






















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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
 tincture.
 wasto swallow
  upon
 a
  and
 for

 stomach,
This 
the student
fasting
threedaysfollowing
 acephalic
  
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)

2 p 3  p dp

2
MECHANICS
1
A particle P moves in a straight line with constant velocity. Initially P is at the
point A with position vector (2i  j) m relative to a fixed origin O, and 2 s later it
is at the point B with position vector (6i + j) m.
(a) Find the velocity of P.
(b) Find, in degrees to one decimal place, the size of the angle between the
direction of motion of P and the vector i.
Three seconds after it passes B the particle P reaches the point C.
(c) Find, in m to one decimal place, the distance OC.
2
A particle of mass 0.3 kg lies on a smooth plane inclined at an angle  to the horizontal,
where tan   34 . The particle is held in equilibrium by a horizontal force of magnitude Q
newtons. The line of action of this force is in the same vertical plane as a line of greatest
slope of the inclined plane. Calculate the value of Q, to one decimal place.
3
A body of mass 2kg is held in limiting equilibrium on a rough plane inclined at 20° to the
horizontal by a horizontal force X. The coefficient between the body and the plane is 0.2.
Modelling the body as a particle find X when the body is on the point of slipping
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
(a)
Up the plane
(b)
Down the plane
4
A car is moving along a straight road with uniform acceleration. The car passes a checkpoint A with a speed of 12 m s-1 and another check-point C with a speed of 32 m s-1. The distance
between A and C is 1100 m.
(a)
Find the time, in seconds, taken by the car to move from A to C.
Given that B is the mid-point of AC,
(b)
find, in m s-1 to 1 decimal place, the speed with which the car passes B.
5
A particle of mass 2kg is attached to the lower end of a string hanging vertically. The
particle is lowered and moves down with an acceleration of 0.2 ms-2. Find the tension in
the string.
6
A parcel of mass 8 kg rests on a smooth slope, and is connected by a light inextensible
string which passes over a smooth pulley to a mass of 2kg, which hangs freely. The
system is in equilibrium. Find the angle of the slope.
PURE MATHS
7
(a)
(b)
8
(b)
sin x  12 cos x  1  0
 
(b)
log 2 x 2  4 x  5  log 2 x 2  x  4
log x 2  log 2 x  2
(d)
2 log 4 x  log 4  x  1 
tan 2 x  2 tan x  1  0
Solve the following equations for x:
(a)
(c)
10
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 
32 x  5 3x  4  0




1
2
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
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Answers:
5 7
(3) 2.50
,
4 4
1
1
C: (1) t 2  t  c (2) p 4  p 2  c
2
2
A: (1)
3π 7π
,
4 4
(2)
(3)
(1a) 2𝒊 + 𝒋 (1b) 𝜃 = 27𝑜 (1c) 𝑂𝐶 = 12.6𝑚
(4a) 50 s
(4b) 24.2 m s-1
(5) 19.2 N
(7a) 1 (7b) tanx
1
3
(9b) x   ,  1
(8a)
 5
4
,
4
(9c) x = 2
(11) x  t 3  t 2  t  1, x  7
1
2
x2  43 x 2  x  c
(2) 2.2N
(6) 14.5o
π 2π 4π
(8b) ,
,
2 3 3
(9d) x  1  3
3
(3a) 12N (2sf) (3b) 3.0N (2sf)
(9a) x  log 3 4 or x = 0
(10) 4.40cm, 18.90cm2
(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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