NUMBERS
A fuel tank is 3/4 full. Bill drives to York and uses 1/10 of a tank of fuel. What fraction of fuel remains in the tank?
13/20
Find the highest common factor (HCF) of 36 and 60
12
In a club there are 𝑥 Year 7 students and 𝑦 Year 8 students. If three students leave the club, find a formula for 𝐶, the number of students left.
C = 𝑥 + 𝑦 − 3
6𝑎 − 5 = 25
a = 5
Find the sum of the interior angles in a 13-sided polygon.
1980
In a theater, 70% of people are adults. The rest are children. Of these children, 1/3 are girls. What fraction of all the people at the theater are boys?
1/5
Madeira cake mixes flour, sugar and butter in the ratio 5 : 3 : 2. How much flour and butter is required to mix with 75 g sugar?
125 g flour
50g butter
Find a formula for 𝐶, the mean of three values, 𝑥, 𝑦 and 𝑦.
C = (x+2y)/3
18 = 6(1 + 𝑦)
y = 2
A regular polygon has an exterior angle of 36°. How many sides does the regular polygon have?
10 sides
Aleeza sells her headphones second-hand for £52.40, making a 20% loss on the price she originally paid. How much did Aleeza pay for the headphones?
65.50
The angles in a quadrilateral are in the ratio 5 : 7 : 4 : 2. Find the size of each of the angles.
100°, 140°, 80°, 40°
The cost of hiring a scooter is £3 per day plus an administrative charge of £𝑥. Find a formula for the cost 𝐶 of hiring a scooter for 𝑦 days.
C = x+3y
6𝑥 + 5 = 3𝑥 − 10
x = -5
A regular polygon has an interior angle of 150°. How many sides does the regular polygon have?
12
Maria buys a mobile phone for £57.20 in an online sale. If the phone was reduced by 35%, what was its original price?
88.00
120 ml of orange drink is made with cordial and water in the ratio 1 : 4. To make the drink stronger, 10 ml more of cordial is added. What is the ratio of cordial to water for the new drink?
17:48
(2𝑥 + 3)(𝑥 − 4)
2𝑥^2 − 5𝑥 − 12
2𝑥 − 7 ≤ 𝑥 + 1
x ≤ 8
A cylinder with height ℎ 𝑐𝑚 and radius 6 𝑐𝑚 has the same volume as a sphere with radius 9 𝑐𝑚. Find the value of h.
h = 27cm
Elia has 10 hours of free time per week. She spends 7/20 of her free time doing homework. She spends 4 hours per week watching TV and films. The rest of her free time is split between football and hockey in the ratio 3∶2. Find the percentage of her free time Elia spends on football.
15%
A school contains 910 students. The ratio of boys to girls is 4 ∶ 3. 15% of the boys are left-handed, and 2/15 of the girls are left-handed. Find the percentage of students in the school that are left-handed. Give your answer to 1 decimal place.
14.3%
(2𝑥 + 3)(𝑥 − 1)(𝑥 + 5)
2𝑥^3 + 11𝑥^2 + 2𝑥 − 15
x − 2 < 3𝑥 + 1 ≤ 19
− 3/2 < 𝑥 ≤ 6
Colin has a circular pond of radius 1.3 meters. He wants to put an edging around the pond. Edging costs £12.99 per meter and is sold in one-meter lengths. How much will it cost Colin to put the edging around his pond?
£116.91