📄 Exam Questions & Readable Text Transcript
Full OCR-extracted text of questions, syllabus codes, and exam instructions.
Extracted Content: 4027q1 Specimen paper
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énrname Forename(s) Centre Number Candidate NumberFy a
ZIMBABWE SCHOOL EXAMINATIONS COUNCIL
General Certificate of Education Ordinary L evel
PURE MATHEMATICS 4027/1
PAPER 1
Aon
ars
SPECIMEN PAPER 2 hours 30 minutes
Candidates answer on the question paper.
Additional materials: Formulae booklet
Mathematical tables/ electronic calculator
\<strong></strong> Allow candidates 5 minutes to count pages before the examination.
This booklet should not be punched or stapled and pages should not be removed.
TIME 2 hours 30 minutes
INSTRUCTIONS TO CANDIDATES
Write your name, Centre number and candidate number in the spaces at the top of this page and
your Centre number and Candidate number on the top right corner of every page of this paper.
Answer all questions.
Check that all the pages are in the booklet and ask the invigilator for a replacement if there are
duplicate or missing pages.
Write your answers in the spaces provided on the question paper using black or blue pens.
If working is needed for any question it must be shown in the space below that question.
Omission of essential working will result in loss of marks.
Decimal answers which are not exact should be given correct to three significant figures unless
stated otherwise. Answers in degrees should be given correct to one decimal place.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question.
Electronic calculators or Mathematical tables may be used to evaluate explicit numerical expressions.
This specimen paper consists of 13 printed pages and 3 blank page.
Copyright: Zimbabwe School Examinations Council, Specimen.
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2 Answer all questions1 Solve the simultaneous equations:
y =x’ 4x- 3
2y =3x-2
Answer
2 @ Find the gradient of the curve y =x’ 424 x # 0, ata point P (2; 16).
XxX
Answerr(@) [2]
di The tangent to the curve in (i) at P meets the x- axis at A and the y- axis at B.
Calculate the area of the triangle AOB where O is the origin.
Answer (ii) [3]
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33 (a) A circular cylinder has radius rcm, height 4r cm and volume Vem’.
Express Vin terms of rand hence find *
r
Amswer eee [2]
(b) The coefficient of x? in the expansion of (2 tax)(1- 3x y is 405.
Find the value of a
Answer [3]
4 The points A, B and C have coordinates (— 2; 1), (3; 11) and (- 1; 8)
respectively. The line from C is perpendicular to AB and meets AB at the
point N.
(a) Find the equations of AB and CN.
Answer [4]
(b) Calculate the coordinates of N.
Answer [3]
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45 (a) Solve the inequality x? +4x- 5 <Sx- 3.
Answer [4]
(b) The expressions x<em>- ax +a’ and ax</em> +x*- 17 have the same
remainder when divided by «—2. Find the possible values of a.
Answer [4]
6 A function f is defined by f:ix5-2, x10.
x
(@ Find £*(x}.
Answer [3]
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)6 (b)__ Find the value of x forwhich f(x) is undefined.
Answer [3]
(© Find the values of xfor which f(x) = £?(x).
Answer [4]
7 The position vectors of points A and B relative to an origin O, are
OA = 10i+9j and OB = 14: + 2j
(a) Find angle AOB.
Answer [4]
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7 (b) _ A third point P has position vector OP = qi+13}.Find the
@ vector AP in terms of q,
Answer [1]
di vector BP in terms of q,
Answer [1]
(ii) values of q for which AP and BP are perpendicular,
Answer [3]
(ii) value of qfor which AP and BP are equal in length.
Answer [3]
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78 The following table shows the experimental values of two variables x and y.
x 7 8 9 10 11 12
y 40 46 53 60 69 78
The variables x and y are related by the equation y = ax? +b.
(a) _ Draw asuitable straight line graph on page 7.
Answer on graph [7]
(b) Use the graph to estimate the
@ values of aandb,
Answer a=
b= [3]
(iii) value of ywhen x= 8,4.
Answer y = [2]
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977)
9 (a) Evaluate o (3 sinx- 4cos2x }dx
Answer [4]
(b) Given that, Sin b=p where Sis an acute angle measured in
degrees, obtain an expression, in terms of p, for
@ tan 0,
Answer [2]
Gi) = Sin( 180 + D).
Answer [2]
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10©
D
The diagram shows a sector OAB of a circle centre O and radius 12cm.
AOB =q radians. The area of the sector is 150 cm’.
Calculate the
@ size of angle AOB,
Answer [2]
di length of arc AB.
Answer [2]
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11 10 A curve is represented parametrically by x=? +3t y =t - 2t.Find
. dy.
(a) an expression for * in terms of t,
‘xX
Answer [4]
(b) the coordinates of the stationary point of the curve.
Answer [4]
() the values of tat the points of intersection of the curve with the
line 4y +x=10,
Answer [4]
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12 11 (‘Find. 4x? 8
0 oT
Answer [3]
(i) 2x-1)ax.
Answer [2]
(b) Find the range of values of p for which the roots of the equation
3x? - 3px +{p°- p- 3) =0 are real.
Answer [4]
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13. 1
© The diagram shows part of the curve y =2 arel »x#-1,
x
a 2 x
Find the volume generated when the shaded area is rotated through 360°
about the xaxis.
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