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

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
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“I was at the mathematical school, where the master taught his pupils after a method scarce imaginable to
us in Europe. The proposition and demonstration were fairly written on a thin wafer, with ink composed of

 
 wasto swallow
  upon
 a
  and
 for
 stomach,
 acephalic
tincture.
This 
the student
fasting
threedaysfollowing
 
eat nothing but bread and water. As the wafer digested the tincture mounted to the brain, bearing thee
proposition along with it.”
Jonathan Swift in Gulliver’s Travels
AS Maths Assignment  (xi)
Remember - you need to complete this assignment, so start early and use the help available!
DRILL
Section A

Solve the following equations on the interval
(1) sin 2 x  1
(2)
0  x  2
 1

cos x   
2
2

(3)
 x
tan    3
2
y  (2 x  1)( x  1)( x  4)
(3)
y
1
4
x
(3)

x  1 dx
Section B Sketch the following curves:
(1)
y  x  2 2
(2)
Section C Evaluate each of the following:
(1)
 2t  1 dt
(2)
2p
3
 p dp

2
STATISTICS
1
An ordinary die and two coins are thrown together. Find the probability that it is:
(a)
(b)
(c)
(d)
2
Seven identical balls are marked respectively with the numbers 1 to 7 inclusive. The
number on each ball represents the score for that ball. The seven balls are put into a bag.
If two balls are chosen at random one after the other, find the probability of obtaining a
total score of 11 or more:
(a)
3
two heads and a number less than three,
different faces on the coins and a 4 on the die,
the same face on the coins and an odd number on the die,
a six and at least one head.
If the first ball is replaced
(b)
If the first ball is not replaced
Skewness can be assessed by using the following formula:
3(mean  median)
standard deviation
Calculate this numerical measure of skewness for the following distribution which shows
the ages of patients in a hospital ward: 58, 39, 30, 48, 27, 16, 56, 56, 65, 63
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
4
The weights (in kilograms) of two groups of students are measured and summarised:
Group A
Group B
(a)
(b)
5
x
550
?
n
10
15
x2
32 500
63 500
Calculate the mean and variance of group A
The two groups are now treated as a single sample of 25 students.
Given that the new variance is 60.8, calculate the mean of group B.
The number of patients attending a hospital trauma clinic each day was recorded over
several months, giving the data in the table below.
No of
patients
Frequency
10-19
20-29
30-34
35-39
40-44
45-49
50-69
2
18
24
30
27
14
4
These data are represented by a histogram. Given that the bar representing the 20-29 group
is 2cm wide and 7.2cm high,
(a) Estimate the number of days on which there were between 32 and 41 patients attending
the clinic.
(b) Calculate the dimensions of the bars representing the groups (i) 30-34
(ii) 50-69
(c) Use linear interpolation to estimate the median and quartiles of these data
(d) The lowest and highest numbers of patients were 14 and 67 respectively. Represent
these data with a boxplot on graph paper and describe the skewness of the distribution.
6
For each of the following situations, draw a venn diagram, state the value of P A  B
and evaluate P A | B
(a)
P A  0.3, P( B)  0.3, P( A  B)  0.2
(b)
P A  0.5, P( B)  0.2, P( A  B)  0.6
PURE MATHS
7
(a)
(b)
8
A
to write sin 2 x  cos 2 x in its simplest form.
H
A
sin x
to write
in its simplest form.
cos x
H
Solve the following equations on the interval 0  x  2
(a)
9
O
and cos x 
H
O
Use sin x 
and cos x 
H
Use sin x 
tan 2 x  2 tan x  1  0
sin x  12 cos x  1  0
(b)
Solve the following equations for x:
(a)
32 x  5 3x  4  0
 
(b)
log 2 x 2  4 x  5  log 2 x 2  x  4
(c)
log x 2  log 2 x  2
(d)
2 log 4 x  log 4  x  1 




1
2
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10
Find the length of r and hence the total area of the shape,
4cm
95°
r
r
60°
40°
11
Given that
dx
 3t 2  2t  1 and that x = 2 when t = 1, find the value of x when t = 2
dt
Answers:
3π 7π
,
A: (1)
4 4
(2)
5 7
,
(3) 2.50
4 4
1 4 1 2
p  p c
2
2
(1a) 1/12
(1b) 1/12
(1c) ¼
(2b) 4/21
(3) – 1.16 (4a) A: 55, 225
(5bi) 19.2cm, 1cm (5bii) 0.8cm, 4cm
C: (1) t 2  t  c (2)
(5d)
(8b)
(6a) 0.9, 2/3 (6b) 0.9, ½
1
2
x2  43 x 2  x  c
3
(1d) 1/8
(2a) 10/49
(4b) 65.8kg
(5a) 55
(5c) Q1 = 31.5, Q2 = 37.1, Q3 = 42.3
(7a) 1 (7b) tan x
π 2π 4π
, ,
(9a) x  log 3 4 or x = 0
2 3 3
(10) 4.40cm, 18.90cm2
(3)
(8a)
 5
4
,
1
(9b) x   ,  1
3
(11) x  t 3  t 2  t  1, x  7
4
(9c) x = 2 (9d) x  1  3
(12)
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M THS
ASSIGNMENT COVER SHEET
Name
Current Maths Teacher
Please tick honestly:
Yes
No - explain why.
Have you ticked/crossed
your answers using the
answers given?
Have you corrected all the
questions which were
wrong?
How did you find this homework?
Use this space to outline any problems you’ve had and how you overcame them as well
as the things which went well or which you enjoyed/learned from.
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