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5 COUNCIL OF ZAMBIA ;
a Se eee Certificate Ordinary Level
33
3 i 4030/1
3 Additional Mathematics
a Paper 1
MBER 2019
canebiey 27 NOVE!
ndetiona! Maer:
Sateen ce a pop
Time: 2 hours:
Instructions to Candidates
Write your namé, centre number and candidate number in the spaces on the
Answer Bookle! provided.
‘There are 12 questions in this paper Answer all questions
‘While your answers in the Answer Booklet provided
You use more than one Answer Booklet, fasten the Ans:
wer Booklets together
o nep-exac numerical answers correct to 3 significant figures, ar 1 decimal place in
Save Ol angles in degrees, uniess a different level of accuracy is specified
in the Wes baars (Plat he (3) ios
iwhere'n is a positive mieger and {")
TRIGONOMETRY
‘Menten
Sin'A + cos? A= |
Sec A= 1 an'a
nt
4 Ka
Ox 2y 1 eg
Ra Gear 1D)
ax" hay By 4
Be 4
tay 4 = texag
Sg eg, ere.
Payel
ke + J intersects the eurve:
ae
3 Find the range of values of & for which the line y=
2? = ay © | wt two dist
160, where cand p are constants,
ind an expression fr h'(x) 2
and h'(5) ~ 2, find the value of ¢ and of (41
4 The function is defined by b+ +f
() Given that =I)
s circle with centre O, radius r and angle
$ Inthe diagram below, OABL i
cn? and are ABC is Gem,
AOC = 0 radians. The area of 0
A th ot Cnn 4 Sle
ant (tic ade
Wary et ofl © ae), the
of 2. Find the value of 1
ye-2 his
8 (a) Acurve has the equationy= 7 Find the value eof i for wt ich
ay
a u-4)
2 where the
of the points on the curve y ™ =
(b) Find the x-coordinates
pormal is parallel to the line 4y = ~x + 24
Find al the angles between 0 and 360" which satisfy the equation
{$sin@—3
10 a) A line L passes through
int A(-1, 3) and is in the direction of the
vector FH Find the equation of the line /. in the form ax + dy + ea My
The position vectors of points P and Mare 24° 44 and LO — 4p Find ase
{D__ the coordinates of P and of Q, ax tesa I)
(the area of the shaded region G1
ly one of the fallowing alternatives.
Either
Solutions to this question by scale drawing will not be accepted.
In the diagram below, triangle PRN and triangle PRQ are isosceles: QS is @
perpendicular bisector of PH and the coordinates of N are (5, 4), The equations of
PQ und RN are Ty = 1+ 28 and 3y 4x ~ 6 respectively
Ayr Tee the position vectors of C and of D,
the angle DB makes with the vector 24
