Solve 3(4 x – 2) = 7 – 8 x.
[3]
Represent the solution to the inequality –2 
4n 
4 on the number line below.
[2]
Factorise 2x2 – 14x.
[2]
When selling an apartment, the selling price can be calculated using the price per square metre of floor area.
The scatter diagram shows the price per square metre of 12 apartments and their distance from Educastle city centre. It also shows the line of best fit for the data.
Price per square metre in pounds (£)
Distance from Educastle city centre in miles
Describe the relationship between the price per square metre of an apartment and its
distance from Educastle city centre.
[1]
Use the line of best fit to estimate the price per square metre of an apartment that is
4 miles from Educastle city centre.
[1]
Ellie says,
“All apartments 6 miles from Educastle city centre cost £4600 per square metre.”
Is Ellie’s statement correct?
Yes No
Give the reason for your answer.
[1]
The table below shows information about the house prices of 35 houses on a street outside Educastle city centre.
| Price, p, thousand pounds | Frequency |
100  p  150 | 8 |
150  p 200 | 12 |
| 200 p 250 | 9 |
250  p  300 | 5 |
| 300 p 350 | 1 |
Calculate an estimate for the mean house price on the street.
[4]
The diagram shows a square inside a circle.
Each corner of the square lies on the circumference of the circle. The length of each side of the square is 13 cm.
Calculate the area of the circle. Give your answer correct to 1 decimal place.
You must show all your working.
[5]
Yasmin has two bags, Bag A and Bag B.
Each bag contains some red counters and some blue counters.
Bag A contains 2 red counters and 3 blue counters. In Bag B the number of red counters is three times the number of blue counters.
Yasmin randomly chooses one counter from Bag A and then one counter from Bag B.
Complete the probability tree diagram.
[3]
Calculate the probability that Yasmin chooses at least one blue counter.
[3]
Five straight-line graphs and their equations are shown below. Draw a line to connect each graph to its equation.
One has been completed for you.
[2]
Circle the equation of the straight line that is parallel to y = 3x + 5.
[1]
Make y the subject of the following formula.
[2]
Calculate the length of AB.
[3]
[3]
[6]
A wooden block is shown below.
Zachary saws off a small block that is 30% of the original wooden block.
The mass of Zachary’s small block is 5·4 kg. The density of the wood is 0·75 g/cm3.
Calculate the volume of the original wooden block.
[5]
Zachary converts the volume of the wooden block from cubic centimetres (cm3) to cubic inches (in3). He uses the conversion 2·5 cm ≈ 1 inch.
Zachary says,
“To convert the volume from cm3 into in3 I must divide the volume by 2·5.”
Explain why Zachary’s method is incorrect.
[1]
[1]
[1]
[1]
ABC is a triangle.
The lines AC and DE are parallel. D is a point on the line AB such that AD: DB is in the ratio 5: 2. The length of AC is 23·8 cm.
Calculate the length of DE.
[2]
Prove that (n + 4)2 – (n – 1)2 is a multiple of 5 for all integer values of n.
You must use an algebraic method (not trial and improvement).
[3]
Isaias recorded the number of hours of sleep he had each night last year.
The box plots below show the results.
On which day was the median number of hours of sleep the greatest?
[1]
Calculate the range of the number of hours of sleep on Fridays.
[1]
Complete the following sentence. On 25% of Mondays Isaias slept longer than
…………........ …….. hours…………........ …….. minutes.
[1]
Isaias recorded the number of hours of sleep he had on the 52 Thursdays last year.
On how many Thursdays last year did Isaias sleep for 7 hours or less?
[2]
Which day of the week is Isaias’s sleep pattern the most consistent?
Give a reason for your answer.
[1]
A hemisphere, centre O, with radius 9 cm is cut into 10 equal pieces.
One piece has been removed.
Calculate the total surface area of the removed piece.
You must show all your working.
[5]
[4]
Calculate the maximum number of tins that can be filled using paint from one of the tanks.
[4]
The diagram below shows points A, B and C on the circumference of a circle with centre O.
The line DAE is a tangent to the circle.
Give a reason for each step of your answer.
[4]
A logo is created by arranging 8 of these kites inside an octagon.
Calculate the area of one shaded triangle.
Hence, calculate the total area of the shaded region of the logo.
[6]
Rohan invests money in a compound interest account with interest paid annually.
The interest rate stays the same for the period of the investment. In 4 years, his investment has increased in value from £7800 to £8950.70.
How much will his investment be worth after a further 3 years?
Give your answer correct to the nearest pound.
After a further 3 years, Rohan’s investment is worth………........ ….…….. to the nearest pound.
[5]
y is directly proportional to the square root of x.
y = 0·14 when x = 0·49.
Find the formula for y in terms of x.
[3]
Calculate the value of y when x = 5·29.
[1]
A large pyramid is shown below.
The base of the large pyramid is a square with sides of length 40 cm.
A small pyramid is removed from the top of the large pyramid. The base of the small pyramid is a square with sides of length 16 cm.
What percentage of the large pyramid’s volume has been removed?
[3]
A boat makes the following journey from Port A to Port C.
• It sails 30 km on a bearing of 108° from Port A to Port B. • It then sails 42 km on a bearing of 065° from Port B to Port C.
On its return journey, the boat travels directly from Port C to Port A. This journey takes 1 hour and 45 minutes.
Calculate the average speed of the boat on its return journey.
The average speed of the boat is………........ ….…….. km/h
[6]
The diagram below shows Circle A and Circle B.
Circle A has its centre at the origin. Circle B has its centre at (7,0) and passes through the origin. Circle A and Circle B touch at the same point on the x axis.
Write down the equation of Circle A.
[2]
[2]
The graph below shows a curve and a straight line.
Use five vertical strips of equal width to calculate an estimate for the area of the shaded
region. You must show all your working.
[5]
A tank containing 1000 litres of water was emptied in two stages.
During the first stage, 400 litres were emptied out of the tank at a constant rate. This took x minutes. During the second stage, the remaining water was emptied out at a different constant rate. This took x – 26 minutes.
During the second stage, the rate of flow of the water from the tank was 17 litres per minute faster than the rate of flow during the first stage.
Show that 17x2 – 642x – 10 400 = 0.
[5]
By solving 17x2 – 642x – 10 400 = 0, find the value of x.
You must show all your working.
[3]
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