Transcript KS2 Maths Challenge semifinalquestions2009

PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
240 ÷ 4 = 60
12 X 5 = 60
÷ 4
12 x
5
Which number must go into the box on the right side of
the scales to balance them with the left side?
Answer 240
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Amy has 6 different coins in her purse.
She has £2.68 altogether
Which six coins does she have?
Write your answer starting with the smallest coin.
1p, 2p, 5p, 10p, 50p, £2
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Jack colours the empty triangles on this
shape red
How many sixteenths does he shade
red?
10
16
5
8
X2 =
10
16
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
200C
The arrow indicates the temperature in a town at
9:00 a.m.
By mid-afternoon the temperature has risen by
70C.
120C
The temperature then falls by 130C.
What is the new temperature?
00C
-10C
- 10C
-200C
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
In his cricket innings Tom scores 47 runs.
His score is made up of:
two sixes, three fours, one three and seven twos.
The rest he scores in singles.
How many singles does he score in his innings?
2 x 6 = 12
3 x 4 = 12
1 x 3 =
3
7 x 2 = 14
Total
41
47 - 41 = 6
6 singles
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
24cm
Diameter is 9.5cm
x 2 = 19cm
19cm
24cm
The short side of the rectangle is the same length as the diameter of
the circle.
The radius of the circle is 9.5 cm.
What is the perimeter of the rectangle?
19cm + 24cm = 43cm
43cm x 2 = 86cm
86cm
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The shape above is rotated one quarter turn to the right.
Draw the shape in its new position below.
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Jason subtracts 0.25 from each of these decimals.
Rewrite the new decimals in order starting with the smallest
0.55
0.5
1.8
0.35
1.5
0.3
0.25
1.55
0.1
1.25
0.1
0.25
0.3
1.25
1.55
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
At sports day Joe makes a standing jump of 1.8 m.
Jade jumps 25 cm more than Holly.
Tom jumps 10 cm more than Jade.
Holly jumps 15 cm less than Joe.
How far does Tom jump?
1.8m
Joe
1.65m
Holly
1.9m
Jade
2.0m
Tom
2m or 200cm
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
It takes Amy 25 minutes to walk to school.
School starts at 8:55 a.m.
She likes to arrive 10 minutes early.
What time does Amy normally set off for school?
8:55 - 10 min. = 8:45
8:45 - 25 min. = 8:20
8:20 a.m., 08:20, twenty past eight
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Three different children do the calculations below.
They then add up their answers.
What is the total of their three answers?
Ben calculates a quarter of 464
116
Amy calculates 20% of 900
180
Alex calculates the product of 7 and 45
315
611
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
How many different rectangles are there in this drawing?
10
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Each face of this cube has a surface area of
81cm2
Chelsey wants to build a tower of cubes 216cm
tall.
How many cubes does she need?
24 cubes
The edge of one face is √81cm2
216cm ÷ 9 = 24
= 9cm
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The rule for the sequence below is find a quarter and add two.
Which two numbers complete the sequence?
24
8
4
3
2¾
4 ÷ 4 = 1
1 + 2 = 3
3 ÷ 4 = ¾
¾ + 2 = 2¾
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
SEMI-FINAL ROUND 1 QUESTION NUMBER 20
Calculate one eighth of a quarter of a third of one-half of 72
Your answer will be a fraction.
3/8
72 ÷ 2 = 36
36 ÷ 3 = 12
12 ÷ 4 =
3
3 ÷ 8 = 3/8
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The product of three numbers is 48.
Two of the numbers are 2 and 3.
What is the third number?
8
2 x 3 = 6
48 ÷ 6 = 8
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Joe has one of each coin up to and including £2.
How much less than £10 does he have?
£6.12
£2 + £1 + 50p + 20p + 10p + 5p + 2p + 1p = £3.88
£10 - £3.88 = £6.12
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
15 sheets of paper weigh 7.5 grams.
How much does one sheet of paper weigh?
0.5g
7.5g ÷ 15 = 0.5
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
400
A
700
X
600
C
B
700
In the sketch the isosceles triangles A, B and C are the same size.
Calculate angle X
600
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
91
37
63
49
39
27
51
61
43
35
19
85
21
93
29
15
Identify the five prime numbers located in the grid.
What is the total of the five numbers?
189
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
1 5
4 9 2
7 2
The top number in this puzzle is found by adding all the digits
below together. The bottom number is the product of the three
numbers above.
Calculate the two answers needed to complete the puzzle and
add together your two answers.
87
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
SEMI-FINAL ROUND 2 QUESTION NUMBER 8
The area of this square is 64cm2.
The drawing below is made up of squares the same as this
one.
What is the perimeter of the new shape?
80 cm
8cm
12 sides each 4cm
8cm
8cm
8cm
4cm x 12 = 48cm
8cm x 4 = 32cm
48cm + 32cm = 80cm
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
By Christmas a football team has scored 18 goals.
This is 25% of their final total for the season.
Jack scores 1/3 of the season’s total goals.
Tom scores five less than Jack.
13 goals were scored in January.
Irrelevant
How many goals were scored by the rest of the team?
29
The team scores 18 x 4 goals a season. Total 72
Jack scores 72 ÷ 3 = 24 goals
Tom scores 24 - 5 = 19 goals
Jack and Tom score 24 + 19 = 43 goals
The rest score 72 - 43 = 29 goals
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
28
46
85
57
18
63
102
45
The numbers in the squares are the sum of each number in the
circles on each side.
Which numbers are missing from the blank shapes?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
180km
AYTOWN
360km
BETOWN
CETOWN
Train X sets off from Aytown at 11:30 and travels at 90km per
hour.
Train Y sets off from Cetown at 12:15 and travels at 80km per
hour.
How much later does train Y arrive at Betown than train X?
3hrs 15min,
3 ¼ hours,
195 minutes
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A litre of water weighs 1kg.
Jack fills a plastic bottle with 0.75L of water.
Together the bottle and water weigh 835g.
What is the weight of the bottle?
85 g
The water weighs 750g
Subtract the weight of water from the combined weight of
the water and the bottle.
The bottle weighs 835g - 750g = 85g
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A palindrome number is one that reads the same backwards as it
does forwards, e.g. 8558.
Which of the calculations below produce palindrome
numbers?
A 29 X 24
900
1233
696
B 30 X 30
C 11 X 11 X 11
1331
D 1437 + 2006
3443
E 232 + 1001
A, C, D
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
14cm
14cm
The area of each circle is 38cm2
The diameter of each circle is 7cm.
What is the area of the grey shaded background?
Area of the grey square 14cm x 14cm = 196 cm2
Area of the four circles 152 cm2
44cm2
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Say whether these statements are true or false
A All three digit numbers are divisible by 3 without a remainder
B If you add the digits of a four digit number your answer will be an even number
C All prime numbers are odd
D A square number cannot also be a triangular number
E Numbers ending in 0 are multiples of only 5 and 10.
All are FALSE
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
What fraction of the large square is shaded grey?
Answer in lowest terms
10/16
5/8
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The area of this square is 64cm2.
The drawing below is made up of squares the same as
this one.
What is the area of the new shape?
208cm2
¼ of a large square
is 16cm2
There are two whole squares 64cm2 x 2 = 128cm2
There are 5 quarter squares. Area is 16cm2 x 5 = 80cm2
128cm2 + 80cm2 = 208cm2
Alternatively
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The area of this square is 64cm2.
The drawing below is made up of squares similar to
this one.
What is the area of the new shape?
208cm2
Insert lines to make each
large square into quarters
¼ of a large square
is 16cm2
There are13 quarter squares. Area is 16cm2 x 13 = 208cm2
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
SEMI-FINAL ROUND 2 QUESTION NUMBER 19
40% of a number is 120.
What is one-third of the number?
100
10% of the number is 120 ÷ 4 = 30
100% - the whole number - is 30 x 10 = 300
One-third of 300 is 100
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
÷ 4
12 x
5
Which number must go into the box on the right side of
the scales to balance them with the left side?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Amy has 6 different coins in her purse.
She has £2.68 altogether
Which six coins does she have?
Write your answer starting with the smallest coin.
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Jack colours the empty triangles on this
shape red
How many sixteenths does he shade
red?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
200C
The arrow indicates the temperature in a town at
9:00 a.m.
By mid-afternoon the temperature has risen by
70C.
The temperature then falls by 130C.
What is the new temperature?
00C
-200C
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
In his cricket innings Tom scores 47 runs.
His score is made up of:
two sixes, three fours, one three and seven twos.
The rest he scores in singles.
How many singles does he score in his innings?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
24cm
The short side of the rectangle is the same length as the diameter of
the circle.
The radius of the circle is 9.5 cm.
What is the perimeter of the rectangle?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The shape above is rotated one quarter turn to the right.
On the shape below draw the missing pieces in their new
position to complete the drawing.
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Jason subtracts 0.25 from each of these decimals.
Rewrite the new decimals in order starting with the smallest
0.55
0.5
1.8
0.35
1.5
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
At sports day Joe makes a standing jump of 1.8 m.
Jade jumps 25 cm more than Holly.
Tom jumps 10 cm more than Jade.
Holly jumps 15 cm less than Joe.
How far does Tom jump?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
It takes Amy 25 minutes to walk to school.
School starts at 8:55 a.m.
She likes to arrive 10 minutes early.
What time does Amy normally set off for school?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Three different children do the calculations below.
They then add up their answers.
What is the total of their three answers?
Ben calculates a quarter of 464
Amy calculates 20% of 900
Alex calculates the product of 7 and 45
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
How many different rectangles are there in this drawing?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Each face of this cube has a surface area of
81cm2
Chelsey wants to build a tower of cubes 216cm
tall.
How many cubes does she need?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The rule for the sequence below is find a quarter and add two.
Which two numbers complete the sequence?
24
8
4
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
SEMI-FINAL ROUND 1 QUESTION NUMBER 20
Calculate one eighth of a quarter of a third of one-half of 72
Your answer will be a fraction.
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The product of three numbers is 48.
Two of the numbers are 2 and 3.
What is the third number?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Joe has one of each coin up to and including £2.
How much less than £10 does he have?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
15 sheets of paper weigh 7.5 grams.
How much does one sheet of paper weigh?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A
700
X
C
B
In the sketch the isosceles triangles A, B and C are the same size.
Calculate angle X
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
91
37
63
49
39
27
51
61
43
35
19
85
21
93
29
15
Identify the five prime numbers located in the grid.
What is the total of the five numbers?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
4 9 2
The top number in this puzzle is found by adding all the digits
below together. The bottom number is the product of the three
numbers above.
Calculate the two answers needed to complete the puzzle and
add together your two answers.
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
SEMI-FINAL ROUND 2 QUESTION NUMBER 8
The area of this square is 64cm2.
The drawing below is made up of squares similar to
this one.
What is the perimeter of the new shape?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
By Christmas a football team has scored 18 goals.
This is 25% of their final total for the season.
Jack scores 1/3 of the season’s total goals.
Tom scores five less than Jack.
13 goals were scored in January.
How many goals were scored by the rest of the team?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
85
57
63
45
The numbers in the squares are the sum of each number in the
circles on each side.
Which numbers are missing from the blank shapes?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
180km
AYTOWN
360km
BETOWN
CETOWN
Train X sets off from Aytown at 11:30 and travels at 90km per
hour.
Train Y sets off from Cetown at 12:15 and travels at 80km per
hour.
How much later does train Y arrive at Betown than train X?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A litre of water weighs 1kg.
Jack fills a plastic bottle with 0.75L of water.
Together the bottle and water weigh 835g.
What is the weight of the bottle?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
A palindrome number is one that reads the same backwards as it
does forwards, e.g. 8558.
Which of the calculations below produce palindrome
numbers?
A 29 X 24
B 30 X 30
C 11 X 11 X 11
D 1437 + 2006
E 232 + 1001
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The area of each circle is 38cm2
The diameter of each circle is 7cm.
What is the area of the grey shaded background?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
Say whether these statements are true or false
A All three digit numbers are divisible by 3 without a remainder
B If you add the digits of a four digit number your answer will be an even number
C All prime numbers are odd
D A square number cannot also be a triangular number
E Numbers ending in 0 are multiples of only 5 and 10.
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
What fraction of the large square is shaded grey?
Answer in lowest terms
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
The area of this square is 64cm2.
The drawing below is made up of squares similar to
this one.
What is the area of the new shape?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2009
SEMI-FINAL ROUND 2 QUESTION NUMBER 19
40% of a number is 120.
What is one-third of the number?