Unit 1 (CC)
What is 9-3
1/729
Simplify fully
(2a2b3 x 4ab3)2
64a6b12
100 adults were asked how they keep fit.
Each adult goes to the gym or runs or cycles.
45 of these adults are female.
30 of the 52 adults who go to the gym are female.
35 adults run.
9 males cycle.
How many females run?
11
The 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%
Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have?
360
I have two dogs who eat the same dog food. I have ten tins of dog food. Gnasher eats a tin of food in two days; Nibbles eats a tin of food in five days. What is the latest day on which I must buy some more tins of dog food?
15th day
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
Joan asked each of 60 people to name their favourite vegetable. 24 liked peas. 16 liked carrots. The rest liked mushrooms. What are the angles for each of these sections in a pie chart?
P=144, C=96, M=120
NON CALC
As a decimal, what is the value of (1/9) + (1/11)
0.2020202020...
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
What is 4√75 ÷ 2√3
10
Here are the first 5 terms of a quadratic sequence.
1 3 7 13 21
Find an expression, in terms of n, for the nth term of this quadratic sequence.
n2 -n + 1
a,a,b and 40 are four numbers.
a is the least number.
40 is the greatest number.
The range of the four numbers is 14
The median of the four numbers is 30
Work out the value of a and the value of b.
a=26 b=34
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
A boat is approaching a cliff with a lighthouse on top.
The cliff is 80m high and the lighthouse is 20m tall.
The angle of elevation from the boat to the top of the lighthouse is 25°
Calculate the angle of elevation from the boat to the top of the cliff.
Give your answer to the nearest degree.
20
y2 = (ab)/(a+b)
where a = 3 x 108
and b = 2 x 107
Find y
4.3 x 103
Factorise (x+1)2 - 4(x+1)
(x+1)(x+5)
There are 18 packets of sweets and 12 boxes of sweets in a carton.
The mean number of sweets in all the 30 packets and boxes is 14.
The mean number of sweets in the 18 packets is 10.
Work out the mean number of sweets in the boxes.
20
Ratna invests £1200 for 2 years in a bank account paying r% per year compound interest.
At the end of 2 years, the amount in the bank account is £1379.02.
Calculate r.
7.2%
The sizes in degrees of the interior angles of a pentagon are consecutive even numbers. What is the size of the largest of these angles?
112
The length of the base of the triangle is 2√ 3 cm.
The length of the hypotenuse of the triangle is 6 cm.
Find the area of the triangle
6√ 3
The nth term of a sequence is n2+2n+1.
Find a fully simplified expression (in expanded form) for the (n+1)th term of the sequence.
n2 + 4n + 4
Aaron is asked to choose five integers so that the mode is 2 more than the median and the mean is 2 less than the median. What is the largest possible value of the range of Aaron’s five integers?
15
In a sale, a shopkeeper reduced the advertised selling price of a dress by 20%. This resulted in a profit of 4% over the cost price of the dress. What percentage profit would the shopkeeper have made if the dress had then been sold at the original selling price?
30%
In a right-angled triangle, one of the angles θ has tanθ=1. The length of the hypotenuse is 10cm. What is the area of the triangle?
25cm2