VIMBAI SCHOOL
HIGH
General Certificate of Education Advanced Level
LOWER 6th
PURE MATHEMATICS 6042/1
PAPER 1
END OF YEAR 2018 SESSION 3 hours
Additional materials:
Answer Paper Non-programmable calculator
Graph Paper List of formulae
TIME 3 hours
INSTRUCTIONS TO CANDIDATES
Write your name in the spaces provided on the answer sheet/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.
Questions are printed in the order of their mark allocations and candidates are advised to
attempt questions sequentially.
The use of an electronic calculator is expected, where possible.
You are reminded of the need for clear presentations in your answers.
This question paper consists of 4 printed pages.
Copyright: Tarakino N.P. (Trockers) – Vimbai High School, End of Year 2018
© Tarakino N.P. V.H.S. End of Year 2018 [Turn Over
Typed by Trockers
1. Show that the equation may be written as a quadratic
equation in . [3]
Hence find the values of , satisfying the equation . [2]
2. (i)Expand in ascending powers of up to and including the term in .
State the range of values of for which the expansion is valid. [5]
(ii) By using in the expansion, find an approximation for , leaving your
answer in the form . [3]
3. Find the centre and radius of the circle having and as the end points
of its diameter. [3]
Hence write down the equation of this circle. [2]
4. The position vectors of the points , and relative to the origin are:
, and respectively. Find
(i) , [2]
(ii) the exact value of , [3]
(iii) the exact area of triangle [3]
5. Solve the following equations:
(i) , [3]
(ii) , [4]
(iii) . [4]
6.
The diagram shows a semi-circle with centre and radius . Angle
..
(i) In the case where , calculate the area of the sector [3]
(ii) Find the value of for which the perimeter of sector is one half of the
perimeter of sector . [3]
(iii)By using the value of in above, show that the exact length of the
perimeter of triangle is [3]
7. Find the value of , given that:
[5]
8. Solve the inequality . [4]
9. The cubic polynomial , where and are constants. It is
given that is a factor of and that when is divided by , the
remainder is
(i) Find the values of and . [5]
Hence
(ii) factorise completely. [3]
(iii)Sketch the graphs of the following function without finding the coordinates of
the turning points:
a) , [2]
b) , [2]
c) . [2]
10.
Variables and are related by the equation , where and are constants.
When the graph of against is drawn, the resulting line passes through the
points and as shown in the diagram. Find the values of and [6]
[Turn Over
11. Let .
(i) Express in partial fractions. [5]
(ii) Show that, when is sufficiently small for and higher powers to be
neglected, . [4]
12. The curve and the line intersect at two points. Find
(i) the coordinates of the two points, [4]
(ii) the equation of the perpendicular bisector of the line joining the two points. [4]
13. (i) A debt of is repaid by weekly payments which are in AP. The first
payment is and the debt is fully paid after . Find the third payment. [4]
(ii) Find the sum to infinity of the GP whose first term is and whose second term is
. [3]
14. Functions are defined by:
(i) Find the value of for which . [3]
(ii) Express each of and in terms of [3]
(iii) Show that the equation has no real roots. [3]
(iv) Sketch, on a single diagram, the graphs of and , making
a clear relationship between these two graphs. [3]
15. (i) Prove that . [3]
(ii) Hence
a) solve for , the equation , [4]
b) find the exact value of . [2]
JOSHUA 1 VS 9 and EXODUS 14VS 13
