-final question
Three-fifths of a number is 45
25
What is one-third of the same number?
If three-fifths of the number is 45 then
one-fifth is 45 3 15
Number
Three-fifths
45
15
15
15
Two-fifths
15
15
The whole number is 15 multiplied by 5 75.
75
One-third of the number is 75 3 25 .
75
25
25
25
Answer sequence
15
Sample semi-final question
Triangle ABC is equilateral
A
X
1200
B
C
What is the value of angle X?
There are many different ways to find this
answer. How many can you find?
Answer sequence
16
Sample semi-final question
Which numbers are missing from these number
sentences?
A. - 7 35
42
B. X 7 35
5
28
C. 7 35
63
D. 7 9
Answer sequence
17
Sample semi-final question
These shapes each have properties in common.
Identify 2 common properties
Some possibilities
All quadrilaterals
All have parallel lines
All have at least one line of symmetry
Answer sequence
18
Sample semi-final question
Jack makes five statements. Some are true, some
are false.
T
A. All squares are rectangles, but not all
rectangles are squares
F
B. An isosceles triangle has two right angles
F
C. To multiply any number by 10 just put a zero
on the end
T
D. For every decimal fraction there is an
equivalent ordinary fraction
T
E. A regular pentagon has five lines of symmetry
Write T or F next to each statement
Answer sequence
19
Sample semi-final question
Jade starts with an even number. She doubles
it. She continues to double until she reaches 144.
What are the other numbers in her sequence before
she reaches her total?
Start with 144 and continue halving until she
reaches her starting number.
144
72
36
18
Answer sequence
20
Sample semi-final question
8
How many different triangles can you find in this
drawing?
2
1
3
4
Answer sequence
21
Sample semi-final question
Two of these nets will not make a closed cube.
A
B
C
D
E
Write the letters of the nets that will make a
closed cube
Answer sequence
22
Sample semi-final question
In a football match the score at half time is 1
0 to the home side. In the second half three more
goals are scored.
What are the possible full-time results? Include
both home and away possibilities.
4 - 0
3 - 1
2 - 2
1 - 3
Answer sequence
23
Sample semi-final question
A ream of A4 paper is 500 sheets. The height of a
ream is 5.5 cm
0.11 mm
What is the thickness of one sheet of paper in
millimetres?
Change 5.5 cm to 55 mm. Divide 55m by 500
0.11mm
Answer sequence
24
Sample semi-final question
Here are some lists.
Which is the odd one out in each list?
1a 0.4 b. Two-fifths c. 40
d. 16 e. 4

40
2a 25 x 15 b. 750 0.5 c. 250
125 d. 750 e. 1000 -
625 2
3a rhombus 3b pollygon 3c paralellogram 3d
isocseles 3e trapesium
Answer sequence
25
Sample semi-final question
Each apex of the red equilateral triangle is in
the centre of a circle. The circles are the same
size. The perimeter of the triangle is 45 cm
7.5 cm
Each side of the triangle is 15 cm.
The radius of these circles is half the length of
one side of the triangle 15 cm 2 7.5 cm
What is the radius of each of the circles?
Answer sequence
26
Sample semi-final question
A shop reduces the price of sports shoes by
20 The new price is 60
75
What was the original price of the shoes?
The new price is four-fifths of the old
price. The new price is four parts of the old
price, this is 60 4 15 So the original
price was 60 15 75
Answer sequence
27
Sample semi-final question
There are three prime numbers between 80 and 100
269
What is their total?
None of the even numbers can be prime in this
case. This leaves -
81 83 85 87 89 91 93 95
97 99
Can be divided by 3, 5 or 7 so are not prime
numbers.
Are prime numbers.
83 89 97 269.
Answer sequence
28
Sample semi-final question
The two triangles are isosceles and the same
size. They each have a perimeter of 20.5 cm.
17 cm
B
The third side is the perimeter of the triangles
20.5cm - 12 cm (the total length of the equal
sides) 8.5 cm
The two equal sides of each triangle are 6 am
long because they are the same length as the
short side of the rectangle.
6 cm
Line AB is 2 x 8.5 cm 17 cm
A
How long is line AB?
Answer sequence
29
Sample final question
Two straight lines cross as shown in the drawing
1050
A
750
What is the size of angle A and angle B?
B
1050
Angle A is 1800 - 1050 750
Angle B is 1800 - 750 1050
Answer sequence
30
Sample final question
The sum of the edges of each of these squares is
1000
450
Which three numbers are missing?
150
B
775
A
400
50
100
125
555
C
395
Answer sequence
31
Sample final question
Six people play each other once at golf.
15
How many games are played altogether?
Player E
Player F
Player D
Player B
1 Game
Player F
Player C
Player E
Player C
2 Games
Player D
Player F
Player A
Player D
3 Games
Player E
Player E
Player F
Player F
4 Games
5 Games
Answer sequence
32
Sample final question
Gavin weighs one-third more than Sally. Mum
weighs twice as much as Gavin. Mum and dad weigh
140kg altogether. Sally weighs 24kg.
How much do mum and dad each weigh?
Mum weighs 64kg. Dad weighs 76kg.
Gavin weighs 24kg 8kg 32kg.
Mum weighs 32kg x 2 64kg.
Dad weighs 140kg - 64kg 76kg.
Answer sequence
33
Sample final question
Jade uses five 5s to write a number sentence. She
uses two signs and one x sign. The answer to
her sentence is 555.
What could her number sentence have been?
555
(5 5) x 55 5
The 5s in her answer are not part of the five 5s
she uses to work out her problem.
Answer sequence
34
Sample final question
The drawing shows part of number grid six columns
wide.
5
10
15
0
5
10
15
20
25
45
30
35
40
45
70
65
70
85
A
110
110
B
130
130
Which numbers are missing from squares A and B?
Answer sequence
35
Sample final question
The area of this square is 64cm2
Joe uses similar squares to make a new shape.
80cm
The area is 64cm2 so each side is 8cm. There are
ten sides to the new shape. 10 x 8cm 80 cm
What is the perimeter of the new shape?
Answer sequence
36
Sample final question
Amy and Jade live in different villages. Their
villages are both 90km away from the town. They
agree to meet in the town at noon. Amy travels
at a speed of 40km per hour and Jade travels at
a speed of 60km per hour.
At what time should they each set off from their
villages to arrive in the town at noon?
Amy sets off at 945 a.m. Jade sets off at 1030
Amys journey time is 2¼ hours.
Jades journey time is 1½ hours.
Answer sequence
37
Sample final question
There are three mathematical terms jumbled in
this sequence of letters.
S M S U U Y B L M T T M R I E A P T C L R T Y Y
S M S U U Y B L M T T M R I E A P T C L R T Y Y
S U B T R A
C T
M U L T I P
L Y
S Y M M E
T R Y
What are the three terms?
SUBTRACT
MULTIPLY
SYMMETRY
Answer sequence
38
Sample final question
Fred cuts discs this size from a
sheet of metal as shown below.
Each disc has a diameter of 3cm.
The sheet is 4 discs (12cm) long
The area of the sheet is 9cm x 12cm 108cm2
The sheet is 3 discs (9cm) wide
What is the area of the sheet of metal?
108cm2
Answer sequence
39
Sample final question
Five children run 50m in a race. Their finishing
times are
7.65 sec
7.5 sec., 8.00., 7.75., 8.5 sec. and 6.5 sec.
What is their average (mean) time for running 50m?
7.5 8.00 7.75 8.5 6.5
38.25sec 38.25 5 7.65 sec.
Answer sequence
40
Sample final question
Chloe takes the number 2. She then applies a
rule (does something to it) and gets the answer 8.
She uses the same rule with some other numbers.
Start number 4 finish number 18
Start number 3 finish number 13
Start number 6 finish number 28
Start number 1 finish number 3
Can you work out what her rule is?
Multiply the start number by 5 then subtract 2
Answer sequence
41
Sample final question
Calculate the outcome if Tom puts the following
sequence into his calculator

7
9
4
x
-
0
3
12



v
3
Answer sequence
42
Sample final question
The number shown by A in the centre of the
drawing is the product of the numbers linked by
the arrows opposite each other.
15
What are the values of A and B?
A
3
B
120
40
8
Answer sequence
43
Sample final question
The numbers in this sequence start at 27 and
reduce by the same number each time.
27
?
?
?
?
12
24
21
18
15
Which numbers are missing from the sequence?
The sequence decreases by 3 from left to right.
The sequence increases by 3 from right to left.
Answer sequence
44
Sample final question
One person sits on each side of a square table
Jack has five similar tables that he joins
together to make one long table.
12
How many people can be seated around the new
table?
Answer sequence
45
Sample final question
In a family each boy has one sister and each girl
has one brother.
How may people are in the family including mum
and dad?
4
Answer sequence
46
Sample final question
What is 25 of one-third of 240?
One-third of 240 is 80
25 (or ¼) of 80 is 20
20
Answer sequence
47
Sample final question
In championship tennis the balls are new at the
start of the match. They are changed after the
first seven games and then every nine games after
that.
5
Roger Federer beats Tim Henman 6 3, 7 6, 2
6, 6 - 4
How many sets of new balls are used in the match?
40 games are played. Subtract 7 (1st set of
balls) leaves 33 33 games 9 uses 3 sets of
balls (27 games) with 6 extra games left. An
extra set is needed for the six games. 3 1
1 5
Answer sequence
48
Sample final question
Inside the drawing of a square there are 3
shapes. Points A and B are the middle of the
sides of the square. The length of each side of
the square is 8cm.
What is the area of each shape?
1
1. 16cm2 2. 32cm2 3. 16cm2
2
A
3
The area of the square 8cm x 8cm 64 cm2
Shape 1 is ¼, shape 2 is ½ and shape 3 is ¼ of
the square
B
Answer sequence
49
Sample final question
The sum of three single-digit numbers is
10. Their product is 30.
What are the three numbers?
2
3
5
Answer sequence
50
Sample final question
A large rectangle is divided into smaller
rectangles
The perimeter of this rectangle is 18 cm.
3cm
42cm2
6cm
7cm
7cm
What is the area of the pink rectangle?
The pink rectangle is 7cm by 6cm 42 cm2
Answer sequence
51
Sample final question
Which design comes next in this sequence?
The pattern is the numbers 1 to 9 made up of
straight lines and placed back to back
Answer sequence
52
Sample final question
A large rectangle is made up of smaller squares.
75
What percentage of the large rectangle is not
shaded blue?
There are 40 small squares. Ten are blue. This is
a quarter, so three-quarters, or 75 are not blue.
Answer sequence
53
Sample final question
Tom forgets the three-digit combination to his
case. He knows that the first number is an odd
prime number more than 3. The last number is not
odd but is less than six and more than one. No
two digits in the combination are the same. The
middle number makes the total of the three digits
add up to 13.
What are the possible combinations for Toms lock?
562
742
724
Answer sequence
54
Sample final question
A regular octagon has an area of 86 cm2
3.5cm2
The square surrounding the octagon has a
perimeter of 40 cm.
What is the area of one of the small triangles if
they are all the same size?
The area of the square is 10cm x 10cm 100 cm2
The area of the four triangles altogether is 100
cm2 - 86cm2 14cm2
14cm2 4 3.5cm2
Answer sequence