The numbers from 1 to 14 are shown in the Venn diagram.
List the members of the set A 
B
(1)
List the members of the set Bʹ
A number is picked at random from the numbers in the Venn diagram.
(1)
Find the probability that this number is in set A but is not in set B.
(2)
Toy cars are made in a factory. The toy cars are made for 15 hours each day. 5 toy cars are made every 12 seconds.
For the toy cars made each day, the probability of a toy car being faulty is 0.002
Work out an estimate of the number of faulty toy cars that are made each day.
(4)
On the grid, draw the graph of y = 7 – 4x for values of x from −2 to 3
(3)
Here is a list of six numbers written in order of size.
4 7 x 10 y y
The numbers have
a median of 9 a mean of 11
Find the value of x and the value of y.
(4)
Write 5.7
10–3 as an ordinary number.
(1)
Write 800 000 in standard form.
(1)
A rocket travelled 100 km at an average speed of 28 440 km/h.
Work out how long it took the rocket to travel the 100 km. Give your answer in seconds, correct to the nearest second.
(3)
Solve 5(4 – x) = 7 – 3x Show clear algebraic working.
(3)
Hence, solve y2 – 2y – 48 = 0
(1)
Here is a 10-sided polygon.
Work out the value of x.
(4)
In a sale, normal prices are reduced by 20%
A bag costs 1080 rupees in the sale.
Work out the normal price of the bag.
(3)
A = 2 
343 B = 16 337
Find the highest common factor (HCF) of A and B.
(1)
Express the number A 
B as a product of powers of its prime factors. Give your answer in its simplest form.
(2)
The diagram shows trapezium ABCD in which BC and AD are parallel.
The trapezium has exactly one line of symmetry.
BC = 8.4 cm AD = 17.6 cm
The trapezium has area 179.4 cm2
Work out the size of angle ABC. Give your answer correct to 1 decimal place.
(6)
Solve the simultaneous equations
7 x – 2 y = 34 3 x + 5 y = −3
Show clear algebraic working.
(4)
Jan invests $8000 in a savings account. The account pays compound interest at a rate of x% per year.
At the end of 6 years, there is a total of $8877.62 in the account.
Work out the value of x. Give your answer correct to 2 decimal places.
(3)
F is inversely proportional to the square of v.
Given that F = 6.5 when v = 4
find a formula for F in terms of v.
(3)
Harry has two fair 5-sided spinners.
Spinner A Spinner B
Harry is going to spin each spinner once.
Complete the probability tree diagram.
(2)
Work out the probability that at least one of the spinners will land on green.
(3)
L, M, N and P are points on a circle, centre O
Angle MNP = 58°
Find the size of angle MLP
(1)
A metal block has a mass of 5 kg, correct to the nearest 50 grams. The block has a volume of (1.84 
10–3) m3, correct to 3 significant figures.
Work out the upper bound for the density of the block. Give your answer in kg/m3 correct to 1 decimal place. Show your working clearly.
(4)
The table gives information about the heights, in centimetres, of some plants.
| Height (h cm) | Frequency |
10  h  20 | 35 |
20  h  35 | 45 |
35  h  50 | 75 |
50 h  70 | 40 |
70 h  80 | 8 |
On the grid, draw a histogram for this information.
(3)
Work out an estimate for the number of these plants with a height greater than 40 cm.
(2)
R and S are two similar solid shapes.
Shape R has surface area 108 cm2 and volume 135 cm3 Shape S has surface area 300 cm2
Work out the volume of shape S.
(3)
Express
as a single fraction in its simplest form.
(5)
ABCD is a rhombus.
The diagonals, AC and BD, intersect at the point M. The coordinates of M are (6, −11)
The points A and C both lie on the line with equation 2y + 7x = 20
Find the exact coordinates of the point where the line through B and D intersects the y-axis.
(4)
23Curve C has equation y = px3 − mx where p and m are positive integers.
Find the range of values of x, in terms of p and m, for which the gradient of C is negative.
(4)
Here are the first five terms of an arithmetic sequence.
8 15 22 29 36
Work out the sum of all the terms from the 50th term to the 100th term inclusive.
(4)
The curve with equation y = g(x) is transformed to the curve with equation y = −g(x) by the single transformation T.
Describe fully the transformation T.
The diagram shows the graph of y = f(x)
(1)
On the grid, draw the graph of y = 2f(x – 1)
(2)
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