Unit 1 (NC)
What is 9-3
1/729
Write as one term
(2a2b3 x 4ab3)2
64a6b12
The cross section of the prism is a trapezium.
The lengths of the parallel sides of the trapezium are 11 cm and 7 cm.
The perpendicular distance between the parallel sides of the trapezium is 10 cm.
The length of the prism is 12 cm.
Work out the volume of the prism.
1080cm3
Helen’s savings increased from £155 to £167.40.
Work out the percentage increase in Helen’s savings.
8% increase
A type of cat food has 10 packets in a box.
The probability that the variety is chicken is 0.7
What is the probability that the variety is not chicken?
0.3
Write the number 28 000 000 in standard form.
2.8 x 107
Factorise
12d2e - 16d2e2
4d2e(3 - 4e)
A square of side 15.7 cm is made from a length of wire.
The same length of wire is then made into a circle.
Work out the diameter of the circle.
20
Jonah invests £2000 for 2 years in a savings account.
He gets 3% per annum compound interest.
How much money is in Jonah’s savings account at the end of 2 years?
£2121.80
The probability that a biased coin will land on Heads is 0.43
Azmol is going to throw the coin 600 times.
Work out an estimate for the number of times the coin will land on Tails.
What is the smallest number with exactly 7 factors?
64
Simplify
7x - 2(x - 3y) - 4y
5x + 2y
From point A, Stanley walks 200 m due east to point B.
From B, he then walks 160 m due south to point C.
Work out the length of AC.
Give your answer correct to 3 significant figures.
256
he Grand Old Duke of York had 10 000 men. He lost 10% of them on way to the top of the hill, and he lost 15% of the rest as he marched them back down the hill.
What percentage of the 10 000 men were still there when they reached the bottom of the hill?
76.5%
A teacher has some coins in his pocket.
He is going to take one of the coins at random.
He says: There are more than 4 coins in my pocket. The total value of them is 25p. The probability I take 1p is 1/4.
List all the coins in his pocket.
1p, 1p, 2p, 2p, 2p, 2p, 5p, 10p
A giant thresher shark weighing 1250 pounds, believed to be the heaviest ever caught, was landed by fisherman Roger Nowell off the Cornish coast in November 2007. The fish was sold by auction at Newlyn Fish Market for £255. Roughly, what was the cost per pound?
20p
Dilly is 7 years younger than Dally. In 4 years time she will be half Dally’s age. What is the sum of their ages now?
13
Percy sells paint in standard tins and large tins.
The standard tin covers 40 m2 and the large tin covers 60 m2. The standard tin and the large tin are mathematically similar. The volume of the large tin is 50% more than the volume of the standard tin.
Both tins are cylinders. The radius of the standard tin is 10 cm.
Calculate the radius of the large tin.
11.4cm
Sally divided a two-digit number by another two-digit number.
Her answer was 3.18181818 ......
Find two numbers that Sally could have used
35 and 11 or 70 and 22
Three monkeys Barry, Harry and Larry met for tea in their favourite café, taking off their hats as they arrived. When they left, they each put on one of the hats at random. What is the probability that none of them left wearing the same hat as when they arrived?
1/3
A certain positive integer has exactly eight factors. Two of these factors are 15 and 21.
What is the sum of all eight factors?
192
Andrew divided some apples into six equal piles. Boris divided the same number of apples into five equal piles. Boris noticed that each of his piles contained two more apples than each of Andrew’s piles.
How many apples did Andrew have?
60
A water tank is in the shape of a cylinder.
It has diameter 0.44 m and height 1.2 m.
Water flows into the tank at a rate of 20 litres per minute. 1 litre = 1000 cm3. How long will it take to fill the tank, in mm, to two decimal places.
9.12 minutes
When I have walked 20% of the way to school, I have 1200 metres more to walk than when I have 20% of the walk remaining.
How far, in metres, is it from my home to my school?
2000
Six students who share a house all speak exactly two languages. Helga speaks only English and German; Ina speaks only German and Spanish; Jean-Pierre speaks only French and Spanish; Karim speaks only German and French; Lionel speaks only French and English whilst Mary speaks only Spanish and English.
If two of the students are chosen at random, what is the probability they speak a common language?
0.8