Transcript Maths Challenge Semi-Final questions 2008

SEMI-FINAL ROUND
QUESTIONS WITH ANSWERS
POWERPOINT
Some of the questions have been modified and may appear
slightly different from those in the actual competition.
To access answers simply left click the mouse and an
automatic answer sequence will appear with an
explanation where appropriate
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Each arm of the cross totals 50
19
17 18 15
13
Which two numbers are missing from the empty
boxes?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Find the mathematical terms mixed up in the capital letter strings
written below. A clue is given for each one
MATURE PETER - can be measured
TEMPERATURE
SO LESS ICE – can be shapely
ISOSCELES
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Emily multiplies three different numbers together.
Each number is greater than one.
Her answer is 24.
What could her numbers have been?
2
X
3
X
4
6
X
4
=
24
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Apples cost 15p each.
Jack buys seven apples
£1.10
How much change does Jack receive from £2.00?
Two apples can be bought for 25p
Six apples can be bought for 75p
Add the cost of a single apple to 75p
75p + 15p = 90p
£2.00 -
Buy 2 for 25p.
90p = £1.10
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
The perimeter of this regular pentagon is 40 cm
One side measures
40 cm ÷ 5 = 8cm
Amy joins two congruent pentagons together
There are 8 sides to
Amy’s new shape
What is the perimeter of Amy’s new shape?
The new perimeter is
8cm x 8 = 64cm
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
True or false?
Look at the statements below and say whether each is true (T)
or false (F)
A. All quadrilaterals have four right angles
F
B. All quadrilaterals have at least one line of symmetry
F
C. A right angle triangle may be isosceles
T
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
This shape has been rotated 900 clockwise at point A.
A
Which shape below shows its original position? D
A
B
C
D
E
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Laura says that 20% of the number she is thinking of is 36.
She asks Ben to find out what her number is and then make his
answer up to 225.
45
What is the number that Ben should add to Laura’s
number to make 225?
20% is equal to one-fifth
Laura’s original number is 36 x 5 = 180
Ben subtracts 180 from 225 to find his number
225 - 180 = 45
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
A football team scores 45 goals in a season.
Adam scores 18 goals.
Tom scores one-third of them.
1/3 of 45 is 15
Nick scores three.
How many goals were scored by other team
members?
The three players score 18 + 15 + 3 = 36
The other players score 45 - 36 = 9 goals
9
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Carpet cost £15 per m2.
Jason has a room like the plan in the drawing.
Jason covers the floor with carpet.
6m
A
3m
5m
3m
B
2m
3m
How much does the carpet for the room cost altogether?
Split the room into two rectangles to find the total area
Area A is 6m x 3m = 18m2
Area B is 3m x 2m = 6m2
The total area is 24m2
The total cost is 24m2
x £15 = £360
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Ben draw square with sides 6.5 cm long.
Amy draws a square with sides twice as long as Ben’s square.
What is the area of Amy’s square?
6.5cm
6.5cm
13 cm6.5cm
6.5 cm
6.5 cm
13 cm
6.5 cm
The area of the new square is 13cm
x
13cm
=
169cm2
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
This sequence follows the pattern of double and add one
5
11
Subtract one from 11
and
halve the answer
23
47
95
191
383
Double the previous
number and add 1
Which three numbers are missing from the sequence?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
The missing numbers above the blue boxes are found by adding the two numbers in the
boxes directly below
13
8
5
5
3
15
2
6
90
The missing numbers below the blue boxes are found by multiplying the two numbers
in the boxes directly above
Write in the missing numbers on the drawing
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
What is one-third of 25% of a half of
4800?
200
Half of 4800 is 2400
25% (or ¼) of 2400 is 600
1/3 of 600 is 200
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
The area of the triangle A in this drawing is 80cm2.
The total area of the whole drawing is 130 cm2
The two squares are the same size.
What is the length of one side of each square?
The area of the two squares is 130 - 80cm2 = 50cm2
A
The area of one square is 50cm2 ÷ 2 = 25cm2
The length of one side of each square is 5cm
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
George bought a sports car for £15 000.
When he sold it two years later he received 11%
less than he paid for it.
What was the price he sold his car for?
Partition 11% into 10% and 1%
10% of £15 000 is £1 500 (£15 000 ÷ 10)
1% of £15 000 is £1 500 divided by 10 or £15 000 ÷ 100
1% of £1 500 is £150
11% of £15 000 is £1 500 + £150 = £1 650
George sells the car for £15 000 - £1 650 = £13 350
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
The cost of Sunday lunch at a restaurant is £12.50 for two courses
and £15.75 for three courses.
Five people in a party book Sunday lunch.
Two have three courses and three have two courses.
How much is left out of £100 when the bill has been paid?
2 x £15.75 = £31.50
3 x £12.50 = £37.50
£31.50 + £37.50 = £69
£100 - £69 = £31 left over
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
a = 5,
b = 3,
c = 4,
d = 6
Amy uses the numbers to calculate the fraction shown below
c x b
4 x 3 = 12
a x d
6 x 5 = 30
Write the fraction shown in Amy’s problem in its lowest terms
12
2
=
30
5
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
What weight must be added to the left side of the scales to balance them up
with the right side?
750g
2.5Kg
2 500g (2.5 Kg) - 750g = 1 750g
1 750g or 1.75Kg or 1Kg 750g
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Jody has the money shown.
She buys 3 packets of crisps and 2 bars of
chocolate
How much money will Jody have
left?
3 packets of crisps 32p x 3 = 96p
2 bars of chocolate 47p x 2 = 94p
96p + 94p £1.90
There is £5.17 in coins
32p
47p
£5.17 - £1.90 = £3.27
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Jack has three different rectangles each with an area of 24cm2
Each side of his rectangles is bigger than 1cm.
Each side is a whole number of centimetres long.
What are the possible perimeters of his three rectangles?
Find the lengths of the sides of each rectangle using the
area as a starting point
12cm
3cm
2cm
Perimeter 28cm
6cm
8cm
4cm
Perimeter 22cm
Perimeter 20cm
The three rectangles may be used to help you with any calculation you may need
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
A single cube has sides 13 mm long.
Ellie makes a chain of attached cubes like the one shown.
What is the length of Ellie’s chain of cubes when it is
rounded to the nearest centimetre?
There are 19 cubes
The total length of the cubes is 19 x 13mm = 247mm
247mm = 24.7cm
24.7cm rounded to the nearest centimetre is 25cm
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Tom works out this brackets problem.
What is his answer?
( 7 x 5 ) + ( 55 ÷ 5 ) + ( 9 x 4 ) + ( 108 ÷ 6 )
35
11
36
35 + 11 + 36 + 18 = 100
18
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Lucy enters the number 4327.5 into her calculator.
She meant to enter 4523.7
What is the difference between the number she wanted to put
in and the number she put in?
4523.7 - 4327.5
= 196.2
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
The difference between two numbers is 25.
30 -
5
= 25
Their product is 150.
30 x
5
= 150
30 +
5
= 35
Their total is 35.
What is the answer when one number is divided by the other?
The two numbers are 5 and 30
÷
30
5
= 6
Or possibly
5
÷
30
=
1/6
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
James draws some shapes on a grid. Each grid square is 1cm long
and 1cm wide.
A. Which shapes have only
one acute angle?
3
3 and 4
2
1
5
4
B. Which shape has only right
angles?
5
C. Which shapes each have an
area of 12.5cm2?
1 and 4
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Tom earns £1.50 for working on day one and double this amount on
day two.
On days three, four and five he continues to earn double the amount
earned on the previous day.
How much has Tom earned altogether over the five days he
works?
Day 1
£1.50
Day 2
£3.00
Day 3
£6.00
Day 4
£12.00
Day 5
£24.00
Total
£46.50
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Kayleigh finds the sum of the non-prime numbers between 40 and 50.
She then adds the digits of her answer together.
What is the total of the digits?
The numbers are 42, 44, 45, 46, 48 and 49
The total is 274
The sum of the digits is 13
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
The area of each circle is 124cm2.
The red square has sides of 12cm.
What is the area of the part of the drawing shaded yellow?
The two semi-circles
are the same area as
one large circle, i.e.
124cm2
The area of the whole
square is
12cm x 12cm = 144cm2
The area of the yellow part is
144cm2 - 124cm2 = 20cm2
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Fred’s teacher asks him to add together each pair of corner numbers
in this target board.
Write down Fred’s answers.
19 12 21 17
11 24 14 13
40 32 9 30
16 18 10 15
There are six possible combinations
15 + 16 = 31
15 + 17 = 32
16 + 17 = 33
19 + 15 = 34
19 + 16 = 35
19 + 17 = 36
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
y
A
The interval on the grid is 1 or -1.
Jade translates her shape to the
second quadrant. One new line
has been drawn for you
B
-x
What are the co-ordinates of
the new position of the points
A and B?
x
0
A (- 5, 6)
B (- 2, 1)
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Tom follows the route around the drawing as shown by the arrows and
finishes in the yellow middle square.
Every time he enters a circle he adds 0.5. Every time he enters a square
he subtracts 0.2
0.5 0.3 0.8 0.6
1.7 1.5 1.1
1.2 1.4 0.9
What number does he finish with in the yellow square?
PRIMARY SCHOOLS’ MATHEMATICS CHALLENGE 2008 SEMI FINAL
Look at the number grid below and read it from left to right in all questions
Row 1 2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
Row 2 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Row 3 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
Row 4 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
A.
What is the total of all the numbers in row 1?
18 x 7 = 126
B.
126 + 9 = 135
Find the product of the first and last prime numbers in row 3 ?
37 x 43 = 1591
C.
In row 2 which pair of numbers have a product of 475 ?
19 x 25 = 475
D.
In row 4 which five consecutive numbers total 250?
48, 49, 50, 51, 52