Primary Schools'

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Primary Schools' Mathematics Challenge 2008
SEMI-FINAL ROUND QUESTIONS WITH ANSWERS POWERPOINT
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Some of the questions have been modified and may
appear slightly different from those in the
actual competition. To access answers simply
left click the mouse and an automatic answer
sequence will appear with an explanation where
appropriate
HAVE FUN
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Each arm of the cross totals 50
19
17
18
15
13
Which two numbers are missing from the empty
boxes?
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Find the mathematical terms mixed up in the
capital letter strings written below. A clue is
given for each one
MATURE PETER - can be measured
TEMPERATURE
SO LESS ICE can be shapely
ISOSCELES
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Emily multiplies three different numbers
together. Each number is greater than one. Her
answer is 24. What could her numbers have been?
2
3
4
X
X
6
4
X

24
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Apples cost 15p each. Jack buys seven apples How
much change does Jack receive from 2.00?
1.10
Two apples can be bought for 25p
Six apples can be bought for 75p
Add the cost of a single apple to 75p
75p 15p 90p
2.00 - 90p 1.10
Buy 2 for 25p.
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
The perimeter of this regular pentagon is 40 cm
One side measures 40 cm 5 8cm
Amy joins two congruent pentagons together
There are 8 sides to Amys new shape
What is the perimeter of Amys new shape?
The new perimeter is 8cm x 8 64cm
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
True or false? Look at the statements below and
say whether each is true (T) or false (F)
F
A. All quadrilaterals have four right angles
F
B. All quadrilaterals have at least one line of
symmetry
T
C. A right angle triangle may be isosceles
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
This shape has been rotated 900 clockwise at
point A.
A
Which shape below shows its original position?
D
E
D
A
B
C
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Laura says that 20 of the number she is thinking
of is 36. She asks Ben to find out what her
number is and then make his answer up to
225. What is the number that Ben should add to
Lauras number to make 225?
45
20 is equal to one-fifth
Lauras original number is 36 x 5 180
Ben subtracts 180 from 225 to find his number
225 - 180 45
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
A football team scores 45 goals in a season. Adam
scores 18 goals. Tom scores one-third of
them. Nick scores three. How many goals were
scored by other team members?
1/3 of 45 is 15
The three players score 18 15 3 36
The other players score 45 - 36 9 goals
9
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Carpet cost 15 per m2. Jason has a room like the
plan in the drawing. Jason covers the floor with
carpet.
6 m
A
3m
5 m
3m
2 m
B
3m
How much does the carpet for the room cost
altogether?
Split the room into two rectangles to find the
total area
Area A is 6m x 3m 18m2 Area B is 3m x 2m
6m2 The total area is 24m2
The total cost is 24m2 x 15 360
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Ben draw square with sides 6.5 cm long. Amy draws
a square with sides twice as long as Bens
square. What is the area of Amys square?
6.5cm
6.5cm
13 cm
6.5cm
13 cm
6.5 cm
6.5 cm
6.5 cm
The area of the new square is 13cm x 13cm
169cm2
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
This sequence follows the pattern of double and
add one
11
23
47
191
5
95
383
Subtract one from 11 and halve the answer
Double the previous number and add 1
Which three numbers are missing from the sequence?
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
The missing numbers above the blue boxes are
found by adding the two numbers in the boxes
directly below
13
8
5
5
3
2
15
6
90
The missing numbers below the blue boxes are
found by multiplying the two numbers in the
boxes directly above
Write in the missing numbers on the drawing
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
What is one-third of 25 of a half of 4800?
200
Half of 4800 is 2400
25 (or ¼) of 2400 is 600
1/3 of 600 is 200
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
The area of the triangle A in this drawing is
80cm2. The total area of the whole drawing is 130
cm2 The two squares are the same size. What is
the length of one side of each square?
The area of the two squares is 130 - 80cm2
50cm2
The area of one square is 50cm2 2 25cm2

A
The length of one side of each square is 5cm
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
George bought a sports car for 15 000. When he
sold it two years later he received 11 less than
he paid for it. What was the price he sold his
car for?
Partition 11 into 10 and 1
10 of 15 000 is 1 500 (15 000 10)
1 of 15 000 is 1 500 divided by 10 or 15
000 100
1 of 1 500 is 150
11 of 15 000 is 1 500 150 1 650
George sells the car for 15 000 - 1 650
13 350
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
The cost of Sunday lunch at a restaurant is
12.50 for two courses and 15.75 for three
courses. Five people in a party book Sunday
lunch. Two have three courses and three have two
courses. How much is left out of 100 when the
bill has been paid?
2 x 15.75 31.50
3 x 12.50 37.50
31.50 37.50 69
100 - 69 31 left over
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
a 5, b 3, c 4,
d 6 Amy uses the numbers to
calculate the fraction shown below
c x b
4 x 3 12
a x d
6 x 5 30
Write the fraction shown in Amys problem in its
lowest terms
12
2

30
5
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
What weight must be added to the left side of the
scales to balance them up with the right side?
750g
2.5Kg
2 500g (2.5 Kg) - 750g 1 750g
1 750g or 1.75Kg or 1Kg 750g
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Jody has the money shown. She buys 3 packets of
crisps and 2 bars of chocolate
How much money will Jody have left?
3 packets of crisps 32p x 3 96p
2 bars of chocolate 47p x 2 94p
96p 94p 1.90
There is 5.17 in coins
5.17 - 1.90 3.27
47p
32p
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Jack has three different rectangles each with an
area of 24cm2 Each side of his rectangles is
bigger than 1cm. Each side is a whole number of
centimetres long. What are the possible
perimeters of his three rectangles?
Find the lengths of the sides of each rectangle
using the area as a starting point
6cm
12cm
8cm
3cm
4cm
2cm
Perimeter 28cm
Perimeter 22cm
Perimeter 20cm
The three rectangles may be used to help you with
any calculation you may need
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
A single cube has sides 13 mm long. Ellie makes a
chain of attached cubes like the one shown.
What is the length of Ellies chain of cubes when
it is rounded to the nearest centimetre?
There are 19 cubes The total length of the cubes
is 19 x 13mm 247mm 247mm 24.7cm 24.7cm
rounded to the nearest centimetre is 25cm
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Tom works out this brackets problem. What is his
answer?
( 7 x 5 ) ( 55 5 ) ( 9 x 4 )
( 108 6 )
35
11
36
18
35 11 36 18 100
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Lucy enters the number 4327.5 into her
calculator. She meant to enter 4523.7 What is
the difference between the number she wanted to
put in and the number she put in?
4523.7 - 4327.5 196.2
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
The difference between two numbers is 25. Their
product is 150. Their total is 35. What is the
answer when one number is divided by the other?
30 - 5 25
30 x 5 150
30 5 35
The two numbers are 5 and 30
30 5 6
Or possibly
5 30 1/6
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
James draws some shapes on a grid. Each grid
square is 1cm long and 1cm wide.
A. Which shapes have only one acute angle? B.
Which shape has only right angles? C. Which
shapes each have an area of 12.5cm2?
3 and 4
3
2
1
5
4
5
1 and 4
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Tom earns 1.50 for working on day one and double
this amount on day two. On days three, four and
five he continues to earn double the amount
earned on the previous day. How much has Tom
earned altogether over the five days he works?
Day 1 1.50
Day 2 3.00
Day 3 6.00
Day 4 12.00
Day 5 24.00
Total 46.50
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Kayleigh finds the sum of the non-prime numbers
between 40 and 50. She then adds the digits of
her answer together. What is the total of the
digits?
The numbers are 42, 44, 45, 46, 48 and 49
The total is 274
The sum of the digits is 13
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
The area of each circle is 124cm2. The red
square has sides of 12cm. What is the area of the
part of the drawing shaded yellow?
The two semi-circles are the same area as one
large circle, i.e. 124cm2
The area of the yellow part is 144cm2 - 124cm2
20cm2
The area of the whole square is 12cm x 12cm
144cm2
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Freds teacher asks him to add together each pair
of corner numbers in this target board. Write
down Freds answers.
19
12
21
17
11
24
14
13
40
32
9
30
16
18
10
15
There are six possible combinations
15 16 31
15 17 32
16 17 33
19 15 34
19 16 35
19 17 36
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
y
A
The interval on the grid is 1 or -1. Jade
translates her shape to the second quadrant. One
new line has been drawn for you
B
What are the co-ordinates of the new position of
the points A and B?
-x
x
0
A (- 5, 6)
B (- 2, 1)
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Tom follows the route around the drawing as shown
by the arrows and finishes in the yellow middle
square. Every time he enters a circle he adds
0.5. Every time he enters a square he subtracts
0.2
0.5
0.8
0.3
0.6
1.1
1.7
1.5
1.4
0.9
1.2
What number does he finish with in the yellow
square?
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PRIMARY SCHOOLS MATHEMATICS CHALLENGE 2008 SEMI
FINAL
Look at the number grid below and read it from
left to right in all questions
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Row 1
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
Row 2
19
25
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
Row 3
37
43
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
Row 4
48
49
50
51
52
48
49
A. What is the total of all the numbers in row 1?
18 x 7 126 126 9 135

B. Find the product of the first and last prime
numbers in row 3 ?
37 x 43 1591
C. In row 2 which pair of numbers have a product
of 475 ?
19 x 25 475
D. In row 4 which five consecutive numbers total
250?
48, 49, 50, 51, 52