Transcript KS2 Primary Maths Challenge 2010

Primary Maths
Challenge 2010
Primary Mathematics Challenge
Semi-final round 1 Question no.1
You are allowed only one attempt at this
question.
It is worth a total of 10 marks
Amy adds the three numbers between 5 and 9 together
What is her total?
Answer
2010
Mark
Primary Mathematics Challenge
Semi-final round 1 Question no.2
Amy buys 3 pencils and a
sharpener.
40p
90p
How much change does she have
from £5?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no. 3
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Jack calculates 4 x 15 x 3 instead of 5 x 3 x 3 x 4
What is the difference between his two answers?
ANSWER
2010
Total marks
N
Primary Mathematics Challenge
Semi-final round 1 Question no. 4
Jamie is travelling north-west when
he realises he should be travelling
east.
He turns anti-clockwise.
How many degrees does he turn
through to make sure he is
travelling in the right direction?
Try
1
2
3
2010
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no. 5
The numbers in the boxes are found by adding together the two numbers in the boxes
immediately below.
Complete the drawing so that all boxes are filled correctly
50
20
15
50
30
20
10
15
1st try for 10 marks
20
15
10
2nd try for 5 marks
50
2010
30
30
10
3rd try for 5 marks
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Primary Mathematics Challenge
Semi-final round 1 Question no. 6
The names of four mathematical shapes are hidden in this circle. The letters in
pairs of sectors will together make the name of one shape. Write the shapes
correctly in the answer boxes
Find all four shapes – each one is worth five marks each
Ans. In any order
E
X
A
L
Y
N
C
O
G
S
U
2010
H
D
I
M
R
R
A
B P R
N
I
E
D
M
O
H
Y
Total marks
Mark
Primary Mathematics Challenge
Semi-final round 1 Question no. 7
Look at this sentence:
ALL CHILDREN SHOULD HAVE THREE HOURS MATHEMATICS
HOMEWORK EVERY NIGHT
What is the average number of letters per word?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no. 8
James Connolly of the USA won the
triple jump in the Olympic Games of
1896 with a distance of 13.71m.
Nelson Evora of Portugal won the
Beijing event in 2008 with a distance of
17.44m.
How much further did Evora jump?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no.9
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
A rocket travels 5 metres using 25 grams of gunpowder.
Jack’s rocket weighs 500 grams. The casing and stick weigh 125 grams and the
stars inside the rocket weigh 75 grams. The rest is gunpowder.
Jack fires his rocket from the bottle shown below.
Put a cross where you think the rocket lands – the cross must be accurate
40-50m
51-55m
2010
56-60m
61-65m
Total marks
Primary Mathematics Challenge
Semi-final round 1 Question no. 10
Pringles tubes are packed
in larger boxes of 16
A shopkeeper buys 8
larger boxes.
How many Pringles tubes does the
shopkeeper have altogether?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no.11
Beth is on a calorie controlled diet.
She eats 1800 calories each day.
How many calories does she eat in one week?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no. 12
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Each of these questions is worth five marks.
Ans.
1.
How many degrees are there in a triangle?
2.
40 is the total of 12, 17 and which number?
3.
What is a quarter of 96?
4.
How many millimetres in 4.7cm?
Total marks
2010
Mark
Primary Mathematics Challenge
Semi-final round 1 Question no.13
Jack has a tank containing 15 litres of
water.
He transfers some of his water to
two bottles.
He puts a third in the first bottle and
20% in the other bottle.
How much water is left in his tank?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no.14
Jack works five days from Monday to
Friday.
On Monday he earns £1.25.
Each day that he works his pay
doubles from the previous day.
How much does he earn altogether
during the five days?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no.15
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Del Boy buys 20 Martian reject DVD players for £15.50 each.
He sells them all for a total of £550
Answer
How much did he pay in total for
the DVD players? (10 marks)
How much profit did he make on
each DVD player? (10 marks)
Total marks
2010
Marks
Primary Mathematics Challenge
Semi-final round 1 Question no. 16
Beth uses circles to continue the pattern
How many circles will she draw to show the next item in the sequence?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 1 Question no.17
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
A captain sails the shortest route between Fish Island and Ghost island. The scale on
his map is 10mm to every 2 km
Ports
Grid size
Round Island
Ghost Island
Fish Island
Bird Island
How far does the captain sail between the islands?
2010
ANSWER
km
Marks
2cm
Primary Mathematics Challenge
Semi-final round 1 Question no.18
Each square on the co-ordinate grid is 1 unit
long and 1 unit wide
Co-ordinate
(
,
)
(
,
)
(
,
)
(
,
)
Marks
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
The circle intersects with the
triangle and the rectangle on the grid
at four different points
Write the four co-ordinates (in
any order) for 5 marks each
Total marks
0
2010
Primary Mathematics Challenge
Semi-final round 2 Question no.1
You are allowed only one attempt at this
question.
It is worth a total of 10 marks
Two odd numbers with a difference of 2 when multiplied together make 35
Writer the two numbers in the answer box
Answer
2010
Mark
Primary Mathematics Challenge
Semi-final round 1 Question no. 2
Identify one thing that is the same about all six of these numbers
1412
2010
233
53
Try
1
2
3
20006
Answer
35
80
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no. 3
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
In Maths Challenge semi-final round 1 there were 16 schools competing and
in semi-final round 2 there were 14 schools competing. After each semi-final
half the teams from each round went through to the final. Teams have four
children each.
How many children went to the final?
ANSWER
2010
Total marks
Primary Mathematics Challenge
Semi-final round 2 Question no. 4
The perimeter of the equilateral triangle is 60cm.
What is the area of the square?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no. 5
Millie doubles a number and doubles it again.
Her outcome is 0.5
What number did she start with?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no. 6
The bar graph shows the amount
of money collected by five
children in a charity swim
John
Beth
Lucy
Peter
Amy
0
10
20
Money in £s
30
1. How much money did Amy raise?
2. How much more money did Peter raise than Beth?
2010
Try
1 1
2 1
3 1
Answer
2
2
2
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no. 7
10cm
This shape is made up from four squares the
same size. A shaded square is made from the
diagonals of the four squares.
The sides of the smaller squares are each 10cm
10cm
2010
What is the area of the grey square?
Try
1
2
3
Answer
cm2
cm2
cm2
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no.8
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Each of these true or false statements is worth five marks
T or F
1.
You cannot make two squares by folding a
rectangle in half
2.
All even numbers are divisible by both 2 and 4
without a remainder
3.
A regular shape must have all its sides equal and all
its angles equal
4.
45mm is twice the length of 2.25cm
Total marks
2010
Marks
Primary Mathematics Challenge
Semi-final round 2 Question no.9
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
There are six judges in a gymnastics competition. The maximum score each
judge can award is 10.
Jane’s five scores on the bar are
8.5
8.275
8.75
8. 4
8.175
8.45
The highest and lowest marks are not counted and the remaining scores are
added together.
What is Jane’s final total
Answer
Total marks
2010
Primary Mathematics Challenge
Semi-final round 2 Question no.10
Millie rounds two, 2-digit numbers
to the nearest ten.
Her answer in both cases is 50.
Both her numbers are prime
numbers.
What are her two numbers and
what is the total of the two
numbers?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no.11
Look carefully at the sketch.
How many different squares can you
find in the drawing?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no.12
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Which of these numbers is the odd one out according to the information given?
Ans.
There are 5 marks for each answer
49
39
27
19
29
69
1.
The only prime number that is 30 when rounded
to the nearest 10
2.
The only square number
3.
The only multiple of three where the sum of the
digits is a multiple of five
4.
The only number that is a cube number (e.g. 1
is a cube number because it is 1 x 1 x 1)
Total marks
2010
Mark
Primary Mathematics Challenge
Semi-final round 2 Question no.13
Beccy goes on a bicycle journey. She travels for 1½ hours at 18 k.p.h. and
for 45 minutes at 20 k.p.h.
How far does she travel altogether?
2010
Try
1
2
3
Answer
Mark
10
5
5
k.p.h. means kilometres per hour
Primary Mathematics Challenge
Semi-final round 2 Question no.14
Three-fifths of a number is 15.
Two thirds of another number is 6.
Find the product of the two
numbers.
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no. 15
Here is a number function machine. It uses two processes in the rule.
What is the rule used to change the input number to the output number?
Input
Try
1
2
3
2010
Function
Output
15
9
27
13
30
14
Answer
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no. 16
A
B
C
D
Each cube is 1.5 times smaller
than the cube to its right.
Cube B has a volume of 36cm3
What are the volumes of the
other three cubes
2010
Try
1 A
2 A
3 A
Answer
C
D
C
D
C
D
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no.17
There are 240 children in a school.
The chart shows the percentage of
children who like best the subjects shown.
Science
Games
Mathematics
English
How many children like mathematics?
How many children like English?
2010
Try
1 Maths
2 Maths
3 Maths
Answer
science
science
science
Mark
10
5
5
Primary Mathematics Challenge
Semi-final round 2 Question no.18
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
This question is a real challenge!!!
A
Think what you know about isosceles triangles and it will
become easier
250
B
Triangle ABC is isosceles.
900
Angle DAC is 250
Calculate angles BAC and BCD
900
D
C
2010
Answer: angle BAC is
0
10 marks
Answer: angle BCD is
0
10 marks
Total marks
Primary Mathematics Challenge
Final round 1 Question no.1
You are allowed only one attempt at this
question.
It is worth a total of 10 marks
Tom shares 40 sweets equally between himself and three friends.
How many sweets do they each have?
Answer
2010
Mark
Primary Mathematics Challenge
Final round 1 Question no.2
Beth buys a birthday present and has £9.51 change from £20
How much did the present cost?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 1 Question no. 3
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Sophie’s house number is between forty and sixty-one.
Her house number is an odd number.
Rounded to the nearest 100 it is 100.
What are all the possibilities her house number could be?
ANSWER
2010
Total marks
Primary Mathematics Challenge
Final round 1 Question no.4
In this row of numbers Amy halves the even numbers and doubles the odd numbers.
She the rewrites them in order starting with the smallest
11
24
10
7
19
14
8
21
Rewrite her new numbers in order in the try boxes below
1st try
10 marks
2nd try
5 marks
3rd try
5 marks
2010
Primary Mathematics Challenge
Final round 1 Question no. 5
Find the average height in cm of the three children below.
2m
1m
0m
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 1 Question no. 6
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
The rule for this function machine is double the input number and subtract 4
For five marks each, write the missing numbers in the spaces
INPUT
FUNCTION
OUTPUT
45
18
3.25
8.8
TOTAL MARKS
2010
MARKS
Primary Mathematics Challenge
Final round 1 Question no. 7
What is the difference in area
between the square and the
triangle?
Each square in the drawing is 1cm
long and 1cm wide
Try
1
2
3
2010
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 1 Question no. 8
In the first modern Olympic
games in Athens in 1896 the 100m
was won by Francis Lane of the
USA in a time of 12.20 sec.
In Beijing 2008 Usain Bolt was
quicker by 2.51 sec. in the same
event.
What was Usain Bolt’s time?
2010
Try
1
2
3
Answer
Mark
10
5
5
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Primary Mathematics Challenge
Final round 1 Question no. 9
Each of these wheels is a mathematical process, item or term.
Work out each one and write the answer – correctly - in the boxes below
Each answer is worth five marks
A
E
T
C
E
L
N
G
R
C
S
E
I
O
L
E
S
S
I
O
T
P
R
T
N
A
I
Total marks
2010
U
T
M
O
N
R
E
A
R
Primary Mathematics Challenge
Final round 1 Question no. 10
In a Sudoku puzzle there are nine large squares, each with nine smaller
squares containing each of the numbers 1-9.
What is the total of all the digits used when the whole puzzle is
completed?
Sample
2 3 9 8
5 8 6
2010
1
7
1
4 6
1
9 5 4
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 1 Question no. 11
Three of these drawings show
three-fifths shaded grey
Write the letters of these
drawings in the answer box
A
2010
B
C
D
Try
1
2
3
E
Answer
F
Mark
10
5
5
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Primary Mathematics Challenge
Final round 1 Question no. 12
Each of the single digit numbers in the list can be added to a 2-digit number to
make a square number. Each pair and correct solution are worth 5 marks
Write each pair in the answer boxes along with the square number you have
made.
10
2010
9
29
8
16
Pair no 1
=
Pair no 2
=
Pair no 3
=
Pair no 4
=
6
Total marks
7
56
Primary Mathematics Challenge
Final round 1 Question no. 13
In the early days of making cartoon films the animator had to draw a minimum of
12 pictures for every second of film.
What was the minimum number of pictures drawn for two minutes of cartoon?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 1 Question no. 14
Jack works five days from Monday to
Friday.
Each day that he works his total pay
is double the previous day.
At the end of five days he has earned
£192
How much did he earn on Monday?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 1 Question no. 15
Jack has three numbers, they are 3, 5 and 7
Calculate the difference between their product and their total
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 1 Question no. 16
A sports shop reduces all prices by 20% in a sale.
What was the old price of a cricket bat?
Now
£120
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 1 Question no. 17
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Jack has a five digit combination lock.
No two digits are the same. Each box contains a single digit
Using the clues below work out Jack’s combination.
The first and last digits total 5
The middle digit is even and a prime number
The first three digits are even, odd, even
The second digit is a square number greater than one
The fourth digit is the sum of three of the other digits
Jack’s combination is:
2010
Total marks
Primary Mathematics Challenge
Final round 1 Question no.18
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Tom calculates the area of each of these rectangles.
He then writes them in order starting with the largest at the top.
Calculate each area and write the letters of each rectangle in order of size in
the answer column. 5 marks for each correct answer in the right place
9cm
6cm
Shape
A
12cm
Each square is 0.5cm
The
width is
half the
length
B
D
2010
C
140mm
Total marks
5cm
Mark
You are allowed only one attempt at this
question.
It is worth a total of 10 marks
Primary Mathematics Challenge
Final round 2 Question no.1
Lucy looks at this part of a 1-100 number square.
She subtracts the two missing numbers.
What is her answer?
44
45
65
Answer
2010
Mark
Primary Mathematics Challenge
Final round 2 Question no. 2
In each 480 gram box of chocolates there are two identical layers of chocolates.
In each layer there are 12 chocolates.
What is the average weight of each chocolate?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 2 Question no. 3
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
A double-decker bus has the following passenger spaces:
Lower deck 24, upper deck 36, 8 standing.
How many people are on the moving bus altogether when it is full?
(think very carefully before you answer!!)
ANSWER
2010
Total marks
Primary Mathematics Challenge
Semi-final round 2 Question no. 4
The sequence is made from two alternating sequences.
1
0
4
2
7
4
10
6
13
8
Which two numbers come next?
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 2 Question no. 5
Lisa starts in the grey box. When she moves to a circle she adds 5 to the number she has
just left. When she moves to a square she subtracts 2 from the number she has just left.
What number does Lisa finish with in the grey circle?
50
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 2 Question no. 6
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
How many cubes have been used to make this shape.
Circle the answer you think is correct
18
19
20 21
22
23 24
2010
Total marks
Primary Mathematics Challenge
Final round 2 Question no. 7
0cm
10cm
20cm
30cm
40cm
Tom uses the gauge to measure the width of his octagon in mm
How wide is Tom’s octagon in mm?
2010
Try
1
2
3
Answer
mm
mm
mm
Mark
10
5
5
Primary Mathematics Challenge
This question is worth 20 marks.
Final round 2 Question no. 8
You will have only one attempt to
complete your answer
The 24-hour digital clock display shows the time Sally’s train leaves the station.
Her journey takes 2 hours and 52 minutes.
Shade in the bars on the 24-hour digital clock below to show her arrival time.
2010
Total marks
Primary Mathematics Challenge
Final round 2 Question no. 9
Sarah produces a tally chart of
stickers collected by her friends
Number of stickers
20
Number of stickers
Jack
Lucy
Tom
Amy
Ben
She makes it into a graph
but it is not complete
Your tasks
10
0
2010
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
1. Use the tally chart information
to write the 5 children’s names in
the correct place on the vertical
boxes on the horizontal axis. (10
marks)
2. Complete the tally chart by
putting in Tom’s tally. (10 marks)
Total marks
Primary Mathematics Challenge
Final round 2 Question no. 10
Jack and Amy agree to share the cost of a skateboard.
Jack pays 40% of the cost and Amy the rest.
£140
How much do they each pay?
2010
Try
1 Amy
2 Amy
3 Amy
Answer
Jack
Jack
Jack
Mark
10
5
5
Primary Mathematics Challenge
Final round 2 Question no. 11
How many of the linked shapes
below are pentagons?
Write the letters of the
identified shapes in the answer
box
B
A
2010
C
F
D
G
H
E
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 2 Question no. 12
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
Each correct answer is worth five marks
1.
Identify this 3-d shape
2.
Which regular 2-d shape has 3 lines of
symmetry?
3.
The net of a cylinder is made from two
circles and which other shape?
4.
A hexagonal prism has how many faces?
2010
Ans.
Total marks
Mark
Primary Mathematics Challenge
Final round 2 Question no. 13
The chart shows the number of books read
by five children during a school year.
How many books did they read
altogether?
Jack
Amy
Lucy
Tom
Ben
Four books
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 2 Question no. 14
6
18
8
16 19 15 11 23 47 21 14 17
Tom adds 19 to each of these numbers
Write the numbers from the list that will give him an answer between 25 and 35
2010
Try
1
2
3
Answer
Mark
10
5
5
Primary Mathematics Challenge
Final round 2 Question no. 15
Jack finds ¾ of a number, Amy finds ½ of the same number, Ben finds 2/3 of
the same number and Lucy finds 3/8 of the same number.
Ben’s answer is 16.
What were the answers found by the other three children?
2010
Try
1 Jack
2 Jack
3 Jack
Answer
Amy
Amy
Amy
Lucy
Lucy
Lucy
Mark
10
5
5
Primary Mathematics Challenge
Final round 2 Question no. 16
Which two criteria have been used to sort this Venn Diagram?
1st try
A.
B.
81
4
36
64
75
25
9
10 marks
101
13
2nd try
A.
B.
5 marks
3rd try
A.
B.
5 marks
2010
Primary Mathematics Challenge
Final round 2 Question no. 17
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
8cm
16cm
Lucy uses squares and rectangles like those above to make shape below
What is the perimeter of Lucy’s new shape?
2010
Answer
Total marks
Primary Mathematics Challenge
Final round 2 Question no.18
Each square on the co-ordinate grid is 1 unit
long and 1 unit wide
You are allowed only one attempt at this
question.
It is worth a total of 20 marks
The kite shape is translated to a new
position on the grid.
Two of the new lines have been drawn
for you.
Complete the shape in its new position
on the grid.
0
Write the four new co-ordinates (in
any order) for 5 marks each
Co-ordinate
(
,
)
(
,
)
(
,
)
(
,
)
Total marks
2010
Marks
Primary Mathematics Challenge
Tie break question
How many right-angle triangles are
there in the drawing?
School
2010
Answer