Primary Schools’ Mathematics Challenge 2008 Final Round Questions Here is a selection of questions asked over two rounds. To access answers left click

Primary Schools’ Mathematics Challenge 2008

Final Round QuestionsHere is a selection of questions asked over two

rounds.

To access answers left click mouse and an automated sequence will appear.

The questions may very slightly from those presented and are not in the order they were asked.

PRIMARY MATHEMATICS CHALLENGE 2008 - FINAL

The sum of three consecutive numbers is 15.

What is their product?

Clue: 97, 98, 99, 100 and 101 are consecutive numbers.

The consecutive numbers are 4 5 6

Their product is 4 x 5 x 6 =

20 x 6 = 120


The top number is the product of the two numbers below

The bottom number is the difference between the two numbers above

Which numbers could be missing from the grid below?

94

455 9

4

11713

Two possible answers


An oval dog racing track is 240 metres all round.

Jack the Flash wins a three lap race in a time of 1 min. 30 seconds.

How many metres does the dog run on average per second?

The dog travels 720 metres (3 x 240m) in 90 seconds

Divide 720m by 90.

720m ÷ 90 = 8m per second on average

Quick isn’t he?


2 + 6 10 - 8 2 x 5+ 9 ÷ 3

+ 15 - 9

+

A

The grid is completed by adding together the boxes as shown by the arrows.

Which number fits into box A?

6 X 5 +

40 19+

2 3

610

8

30

10

13

59

40 19


Which five numbers are missing from this number track?

25 x3 Minus 19 Divide by 8

Multiply by 7Add 1

75 56

50 49 7


The rule for this sequence is find a quarter and add 11.

Write in the two missing numbers in the sequence below.

4 12 14 14.5

¼ of 12 is 3. 3 + 11 make 14

¼ of 14 is 3.5 3.5 + 11 make 14.5


The rectangle has the same perimeter as the square.

What is the length of the shorter side of the rectangle?

Square Area

81cm2

10.75 cm

The length of one side is 9cm

The perimeter is 36cm (9cm x 4)

The perimeter is 36cm

Two of the sides total 21.5 cm (10.75 x 2)

The other two sides total 36 - 21.5 = 14.5 cm

The short side is 14.5cm ÷ 2

The short side is 7.25cm


Tom finds the denominator of a fraction by calculating three-fifths of 25.

He finds the numerator by finding a quarter of a half of 16

What is Tom’s fraction?

15

2

2

15


Here are six number cards.

The 12 card must be used in each fraction.

16 3 12 4 8 9

Use the cards to make two different fractions equivalent to ¾

12

12

16

9


What fraction of the large square is not shaded grey?

The denominator is 16.

10 squares are not grey

The fraction not shaded is 10/16 or 5/8


Add 0.25 to each of the decimal fractions below.

0.35 0.050.15 0.5 0.55

Rewrite the new decimal fractions in order starting with the largest.

0.35 0.050.15 0.5 0.55

Add 0.25 to each decimal

0.6 0.30.4 0.75 0.8

Rewrite starting with the largest decimal

0.8 0.75 0.6 0.4 0.3


This diagram is placed in the middle of a square grid.

The new grid is the same height as the diagram shown

What percentage of the new large square grid is red?

Because the diagram is five squares high the new big square

is made up of 25 smaller squares.

The diagram fits in the middle.

Three out of the 25 squaresare red.

As a percentage this is 12 out of 100 or 12%


Which mathematics terms are hidden in these anagrams?

ALL PALER

MYSTERY M

ALL CUT ACE

Then find your answers on the word search grid.

U PA T E A L Y

N AA A S F E T

E R`S P A A L E

L AC U L T E N

A LC T Y S Y M

S EY M M T R Y

T LC M E I N K

S LY M E Z X P

P

A

R

A

L

L

E

L

S

Y

M

C

E

T

Y

R

PARALLEL

SYMMETRY

CALCULATE

P

A

R

A

L

L

E

L

S EY M M T R Y

L AC U L T EAC


A

T U RQLIE

RLNUEGESQ

Three mathematical words are mixed up in this circle of letters.

Each word must contain the centre letter A once only

U R

E

SQ

U R ES Q AE

Q

U

E

L

Q

U

E LQ UE

T

LI

RNEG

T LIR N EG

A

A


You have a zero to ninety-nine hundred square.

A. How many times does the 9 digit appear?

B. Which digit appears the least number of times?

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99

9

19

29

39

49

59

69

79

89

9990 91 92 93 94 95 96 97 98

0

10

20

30

40

50

60

70

80

90

11 times

9 times

10 times

11 + 9 = 20

0 ten times


All the triangles in this shape are equilateral.

The perimeter of the large triangle is 108cm.

What is the perimeter of the blue rhombus made by the two equilateral

triangles?

The side of the large triangle is 108cm ÷ 3 = 36cm

One side of the rhombus is 36cm ÷ 2 = 18cm

The perimeter of the rhombus is 18cm x 4 = 72cm


Use the symbols < > = to make these number sentences correct

A. ( 2 x 19 ) + 15 13 x 4

B. 10 x 10 x 10 40 x 25

C. 9.9 - 3.3 9.3 - 3.9

38 + 15 = 53 52

1000 1000

6.6 5.4

>

=

>


A bag of crisps weights 25g

How many bags of crisps are in a box if its contents weigh 2Kg?

2 Kg = 2000 g

2000 g ÷ 25 = 80


In a sale a shop makes the following offer:

Buy one item and get a second item at a 20% discount.

The discount applies to the cheaper item bought.

Jack buys a football and a pair of trainers.

How much does he pay altogether?

£25.49

£19.99

£10.50

The football is cheaper so£10.50 ÷ 5 (20%) = £2.10 this is his discount.

He pays £10.50 - £2.10 = £8.40 for the football

For the trainers and the football Jack pays £25.49 + £8.40 = £33.89

20% is the same as one-fifth


School starts at 8:50 a.m.

Amy arrives 13 minutes early. Ben is late.

Ben and Amy arrive 35 minutes apart.

What time does Ben arrive at school?

Amy arrives at ( 8:50 - 13min. ) 8:37

Ben arrives at ( 8:37 + 35min. ) 9:12

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18cm

Jade has three Russian Dolls.

Each doll is 1½ (1.5) times bigger than the previous one.

A B C

How tall are dolls A and C?

Doll A is 12 cm. 18 cm ÷ 1.5 = 12 cm

Doll C is 27 cm. 18 cm x 1.5 = 27 cm


A transit van and its parcels weigh 2.25 Tonnes altogether.

The van weighs 1.75 Tonne.

Jack loads the van with 125 similar parcels.

How much does each parcel weigh?

Altogether the parcels weigh

2.25T - 1.75 T = 500 Kg

(2250 Kg - 1750 Kg)

Each parcel weighs

500 Kg ÷ 125 = 4 Kg


Look at the three separate problems below.

A = 19 + y B = y2 C = (5 x y) - (120 ÷ y)

y = 15, what is the answer to each problem?

A. 19 + 15 = 34

B. 15 X 15 = 225

C. 75 - 8 = 67


Amy is facing east.

She turns anti-clockwise to face north-west

Through how many degrees does she turn?

E

N

W

N..W.

900450

900 +

450 = 1350


A

B

X

800

800

Isosceles triangles A and B are the same size.

What is the value of angle X?

This angle is 1800 - (800 + 800)

= 1800 - 1600 = 200

This angle is also 200 because the triangles are the same size.

Angle X is 1800 - (200 + 200)

= 1800 - 400 = 1400


ABC

D

E

Sam is snookered on all the reds.

He plays his shot along the line shown by the white dots.

Which red is he most likely to hit if the ball bounces off the cushion at a right angle?

A


Art gallery

ENTRY FEE

£1.25 per person

220 people went to the art gallery on Saturday.

How much money is this altogether?

£1.25 X 220 = £275


Five friends have the weights shown below.

Amy 42 Kg, Ben 51 Kg Jade 46Kg Laura 51Kg Tom 47Kg

What is the difference in Kg between their modal weight and their median weight?

Their modal weight is 51 Kg

Their median weight is 47 Kg

51 Kg - 47 Kg = 4 Kg


5 4 = 60 3

15 7 = 7 1

You may use the symbols + - x ÷ once only.

Complete these equations (number sentences)

-

x ÷

+


Here is part of a multiplication problem solved by using the grid method.

x 30

20

4 20

What is the answer to the calculation when complete?

700 + 140 = 840

5

600 100

120

700

140


Use the rules to find the next number in each sequence

Find he sum of your three answers

Rule: Add 9 5 14 23

Rule: Multiply by 4 4 16 64

Rule: Subtract 8 120 112 104

256

96

32

32 + 256 + 96 = 384


Find the total of all the prime numbers between 1 and 20.

Multiply your result by three.

2 3 7 11 13 17 19+ + 5 + + + + +

Total 77

77 x 3 = 231


The diagram shows some shapes on a square grid

CA B

D E

a. Which two shapes have the same area as A?

b. Which two shapes have the same perimeter as A?

Shape A has an area of 3 units. Shapes B and E have the same area

Shape A has a perimeter of 4 small units and 2 longer units. Shapes D and E have the same area


Which of these shapes have at least one line of symmetry?

CA

B D

E

F

A, C, D, F


Which of the shapes on the grid have more than 1 line of symmetry?

A B D

C

E F

G

Shapes B D E


The shape below is rotated 900 degrees clockwise

Which shape below that shows its new position?

A B C D E F


The top line of the rectangle goes through the centre of each of the three similar circles.

The perimeter of the rectangle is 32cm.

What is the radius of each circle?

4 cm

The longer side of the rectangle is 12 cm

The diameter of each circle is 12 cm ÷ 3 = 4cm

The radius of each circle is 4 cm ÷ 2 = 2cm


x

y

0 2 4 6 8

2

4

6

A. What are the co-ordinates of the centre

of the square?

B. What are the co-ordinates of the

junction of the two straight lines that

make a cross ?

A ( 3, 4 )

B ( 7, 3 )

Documents

Primary Schools’ Mathematics Challenge 2008 Final Round Questions Here is a selection of questions asked over two rounds. To access answers left click