A bag contains red bricks, yellow bricks and green bricks only.
The incomplete table and an incomplete pie chart give information about the colours of the bricks in the bag.
Find the number of red bricks.
(2)
A box contains 9 red bricks and 6 green bricks only.
Asha takes a brick from the bag and a brick from the box.
Complete the tree diagram opposite.
(2)
Calculate the probability that exactly one of the bricks is green.
(2)
A farmer grows 300 pumpkins.
The pumpkins are small or medium or giant.
It cost the farmer $1.25 to grow each small pumpkin.
He sells each small pumpkin for $1.30
Calculate the percentage profit the farmer makes on each small pumpkin he sells.
(2)
The farmer sells each medium pumpkin for 20% more than he sells each small pumpkin.
Calculate the price, in $, that the farmer sells each medium pumpkin for.
(2)
Of the 300 pumpkins, 28% are small.
Calculate the number of small pumpkins the farmer grows.
(2)
The remaining pumpkins are medium or giant.
The ratio of medium pumpkins to giant pumpkins is 3: 5
Calculate the number of giant pumpkins the farmer grows.
(2)
The farmer sells all of his giant pumpkins for the same price.
The farmer’s profit from giant pumpkins is
30% of the selling price of the first 50 giant pumpkins sold, 60% of the selling price of the next 40 giant pumpkins sold, 90% of the selling price of the remaining giant pumpkins sold.
Calculate the percentage of the total selling price of the giant pumpkins that is the farmer’s profit from giant pumpkins.
Give your answer to the nearest whole number.
(4)
The table below shows information about the prices of secondhand cars for sale at a garage.
| Price of secondhand car ($x) | Frequency |
6000  x  12000 | 3 |
12000  x  20000 | 23 |
20000  x  34000 | 21 |
34000  x  40000 | 34 |
40000  x  62000 | 10 |
Calculate an estimate, in dollars, for the mean price of a secondhand car at this garage.
(4)
Each interior angle of a regular polygon is 172°
Calculate the number of sides of the polygon.
(2)
The length of each side of the regular polygon is 5.2 cm to 2 significant figures.
Calculate, in cm2 to 3 significant figures, the upper bound of the area of the polygon.
Sumof interior angles of polygon 
(6)
Part of the curve C with equation y 
x2 x 
is drawn on the grid.
By drawing a suitable straight line on the grid, find estimates, to one decimal place, for the solutions of the equation
(2)
The equation of curve D is given by
Complete the table of values for y 
x3 
x2 
3x, giving your values to 2 decimal places where necessary.
| x |  2 |  1.5 | 1 |  0.5 | 0 | 0.5 | 1 | 1.5 | 2 |
| y | 2 | 3 | 1.63 | 0 |  1.13 | 6 |
(2)
On the grid opposite, plot the points from your completed table and join them to form a smooth curve.
(2)
Curve C and curve D intersect twice in the range 
2 
x 
2
Write down the coordinates, to one decimal place, of these 2 points of intersection.
(1)
Work out the equation of the line that passes through these 2 points of intersection.
Give your answer in the form y = mx + c where the values of m and c are given to one decimal place.
Show your working clearly.
Turn over for a spare grid if you need to redraw your curve.
Only use this grid if you need to redraw your curve.
(3)
The Venn diagram shows information about the numbers of students who play Rugby (R), Basketball (B) or Hockey (H).
The number of students who do not play Basketball is 35
Use this information to complete the Venn diagram.
(1)
Find
One of the students is selected at random.
Given that this student plays Hockey,
calculate the probability that they also play Rugby.
Give your answer in the form 
where m and n are integers.
(2)
The functions f, g and h are defined as
f: x 
x2 
2x
Find the inverse function h
1, giving your answer in the form h
1: x 
...
(3)
Figure 1 shows three points A, B and C on a circle with centre O where AOC is a diameter of the circle.
The length of AB is 2 cm less than the length of BC
calculate the range of possible values for the length, in cm to one decimal place, of BC
(7)
f (x) 
3x3 
ax2 
20x 
b where a and b are integers.
(x + 4) is a factor of f(x)
(x 
2) is a factor of f(x)
Use the factor theorem to find the value of a and the value of b
(3)
One solution of the equation 8x3 18x2 5x 6 0 is 
Without using a calculator and showing all your working, find the other 2 solutions of the equation.
Give your answers in exact form.
(5)
Triangle A and triangle B are drawn on the grid opposite.
Describe fully the single transformation that maps triangle A onto triangle B
(3)
Triangle A is transformed to triangle C under an enlargement with scale factor 3 and centre of enlargement (6, 
2)
On the grid, draw and label triangle C
(2)
Triangle A is transformed to triangle D under a reflection in the line with equation y = 
3
On the grid, draw and label triangle D
(2)
Triangle B is transformed to triangle E under the transformation with matrix P where
Triangle E is transformed to triangle F under the transformation with matrix Q where
Triangle F is the image of triangle B under the matrix N
Given that the determinant of N is 2
find the coordinates of the vertices of triangle F
a b 
Determinant of matrix 
ad 
bc
Turn over for a spare grid if you need to redraw your triangles.
Only use this grid if you need to redraw your triangles.
(7)
A rocket moves vertically so that at time t seconds, the velocity, v m/s is given by
Find the time, in seconds, when the rocket stops accelerating vertically.
(2)
The vertical displacement, d metres, of the rocket at time t seconds, is given by
The rocket is launched from a height of k metres above horizontal ground. The height, in metres, above ground when the rocket is first instantaneously at rest is 20 metres.
Find the value of k
(5)
Figure 2 shows the triangle OAB in which OA → = 3a and OB → = 15b
Find and simplify an expression for BN → in terms of a and b
(3)
M is the point on OA such that B, N and M are collinear.
Find the ratio OM: MA
Show your working clearly.
(5)
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