ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Advanced Level
PURE MATHEMATICS 6042/1
PAPER 1
SPECIMEN PAPER 3 hours
Additional materials:
Answer paper
Graph paper
List of Formulae
Scientific calculator
TIME 3 hours
INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces provided on the answer
paper/answer booklet.
Answer all questions.
If a numerical answer cannot be given exactly, and the accuracy required is not specified in the
question, then in the case of an angle it should be given to the nearest degree, and in other cases it
should be given correct to 2 significant figures.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 120.
The use of a scientific calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
________________________________________________________________________________
This question paper consists of 6 printed pages and 2 blank pages.
Copyright: Zimbabwe School Examinations Council, Specimen paper.
ZIMSEC Specimen paper [Turn over
, 2
1 When a polynomial f(x) is divided by (x – 3) the remainder is –9 and when
divided by (2x – 1), the remainder is -6.
Find the remainder when f(x) is divided by (x – 3) (2x – 1). [4]
8
2 Given that y = 2x 3 + , find the percentage increase in y as x increases
x
from 2 to 2.003. [4]
3
The diagram shows a circle centre O and radius r.
A chord PQ subtends a right-angle at the centre O of the circle. QR is a chord
p
such that angle PQR is .
12
Show that the shaded area bounded by the chords PQ and QR, and the arc PR is
1 2æp 1 ö
r ç + 3 -1÷. [5]
2 è6 2 ø
4 (i) Sketch on the same diagram the graphs of y = 3x + 4 and y = 2x +1.
(ii) Hence or otherwise, solve the inequality 3x + 4 < 2x +1. [5]
5x 2 - 5x +11
5 Express in partial fractions. [5]
( x - 2) ( x 2 + 3)
Expand (3- 2x ) up to and including the term in x 3, simplifying
-3
6 (i)
the coefficients.
(ii) Hence state the set of values of x for which the expansion in (i) is valid.
[5]
6042/1 Specimen paper
General Certificate of Education Advanced Level
PURE MATHEMATICS 6042/1
PAPER 1
SPECIMEN PAPER 3 hours
Additional materials:
Answer paper
Graph paper
List of Formulae
Scientific calculator
TIME 3 hours
INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces provided on the answer
paper/answer booklet.
Answer all questions.
If a numerical answer cannot be given exactly, and the accuracy required is not specified in the
question, then in the case of an angle it should be given to the nearest degree, and in other cases it
should be given correct to 2 significant figures.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 120.
The use of a scientific calculator is expected, where appropriate.
You are reminded of the need for clear presentation in your answers.
________________________________________________________________________________
This question paper consists of 6 printed pages and 2 blank pages.
Copyright: Zimbabwe School Examinations Council, Specimen paper.
ZIMSEC Specimen paper [Turn over
, 2
1 When a polynomial f(x) is divided by (x – 3) the remainder is –9 and when
divided by (2x – 1), the remainder is -6.
Find the remainder when f(x) is divided by (x – 3) (2x – 1). [4]
8
2 Given that y = 2x 3 + , find the percentage increase in y as x increases
x
from 2 to 2.003. [4]
3
The diagram shows a circle centre O and radius r.
A chord PQ subtends a right-angle at the centre O of the circle. QR is a chord
p
such that angle PQR is .
12
Show that the shaded area bounded by the chords PQ and QR, and the arc PR is
1 2æp 1 ö
r ç + 3 -1÷. [5]
2 è6 2 ø
4 (i) Sketch on the same diagram the graphs of y = 3x + 4 and y = 2x +1.
(ii) Hence or otherwise, solve the inequality 3x + 4 < 2x +1. [5]
5x 2 - 5x +11
5 Express in partial fractions. [5]
( x - 2) ( x 2 + 3)
Expand (3- 2x ) up to and including the term in x 3, simplifying
-3
6 (i)
the coefficients.
(ii) Hence state the set of values of x for which the expansion in (i) is valid.
[5]
6042/1 Specimen paper
