THE WESTMINSTER SCHOOL, DUBAI
YEAR 11 – EXTENDED PRACTISE PAPER
1
Triangle PQR is mathematically similar to triangle XYZ.
(a)
Find YZ.
(b)
YZ = ........................................... cm [2]
The area of triangle XYZ is 63.6 cm2 .
Calculate the area of triangle PQR.
......................................... cm2 [3]
2
A line joins the points A( -3,8 ) and B( 2, -2 ).
(a)
Find the co-ordinates of the midpoint of AB.
(....................... , .......................) [2]
2
(b)
(c)
(d)
Find the equation of the line through A and B.
Give your answer in the form y =mx + c.
y = ....................................... [3]
Another line is parallel to AB and passes through the point (0, 7).
Write down the equation of this line.
y = ....................................... [2]
Find the equation of the line perpendicular to AB which passes through
the point (1, 5).
Give your answer in the form ax+ by+c = 0 where a, b and c are integers.
................................................. [4]
3
3
In the pentagon ABCDE, angle EAB = angle ABC = 110° and angle CDE = 84°.
Angle BCD = angle DEA = x°.
(a)
Calculate the value of x.
x = ........................... [2]
(b)
BC = CD. Calculate angle CBD.
(c)
Angle CBD = ........................... [1]
This pentagon also has one line of symmetry. Calculate angle ADB.
Angle ADB = ........................... [2]
4
A train journey takes one hour. The diagram shows the speed-time graph for this
journey.
4
(a)
Calculate the total distance of the journey. Give your answer in kilometres.
(b)
……………………….. km [3]
Convert 3 kilometres/minute into metres/second.
(i)
(ii)
……………………….. m/s [2]
Calculate the acceleration of the train during the first 4 minutes.
Give your answer in metres/second2 .
……………………….. m/s2 [2]
5
200 people run 10km. The table shows some information about the times,
t minutes, taken to run the 10km.
(a)
Howard takes 40 minutes to run the 10km.
Calculate his average speed in kilometres per hour.
........................................ km/h [2]
5
(b)
Calculate an estimate of the mean time.
..........................................min [4]
(c)
Complete the histogram to show the information in the table.
[4]
6
(d)
(i)
Use the frequency table opposite to complete the cumulative
frequency table.
[2]
(ii)
Draw a cumulative frequency diagram to show the information in
the table above.
[3]
(iii)
Use your diagram to find
(a)
the median,
..........................................min [1]
7
(b)
the 90th percentile,
..........................................min [1]
(c)
the number of people who took more than 58 minutes to run
the 10 km.
................................................. [2]
6
(a)
Describe fully the single transformation which maps shape P onto shape Q.
......................................................................................................................
................................................................................................................... [2]
8
(b)
On the grid above, draw the image of shape P after reflection in the line
y = –1.
[2]
7
The probability that a plant will produce flowers is
7
8
.
The flowers are either red or yellow.
If the plant produces flowers, the probability that the flowers are red is
(a)
(i)
3
4
.
Complete the tree diagram by writing a probability beside each
branch.
[2]
(ii)
Calculate the probability that a plant, chosen at random, will
produce red flowers.
................................................ [2]
(iii)
Two plants are chosen at random. Calculate the probability that
both will produce red flowers.
................................................. [2]
9
(b)
(c)
Alphonse buys 200 of these plants.
Calculate the number of plants that are expected to produce flowers. .
................................................ [2]
Gabriel has 1575 plants with red flowers. Estimate the total number of
plants that Gabriel has.
................................................. [2]
8
(a)
Find g(5).
................................................. [1]
(b)
Find hhh(2).
................................................. [3]
(c)
Find x when g (x) = h(3).
x = ................................................ [2]
(d)
Find x when
g-1
(x) = –1
x = ................................................ [2]
10
9
(a)
(i)
Find, as a single column vector, p + 2q.
[2]
(ii)
Calculate the value of | p + 2q |.
................................................ [2]
(b)
In the diagram, CM = MV and OL = 2LV.
O is the origin. ⃗⃗⃗⃗⃗⃗
𝑶𝑪 = c and ⃗⃗⃗⃗⃗⃗
𝑶𝑽 = v.
Find, in terms of c and v, in their simplest forms
(i)
⃗⃗⃗⃗⃗⃗
CM,
................................................ [2]
11
(ii)
the position vector of M,
................................................ [2]
(iii)
⃗⃗⃗⃗⃗⃗
ML .
................................................ [2]
10
The diagram shows a quadrilateral ABCD.
Angle BAD = 49° and angle ABD = 55°.
BD = 80m, BC = 95m and CD = 90m.
(a)
Use the sine rule to calculate the length of AD.
AD = ............................................ m [3]
12
(b)
Use the cosine rule to calculate angle BCD.
(c)
Angle BCD = ................................................ [4]
Calculate the area of the quadrilateral ABCD.
(d)
........................................... m2 [3]
The quadrilateral represents a field. Corn seeds are sown across the
whole field at a cost of $3250 per hectare. Calculate the cost of the corn
seeds used.
1 hectare = 10000m2
$ ................................................ [3]
13
11
In the diagram, B, C, D and E lie on the circle, centre O.
AB and AD are tangents to the circle. Angle BAD = 48°.
(a)
Find
(i)
angle ABD,
Angle ABD = ................................................ [1]
(ii)
angle OBD,
Angle OBD = ................................................ [1]
(iii)
angle BCD,
Angle BCD = ................................................ [2]
(iv)
angle BED.
Angle BED = ................................................ [1]
14
(b)
(c)
The radius of the circle is 15 cm.
Calculate the area of triangle BOD.
......................................... cm2 [2]
Give a reason why ABOD is a cyclic quadrilateral.
......................................................................................................................
......................................................................................................................
……………………………………………………......................................... [1]