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EXAMINATIONS COUNCIL OF ZAMBIA
CoUN

BCEGE
GC
Examination for General Certificate of Education Ordinary Level
P GCE,C

Mathematics 4024/2
Paper 2 {IStcGCLOCI G EGCIG(EGsGCLGCEC(GCG

EatfGCEGKEG(E
Friday AUGUST 2023
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Answer Booktet
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Silent Electronic Calculator (non SGCCECEGC
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Time:2 hours 30 CEGCrGCiGCEGCEGFOCES
minutes CEEGCHSCIGCGCE
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Instructions to Candidates GCreiGiKi CCSuctGLEGTIGCtGCLGCEGCEGCEC
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1 Write the centre number and your examination number on every GCEGCEGCE
CEGCEGERCGsG(E
page of the
separate Answer Booklet provided. (EGCE:CC(3LE3CG

2 Write your answers and working in the separate Answer Booklet provided.
GCECG
3 If you use more than one Answer Booklet, fasten the Answer
CEC GCE612EGCGCBooklets
GCESCEtiC: together.
CEGFGC
4 Omission of essential working will result in loss of marks. SCIGGGC C

5 There are twelve questions in this paper.

(i) Section A
Answer all questions.
(ii) Section B
Answer any four questions.
6 Silent non programmable Calculators may be used.
Information for Candidates
1 The number of marks is given in brackets [ ] at the end of each
question. question or part
2 Ifthe degree of accuracy is not specified in the question, and if
the
give the answer to three signiflcant figures. Give answers in degreesanswer
is not exact,
to one decimal place.
3 Cell phones are not allowed in the examination room.

CECZIGCEI2023/R3 This question paper consists of9 printed pages

Page 2 of9

Mathematical Formulae
1 ALGEBRA

Quadratic Equation

X=
-btvb'-4ac
2a

2 SERIES

Geometric Progression

S = a(l-r) .(r<1)
1-r

S, = alr"-),(r> 1)
r-1

Soo =
1-r
for r|<1

3 TRIGONOMETRY
Formula for A ABC
C

sin A sin B sin C

d=b+c-2bc cos A.
A=bc sin A

4 STATISTICS
Mean and standard deviation
Ungrouped data

Mean()= -, SD =
n

Grouped data

Mean ( )= , SD =
Ef

Mathematics/4024/2 2 0 2 3
 Page 3 of9
Section A(52 Marks)

Answer all questions in this section

1
(a) Simplify 13a 6Sa'b
(2]
(b) Leamers in a Grade 10class were asked
the tyress of drinks they liked. The Venn
diagram showstheir responses.

Fanta
Coke
17 x+2

3
Spri ie

(i Given that 40 learners liked'Fanta, find the value of x. [2]

(ii) Find the total number of lea rners in the class. [1]
(ii) How many learners
(a) did not like Fanta, [1]
(b) liked two types of drinks only? [1)

(a) In a geometric progression, the second term is 21 and the fourth term is 189.
Calculate the

first ternm and the cc ommon ratio, (3]

(ii) síxth term, [2]
(ii) sum of the first 5 terms of the progression. [2]

(b) Given that matrix P =

(i) find the value,ofx for which the determinant of Pis -10, [2]

(ii) hence, find t he inverse of P. (2]

2 3 [Turn over
Mathematics/4024/2 2
 Page 4 of9

9 8 (3]
3 (a) Express as a single fraction in its simplest form.
1-4k 1-3k
picks one apple at random
(b) A girl has 7 green apples aind 6 red apples in a bag. She
from the bag arnd eats it. Sthe picks another apple and eats it.
Draw a tree diagram i'o illustrate allthe possible outcomes. [2]
(i)
(ii) What is the probabilit y th'at the first apple eaten was green? [3]

4 (a) () Construct a triangle KL Mitiwhich KL= 10cm, LM =7cm and

KÛM =120°. [1)

(i) Measure and write the length (M. [1)

(b) Within triangle KLM, draw the locus of points which are
) 5.5cm from M, [1]

(ii) lcm from LM, [1]

(ii) equidistant from M and L. [2]

(C) A point P, within triangle KLM, is such th: it it is less than or equal to
5.5cm from M, greater than or equ al to lcm from LM and nearer to L than M.
Indicate clearly, by shading, the reszion in wB ich P must lie. [2]

(a) The program below is given in the form of a ps. eudocode.

Begin
Enter n
IF n<0 THEN
Display error n must be positive'
ELSE sum = n/2 * [2*a+ (n -- 1) *d]
ENDIF
Display sum
End
Draw acorresponding flowchart for the information give n above. [5]
(b) Solve the equation &x-9x + 2=0., giving your answers orrect to 2 decimal places.
[S]

Mathematics/402412 2 2
 Page 5 of9
6 (a) In the diagram, O¤ = 2a, Aß = b, Oc- 36,Mis the midpoint of OE and OC is
parallel to AB.

3b

A
2a

Express in terms of g and/or b

() [1]
(ii)
8CE. [1]
(ii) [1]
(iv) [2]
(b) The equation of a curve is y =x- 27x. Find the coordinates of the
turning: points of the curve. (3]

Mathematics/4024/2 2 2 3 [Turn over

 Page 6 of9

Section B |48 marks ]

/Answer any four questions in this section.

Each question in this section carries 12 marks.
7 (a) The diagram s hows the positions of three towns P, Q and R. PÌ = 7.lkm,
PR =: 23.8km and angle RPQ = 92.7°.

7.1km

23.8km

92.7°

Cialculat1e the
(i) disstance RQ to 2 decimal places, [S]
(ii) area of the triangle PQR, [2]
(i iüü) sthortest distance ofP from RQgiving your answer to 2 decir nal places.
[2]
(b) SSolve theequation 3 tan = 89 for 0°ses180°,
9x-1
(c) Simplify 9x+3 [2]

Mlathematics/4024/2 2 2 3
 Page 7 of9
8 (a) The diagram shows the frustum of a cone. The perpendicular height is 40cm. The top
and bottom radii are 10cm and 30cm respectively. [Take T as 3.142]

10çm

40cm

30cm

Calculate the volume of the frustum. [6]

(b) Four towns A(70°N,65°W), B(70°N,65°E), C(70°S, 65°E) and D(70°S, 65°W) are on
the surface of the earth. Take as 3.142 andR=3437nm.
(i) Sketch the surface of the earth showing all the four towns A, B, C and D. [2]
(ii) Calculate, in nautical miles, the distance
(a) ABalong latitude 70°N, [2]
(b) BC along longitude 65°E. (2]

Answer the whole of this question on a sheet of graph paper.

A lady intends to baketwo types of cakes, type A and type B for sale. She intends to bake at
least 30 cakes of type A and at least 20 cakes of type B. The number of cakes of type A must
be equal to or more than the number of cakes of type B. The total number of cakes must not
exceed 90.

(a) Taking x torepresent the number of cakes of type A and y to represent the number of
type B cakes, write four inequalities to represent the information above. [4]
(b) Using a scale of 2cm to represent 10 cakes on each axis,draw x and v axes
for 0Sx s90and 0 sys90 respectively andshade the unwanted region to indicate
clearly the region where the solution of the inequalities lie. [S]
(c) The profit on the sale of a type Acake is K30.00 and the profit on a type B cake is
K50.00. How many cakes of each type can be baked to make maximum profit? [2]
(d) Calculate the maximum profit. [1]

Mathematics/4024/2 2 0 2 3 [Turn over

Page 8 of9
10 Answer the whole of this question on a shect of graph paper.

The vertices of triangle ABC are A(0, 4), B(0, 6)and C(-4,6) while the vertices of triangle
A¡B,C, are A(4, 0),B,(6, 0), andC(6, 4).
(a) Using a scale of lcm to represent l unit on cach axis, draw x and y axes
for -4srs8 and-3Sys 12. Draw and label triangle ABC and triangle A,B,C1.[2]
(b) Describe fully a single transformation that maps triangle ABC onto
triangle A,B|C1. [3)

(c) The matrix (| 0) maps triangle ABC onto triangle A,B,C).

(0 2
(i) Find the coordinates of A2, B» and C. [3]
(ii) Draw and label triangle A,BC2.
(d) Triangle A|B|C, is mapped onto triangle A;B;C, with vertices
As(4, 0), B(6, 0) and C(-2, 4).
() Draw and label triangle AsB,C,.
(ii) Find the matrix representing this transformation. (2]

11 The ages (in years) of 100 patients treated at a certain health centre on a particular day are
given in the table below.
Age (in years) 0<x<l0 10 <xs 20 20 <rs30 30 <x<40 40 <x< 50 50 <xs60
Number of patients 10 25 30 20 10

(a) Calculate the standard deviation. [6]

(b) Answer this part of the question on a sheet of graph paper.
(i) Using the table above, copy and complete the cumulative frequency
table below. [)
Age (in years) <0 < 10 <20 < 30 <40 < 50 < 60
Number of patients 0 100

(ii) Using a scale of 2cmto represent 10units on cach axis for 0 xs60 and
0<y< l00, draw a smooth cumulative frequency curve. [3]
(ii) Showing your method clearly, use your graph to estimate the semni-interquartile
range. [2]

Mathematcs/402412 2 0 2 3
 Page 9 of9

12 Evaluate (H - dx. [3]

(a)

(b) The diagram shows the graph of y=-r-Sx -3.

5x-3
15

10

-2 2

-10

-15

(i) Use the graph to find the solution of the equations

(a) x-x- 5x-3 =0, [2]
(b) x - - 5x =x-3. [3]

(ii) Find the

(a) gradient of the curve at the point (-2, -5), [2]

(b) area bounded by the curve, x= 1,y =0 and x=3. [2]

Mathematics/40242 2 2 3