Download ppt - Primary Mathematics Challenge

N. E. Lincolnshire Mathematics Team 1


Sample semi-final questionSample semi-final question

Look at the continuous sequence of squares below

Answer sequence

What colour will the fifty-third square be?

Answer - red

53rd square



Answer sequence

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

Jack draws the shape below

How many rectangles can be found in the drawing?

163

7

6



Answer sequence

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

The perimeter of this rectangle (oblong) is 48 cm. The rectangle is three times as long as it is wide

How long and how wide is the rectangle?

18 cm long

6 cm wide

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

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

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.

What are the two numbers?

60 30



Answer sequence

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

1 5 4

3 3 4

2 4 4

3 1 6 5 3 2

These may be thrown in any order



Answer sequence

The graph shows the percentage scored by 7 children in a test JadePaulLee

AmyJackTom

Chelsey

0 10 20 30 40 50 60 80 90 10070

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 55%between them?

A. Chelsey

B. 35% (½ of 70%)

C. Tom and Jade



Answer sequence

The radius of the yellow circle is 12 cm and x is the centre of the circle

What is the area of the red rectangle (oblong)?

288 cm2

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

x



Answer sequence

The circumference of a bicycle wheel is 140 cm

How far in metres does the wheel travel in thirty revolutions?

The wheel travels 140 cm x 30 = 4200 cm

42 m

4200 cm is the same distance as 42 metres



Answer sequence

Chloe makes a square with four sticks

She then uses some more sticks to make another square on the side

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?

6

4 7 10 13 16 19



Answer sequence

Three-fifths of a number is 45

What is one-third of the same number?25

If three-fifths of the number is 45 then one-fifth is 45 ÷ 3 = 15

One-third of the number is 75 ÷ 3 = 25 .

NumberThree-fifths45

The whole number is 15 multiplied by 5 = 75.

15 15 15

75

752525 25

Two-fifths15 15



Answer sequence

Triangle ABC is equilateral

X

A

B CWhat is the value of angle X?

1200

There are many different ways to find this answer.

How many can you find?



Answer sequence

Which numbers are missing from these number sentences?

A. - 7 = 35

B. X 7 = 35

C. + 7 = 35

D. ÷ 7 = 9

5

28

63

42



Answer sequence

These shapes each have properties in common.

Identify 2 common properties

All quadrilateralsAll have parallel linesAll have at least one line of symmetry

Some possibilities



Answer sequence

Jack makes five statements. Some are true, some are false.

A. All squares are rectangles, but not all rectangles are squares

B. An isosceles triangle has two right angles

C. To multiply any number by 10 just put a zero on the end

D. For every decimal fraction there is an equivalent ‘ordinary’ fraction

E. A regular pentagon has five lines of symmetry

Write T or F next to each statement

TF

FT

T



Answer sequence

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?

144723618

Start with 144 and continue halving until she reaches her starting number.



Answer sequence

How many different triangles can you find in this drawing?

1

2

3

4

8



Answer sequence

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

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 - 03 - 1

2 - 21 - 3



Answer sequence

A ream of A4 paper is 500 sheets.

The height of a ream is 5.5 cm

What is the thickness of one sheet of paper in millimetres?

0.11 mm

Change 5.5 cm to 55 mm.

Divide 55m by 500 = 0.11mm



Answer sequence

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

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

What is the radius of each of the circles?

7.5 cmEach 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



Answer sequence

A shop reduces the price of sports shoes by 20%

The new price is £60

What was the original price of the shoes?£75

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

There are three prime numbers between 80 and 100

What is their total?

81 83 85 87 89 91 93 95 97 99

None of the even numbers can be prime in this case. This leaves -

Can be divided by 3, 5 or 7 so are not prime numbers.

Are prime numbers.

83 + 89 + 97 = 269.

269



Answer sequence

The two triangles are isosceles and the same size.

They each have a perimeter of 20.5 cm.

A

B

6 cm

How long is line AB?

17 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.

The third side is the perimeter of the triangles 20.5cm - 12 cm (the total length of the equal sides) = 8.5 cm

Line AB is 2 x 8.5 cm = 17 cm


Sample final questionSample final question

Answer sequence

1050

AB

750

1050

Two straight lines cross as shown in the drawing

What is the size of angle A and angle B?

Angle A is 1800 - 1050 = 750

Angle B is 1800 - 750 = 1050



Answer sequence

450

150

125100

50

555

A

B

C

The sum of the edges of each of these squares is 1000

Which three numbers are missing?

400

775

395



Answer sequence

Six people play each other once at golf. How many games are played altogether?15

Player A

Player B

Player C

Player D

Player E

Player F

5 Games

Player C

Player D

Player E

Player F

4 Games

Player D

Player E

Player F

3 Games

Player E

Player F

2 Games

Player F

1 Game



Answer sequence

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?

Gavin weighs 24kg + 8kg = 32kg.

Mum weighs 32kg x 2 = 64kg.

Dad weighs 140kg - 64kg = 76kg.

Mum weighs 64kg.

Dad weighs 76kg.



Answer sequence

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?

The 5s in her answer are not part of the five 5s she uses to work out her problem.

= 555 (5 + 5) x 55 + 5


A


Answer sequence

The drawing shows part of number grid six columns wide.

5 10 15

45

70

B

0 5 10 15 20 25

30 35 40 45

65 70 85

110

130

Which numbers are missing from squares A and B?

130

110



Answer sequence

The area of this square is 64cm2

Joe uses similar squares to make a new shape.

What is the perimeter of the new shape?

80cmThe area is 64cm2 so each side is 8cm.

There are ten sides to the new shape.

10 x 8cm = 80 cm



Answer sequence

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 9:45 a.m. Jade sets off at 10:30

Amy’s journey time is 2¼ hours.

Jade’s journey time is 1½ hours.



Answer sequence

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

What are the three terms?

SUBTRACT

MULTIPLY

SYMMETRY

S M S U U Y B L M T T M R I E A P T C L R T Y Y

M U L T I P L Y S U B T R A C T

S Y M M E T R Y



Answer sequence

Fred cuts discs this size from a sheet of metal as shown below.

Each disc has a diameter of 3cm.

What is the area of the sheet of metal?

108cm2

The sheet is 4 discs (12cm) long

The sheet is 3 discs

(9cm) wide

The area of the sheet is 9cm x

12cm = 108cm2



Answer sequence

Five children run 50m in a race.

Their finishing times are:

7.5 sec., 8.00., 7.75., 8.5 sec. and 6.5 sec.

What is their average (mean) time for running 50m?

7.65 sec

7.5 + 8.00 + 7.75 + 8.5 + 6.5 = 38.25sec

38.25 ÷ 5 = 7.65 sec.



Answer sequence

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




Can you work out what her rule is?

Multiply the start number by 5 then subtract 2



Answer sequence

Calculate the outcome if Tom puts the following sequence into his calculator

+7 9 4 x -0 3 12+ =÷ √

3



Answer sequence

The number shown by A in the centre of the drawing is the product of the numbers linked by the arrows opposite each other.

A

15

3B

8

What are the values of A and B?

12040



Answer sequence

The numbers in this sequence start at 27 and reduce by the same number each time.

27 ? ? ? ? 12

Which numbers are missing from the sequence?

24 21 18 15

The sequence decreases by 3 from left to right.

The sequence increases by 3 from right to left.



Answer sequence

One person sits on each side of a square table

Jack has five similar tables that he joins together to make one long table.

How many people can be seated around the new table? 12



Answer sequence

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

What is 25% of one-third of 240?

20

One-third of 240 is 80

25 % (or ¼) of 80 is 20



Answer sequence

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.

Roger Federer beats Tim Henman

6 – 3, 7 – 6, 2 – 6, 6 - 4

How many sets of new balls are used in the match?

5

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

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.

A

B

1

2

3

What is the area of each shape?

1. 16cm2 2. 32cm2 3. 16cm2

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



Answer sequence

The sum of three single-digit numbers is 10.

Their product is 30.

What are the three numbers?

2 3 5



Answer sequence

A large rectangle is divided into smaller rectangles

The perimeter of this rectangle is 18 cm.

3cm

7cm

What is the area of the pink rectangle?

42cm2

The pink rectangle is 7cm by 6cm = 42 cm2

7cm

6cm



Answer sequence

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

A large rectangle is made up of smaller squares.

What percentage of the large rectangle is not shaded blue?

75%

There are 40 small squares. Ten are blue. This is a quarter, so three-quarters, or 75% are not blue.



Answer sequence

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 Tom’s lock?

562 742 724



Answer sequence

A regular octagon has an area of 86 cm2

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?

3.5cm2

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