MATH011101
MATH011101
This question paper consists of 5 printed
pages, each of which is identied by the
reference MATH011101
Only approved basic scientic
calculators may be used.
c UNIVERSITY OF LEEDS
Examination for the Module MATH0111
(January 2011)
Ele
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 5 Functions and Dierentiation
These examples count towards the assessment of the module and should be
handed in on Monday 11th November. Do not use a calculator.
Read Bostock & Chandl
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 6 Further Dierentiation, Chain Rule
These examples count towards the assessment of the module and should be
handed in on Monday 18th November. Do not use a calculator.
Read Bostock &
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 4
1. In this question we use the exchange rate 180 = radians.
(a) 240 /180 = 4/3; /10; 4.
(b) 180 /12 = 15 ; 4 180 /5 = 144 ; 9 180 /4 = 405 .
2. (a) The three angles add up to 180 ,
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 6
In many questions we shall use the chain rule (function of a function),
dy
dy du
=
. Then rewrite anything involving u in terms of x.
dx
du dx
du
dy
1. Let u = 4x + 1, so
= 4. Then
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 5
If we dierentiate xp we obtain p.xp1 , and if we dierentiate axp we get
a.p.xp1 (when a and p are numbers).
1. 6x61 = 6x5 .
2. 60x601 = 60x59 .
3. 2.20.x201 = 40x19 .
4. (4).x41 =
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 4 Trigonometric Functions
These examples count towards the assessment of the module and should be
handed in on Monday 4th November. Do not use a calculator.
Read Bostock & Chandler, p
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 2 Indices
These examples count towards the assessment of the module and should be
handed in on Wednesday 23rd October. Do not use a calculator.
Read Bostock & Chandler, pages 20 30.
S
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 3 Coordinate Geometry
These examples count towards the assessment of the module and should be
handed in on Monday 28th October. Do not use a calculator.
Read Bostock & Chandler, pages
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 3
1. The idea is to express every equation in the form y = mx + c; then the
gradient is m and the intercept c. So we solve each equation for y.
a. No need to solve. m = 4, c = 2,
b.
MATH011101
MATH011101
This question paper consists of 3 printed
pages, each of which is identied by the
reference MATH011101
All calculators must carry an approval
sticker issued by the School of
Mathematics.
c
UNIVERSITY OF LEEDS
Examination for the Mod
School of Mathematics
MATH 0111 Elementary Dierential Calculus
Solutions 2
We repeatedly use the rules: a0 = 1, a1 = a, ap+q = ap aq , ap /aq = apq ,
(a ) = apq , and the pth root of a is a1/p . Some of these calculations can be
done in more than one way
School of Mathematics
MATH 0111
Elementary Dierential Calculus
Examples 1 Basic Algebra
These examples count towards the assessment of the module and should be
handed in on Monday 14th October. Do not use a calculator.
Read Bostock & Chandler, pages 1 19,