MTH204
Assignment1
Due Friday 15th March
1. (a) Solve the equation differential equation .
(b)
[5]
A car moves from rest along a straight road. After seconds the velocity is metres per
second. The motion is modeled by the differential equation
Where and a
MTH102
Assignment 1
Due Friday November 5th , 2012
1. (a) Solve, for real values of the inequality
[5 marks]
(b) Show that no real solution, exists for the inequality
[2 marks]
[4 marks]
2. (a) Find the real values of for which
(b) Solve, for real values
1
TEST CODE 02234020/SPEC
FORM TP 02234020/SPEC
CARIBBEAN
EXAMINATIONS
COUNCIL
ADVANCED PROFICIENCY EXAMINATION
PURE MATHEMATICS
UNIT 2
COMPLEX NUMBERS, ANALYSIS AND MATRICES
SPECIMEN PAPER
PAPER 02
2 hours 30 minutes
The examination paper consists of THR
1
Caribbean Examinations Council
Advanced Proficiency Examination
Pure Mathematics Unit 2
Specimen Paper 01
1 hour 30 minutes
Read The Following Instructions Carefully
1.
Each item in this test has four suggested answers lettered (A), (B), (C), (D). Read
TEST CODE 02134020/SPEC
FORM TP 02134020/SPEC
CARI B B E AN
E XAM I NAT I O NS
CO UNCI L
ADVANCED PROFICIENCY EXAMINATION
PURE MATHEMATICS
UNIT 1
ALGERBRA, GEOMETRY AND CALCULUS
SPECIMEN PAPER
PAPER 02
2 hours 30 minutes
The examination paper consists of
1
Caribbean Examinations Council
Advanced Proficiency Examination
Pure Mathematics Unit 1
Specimen Paper 01
1 1 2 hours
Read The Following Instructions Carefully
1.
Each item in this test has four suggested answers lettered (A), (B), (C), (D). Read
each i
1
CARIBBEAN EAMINATIONS COUNCIL
ADVANCED PROFICIENCY EXAMINATIONS
PURE MATHEMATICS
APPLIED MATHEMATICS
List of Formulae
and
Statistical Tables
DO NOT REMOVE FROM THE EXAMINATION ROOM
2
Arithmetic Series:
Sn
n
2a n 1d
2
Sn
Tn a n 1 d
a r n 1
r 1
Geometr
ARITHMETIC AND GEOMETRIC SERIES
YEA
R
2009
QUESTION
3(b) Find the range of values of x for which the common ratio r of a convergent
2x - 3
.
x +4
3(b) A GP with first term a and common ratio r has sum to infinity 81 and the sum of
the first four terms is
SEQUENCES
YEA
R
2009
QUESTION
3(a) A sequence cfw_ tn is defined by the recurrence relation
tn +1 =tn +5, t1 =11 for all n N .
(i) Determine t2 , t3 and t4 .
(ii) Express tn in terms of n.
2008
3(a) A sequence cfw_ un is defined by the recurrence relati
Chapter 5 Vector Geometry
5 VECTOR
GEOMETRY
Objectives
After studying this chapter you should
be able to find and use the vector equation of a straight line;
be able to find the equation of a plane in various forms;
be able to interchange between cartesia
INTERMEDIATE VALUE THEOREM
YEA
R
2009
2008
2007
2006
QUESTION
10.
y
B(a , b )
A(0,1)
x
y =- x
The diagram above (not drawn to scale) shows the graphs of the two functions
y =e x and y =- x.
(a) State the equation in x that is satisfied at B (a , b ), the
NEWTON-RAPHSON METHOD
YEA
R
2009
QUESTION
4(a) (i) Show that the function f ( x) = x3 - 3 x +1 has a root a in the closed interval [1,
2].
(ii) Use the Newton-Raphson method to show that if x1 is a first approximation to
a in the interval [1, 2], then a s
SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT
COEFFICIENTS
To solve a differential equation of the form write down the auxiliary quadratic equation and
solve it. The general solution of the differential equation then takes one of the three form
MACLAURIN SERIES
YEA
R
2009
QUESTION
2008
3(c)(i) Write down the first FIVE terms in the power series expansion of ln ( 1 +x ) ,
stating the values of x for which the series is valid.
(ii)(a) Using the result from (c)(i) above, obtain a similar expansion
MATRICES AND SYSTEMS OF LINEAR EQUATIONS
YEA
R
2011
QUESTION
6(a)
The matrix
(i)
Show that
(ii)
Matrix is changed to form matrices
and
Write down the
determinant of EACH of the new matrices, giving a reason for your answer
in EACH case.
(a) Matrix is form
BINOMIAL EXPANSIONS
YEA
R
2009
QUESTION
(
)
n
4(a)(i) Find n N such that 5 C2 =2
(
C2 ) .
n +2
5
4
(ii) The coefficient of x2 in the expansion of ( 1 +2 x ) ( 1 + px ) is - 26. Find the
possible
values of the real number p.
2008
4(b)(i) Use the binomial t
SERIES
YEA
R
2009
QUESTION
1
, r N.
r +1
(i) Express f (r ) - f (r +1) in terms of r.
3(c) Let f ( r ) =
n
(ii) Hence, or otherwise, find Sn =
r=
1
4
( r +1) ( r +2 )
(iii) Deduce the sum to infinity of the series in (c)(ii) above.
2008
4(b)(i) Use the bi
MTH102
Assignment 2
Due Friday November 23rd, 2012
1. (a) Without the use of calculators, evaluate
[3 marks]
(i)
[4 marks]
(ii)
(b) By substituting or otherwise, solve, for the equation
.
[6 marks]
(c) By using , or otherwise, solve .
[7 marks]
(d) Solve,
u
1. (See Example I) Determine whether each of the
following sentences is a statement:
(a) A day is 24 hours long.
(it) An hour is 65 minutes long.
(c) Are there more than 30 seconds in a minute?
{d} I think 50 minutes is too little time for a
history cla