Transcript Slide 1

N. E. Lincolnshire Mathematics Team
1
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
N. E. Lincolnshire Mathematics Team
2
Sample semi-final question
The sum of two numbers is 15
Their difference is three.
54
What is their product?
9 + 6 = 15
is their sum or total
9 -
is their difference
6 = 3
9 x 6 = 54
Answer sequence
is their product (multiplied together)
N. E. Lincolnshire Mathematics Team
3
Sample semi-final question
Jack draws the shape below
16
3
7
How many rectangles can be found in the drawing?
Answer sequence
N. E. Lincolnshire Mathematics Team
6
4
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
N. E. Lincolnshire Mathematics Team
5
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
Answer sequence
The width is a quarter
of 24 cm and the length
three-quarters of 24 cm
N. E. Lincolnshire Mathematics Team
6
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
N. E. Lincolnshire Mathematics Team
7
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.
60
One number is half the size of the other.
30
What are the two numbers?
Answer sequence
N. E. Lincolnshire Mathematics Team
8
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
1
5
4
2
4
4
3
1
6
5
3
2
Answer sequence
N. E. Lincolnshire Mathematics Team
These may be thrown
in any order
9
Sample semi-final question
The graph shows the percentage scored by 7 children in a test
Jade
Paul
Lee
Amy
Jack
Tom
Chelsey
A. Chelsey
B. 35% (½ of 70%)
C. Tom and Jade
0
10
20 30 40 50 60 70 80 90 100
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?
Answer sequence
N. E. Lincolnshire Mathematics Team
10
Sample semi-final question
The radius of the yellow circle is 12 cm and x is the centre of the circle
x
288 cm2
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
N. E. Lincolnshire Mathematics Team
11
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
N. E. Lincolnshire Mathematics Team
12
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
Answer sequence
7
10
13
16
N. E. Lincolnshire Mathematics Team
19
13
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
15Three-fifths
45
15 Number
15
Two-fifths
15
15
The whole number is 15 multiplied by 5 = 75.
75
One-third of the number is 75 ÷ 3 = 25 .
25
Answer sequence
75
25
N. E. Lincolnshire Mathematics Team
25
14
Sample semi-final question
Triangle ABC is equilateral
A
X
B
1200
C
What is the value of angle X?
There are many different ways to find this answer.
How many can you find?
Answer sequence
N. E. Lincolnshire Mathematics Team
15
Sample semi-final question
Which numbers are missing from these number sentences?
Answer sequence
A.
42
-
7
= 35
B.
5
C.
28
+ 7 = 35
D.
63
÷ 7 =
X 7 =
35
N. E. Lincolnshire Mathematics Team
9
16
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
N. E. Lincolnshire Mathematics Team
17
Sample semi-final question
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
T
F
C. To multiply any number by 10 just put a zero on the end
F
D. For every decimal fraction there is an equivalent ‘ordinary’ fraction
E. A regular pentagon has five lines of symmetry
T
T
Write T or F next to each statement
Answer sequence
N. E. Lincolnshire Mathematics Team
18
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.
18
Answer sequence
36
72
N. E. Lincolnshire Mathematics Team
144
19
Sample semi-final question
8
How many different triangles can you find in this drawing?
2
3
1
4
Answer sequence
N. E. Lincolnshire Mathematics Team
20
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
N. E. Lincolnshire Mathematics Team
21
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
Answer sequence
3-1
N. E. Lincolnshire Mathematics Team
2-2
1-3
22
Sample semi-final question
0.11 mm
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?
Change 5.5 cm to 55 mm.
Divide 55m by 500 = 0.11mm
Answer sequence
N. E. Lincolnshire Mathematics Team
23
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
N. E. Lincolnshire Mathematics Team
24
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
N. E. Lincolnshire Mathematics Team
25
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
N. E. Lincolnshire Mathematics Team
26
Sample semi-final question
There are three prime numbers between 80 and 100
What is their total?
269
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
N. E. Lincolnshire Mathematics Team
27
Sample semi-final question
The two triangles are isosceles and the same size.
17 cm
They each have a perimeter of 20.5 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
N. E. Lincolnshire Mathematics Team
28
Sample final question
Two straight lines cross as
shown in the drawing
1050
75A0
B0
105
What is the size of angle A
and angle B?
Angle A is 1800 - 1050 = 750
Angle B is 1800 - 750 = 1050
Answer sequence
N. E. Lincolnshire Mathematics Team
29
Sample final question
The sum of the edges of each of these squares is
1000
450
150
Which three numbers are missing?
775
B
400
A
50
100
125
555
395
C
Answer sequence
N. E. Lincolnshire Mathematics Team
30
Sample final question
15
Six people play each other once at golf.
How many games are played altogether?
Player B
Player C
Player A
Player D
Player D
Player E
Player F
Player C
Player E
Player F
1 Game
Player D
Player F
Player E
2 Games
3 Games
Player E
Player F
Player F
5 Games
Answer sequence
4 Games
N. E. Lincolnshire Mathematics Team
31
Sample final question
Gavin weighs one-third more than Sally.
How much do mum and
dad each weigh?
Mum weighs twice as much as Gavin.
Mum and dad weigh 140kg altogether.
Sally weighs 24kg.
Mum weighs 64kg.
Dad weighs 76kg.
Gavin weighs 24kg + 8kg = 32kg.
Mum weighs 32kg x 2 = 64kg.
Dad weighs 140kg - 64kg = 76kg.
Answer sequence
N. E. Lincolnshire Mathematics Team
32
Sample final question
Jade uses five 5s to write a number sentence.
She uses two + signs and one x sign.
What could her number
sentence have been?
The answer to her sentence is 555.
(5 + 5) x 55 + 5 = 555
The 5s in her answer are not part of the five 5s she uses to work out her problem.
Answer sequence
N. E. Lincolnshire Mathematics Team
33
Sample final question
The drawing shows part of number grid six columns wide.
0
5
10
15
30
35
40
45
65
70
20
25
85
110
A
130
B
Which numbers are missing from squares A and B?
Answer sequence
N. E. Lincolnshire Mathematics Team
34
Sample final question
The area of this
square is 64cm2
Joe uses similar squares
to make a new shape.
The area is 64cm2 so
each side is 8cm.
80cm
There are ten sides to
the new shape.
10 x 8cm = 80 cm
What is the perimeter of the new shape?
Answer sequence
N. E. Lincolnshire Mathematics Team
35
Sample final question
Amy and Jade live in different villages.
Their villages are both 90km away from the
town.
At what time should they
each set off from their
villages to arrive in the
town at noon?
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.
Amy sets off at 9:45 a.m. Jade sets off at 10:30
Amy’s journey time is 2¼
hours.
Answer sequence
Jade’s journey time is 1½
hours.
N. E. Lincolnshire Mathematics Team
36
Sample final question
There are three mathematical terms jumbled in this sequence of letters.
SMSUUYBLMTTMRIEAPTCLRTYY
S
U
M
B
U
S
T
L
Y
R
T
M
A
I
M
C
P
E
T
L
T
Y
R
Y
What are the three terms?
SUBTRACT
MULTIPLY
SYMMETRY
Answer sequence
N. E. Lincolnshire Mathematics Team
37
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
N. E. Lincolnshire Mathematics Team
38
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
N. E. Lincolnshire Mathematics Team
39
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
N. E. Lincolnshire Mathematics Team
40
Sample final question
Calculate the outcome if Tom puts the following sequence into his
calculator
7
+
9
÷
4
x
0
-
3
+
12
=
√
3
Answer sequence
N. E. Lincolnshire Mathematics Team
41
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
40
B
120
A
What are the values of
A and B?
3
8
Answer sequence
N. E. Lincolnshire Mathematics Team
42
Sample final question
The numbers in this sequence start at 27 and reduce by the same number
each time.
27
24
?
21
?
18
?
15
?
12
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
N. E. Lincolnshire Mathematics Team
43
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.
How many people can be seated around the new table?
Answer sequence
N. E. Lincolnshire Mathematics Team
12
44
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
N. E. Lincolnshire Mathematics Team
45
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
N. E. Lincolnshire Mathematics Team
46
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.
Roger Federer beats Tim Henman
5
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.
Answer sequence
3 + 1 + 1 = 5
N. E. Lincolnshire Mathematics Team
47
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
2
A
1. 16cm2 2. 32cm2
3. 16cm2
The area of the square 8cm x 8cm = 64 cm2
3
B
Answer sequence
Shape 1 is ¼, shape 2 is ½ and shape 3 is ¼
of the square
N. E. Lincolnshire Mathematics Team
48
Sample final question
The sum of three single-digit numbers is 10.
Their product is 30.
What are the three numbers?
2
Answer sequence
3
N. E. Lincolnshire Mathematics Team
5
49
Sample final question
A large rectangle is divided into smaller rectangles
The perimeter of this
rectangle is 18 cm.
3cm
6cm
7cm
7cm
42cm2
What is the area of the pink rectangle?
The pink rectangle is 7cm by 6cm = 42 cm2
Answer sequence
N. E. Lincolnshire Mathematics Team
50
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
N. E. Lincolnshire Mathematics Team
51
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 threequarters, or 75% are not blue.
Answer sequence
N. E. Lincolnshire Mathematics Team
52
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 Tom’s lock?
562
Answer sequence
742
724
N. E. Lincolnshire Mathematics Team
53
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
N. E. Lincolnshire Mathematics Team
54