Eswatini General Certificate of Secondary Education: Mathematics: Paper 2
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These are the solutions to the EGCSE Mathematics Paper 2 questions.
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Examinations Council of Eswatini
Eswatini General Certificate of Secondary Education
Mathematics
Paper 2 Structured Questions (Core)
Time: 2 hours
Read These Instructions First
(1.) Write your centre number, candidate number and name in the spaces provided.
(2.) Write in dark blue or black pen.
(3.) You may use a soft pencil for any diagrams, graphs or rough working.
(4.) Do not use staples, paper clips, highlighters, glue or correction fluid.
(5.) Do not write on the bar code.
(6.) Answer all questions.
(7.) If working is needed for any question it must be shown below that question.
(8.) The number of marks is given in brackets [ ] at the end of each question or part
question.
(9.) If the degree of accuracy is not specified in the question, and if the answer
is not exact, give the answer to three significant figures.
Give answers in degrees to one decimal place.
For π, use either your calculator value or 3.142.
(10.) The total of the marks for this paper is 90.
60 students take Geography.
86 students take Physics.
The Venn diagram shows part of the information.
P = {Physics students}
G = {Geography students}
(i.) Find the number of students who take Geography only.
(ii.) Find the number of students who take neither Geography nor Physics.
(iii.) Find $n(P \cap G)'$
(b.) ξ = {1, 2, 3, 4, ......, 20}
A = {Prime numbers}
B = {factors of 60}
List members of
(i.) $A$,
(ii.) $A \cap B$,
(iii.) $A \cap B'$
$ (a.) \\[3ex] \underline{\text{Given}} \\[3ex] n(\text{Univsersal set}) = n(\text{Total Number of Students}) = 104 \\[3ex] n(\text{Geography students}) = 60 \\[3ex] n(\text{Physics students}) = 86 \\[3ex] n(\text{Physics students only}) = 40 \\[3ex] n(\text{Both Physics and Geography students}) = 46 \\[5ex] (i.) \\[3ex] n(\text{Geography students only}) = n(P' \cap G) \\[3ex] = n(\text{Geography students}) - n(\text{Both Physics and Geography students}) \\[3ex] = 60 - 46 \\[3ex] = 14\text{ students} \\[5ex] (ii.) \\[3ex] n(\text{Neither Geography nor Physics students}) \\[3ex] + n(\text{Physics students only}) \\[3ex] + n(\text{Geography students only}) \\[3ex] + n(\text{Both Physics and Geography students}) \\[3ex] = n(\text{Total Number of Students}) \\[5ex] n(\text{Neither Geography nor Physics students}) + 40 + 14 + 46 = 104 \\[3ex] n(\text{Neither Geography nor Physics students}) + 100 = 104 \\[3ex] n(\text{Neither Geography nor Physics students}) = 104 - 100 \\[3ex] = 4\text{ students} \\[5ex] (iii.) \\[3ex] n(P \cap G)' = n(\text{Physics students only}) \\[3ex] = 40\text{ students} \\[5ex] (b.) \\[3ex] \xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\} \\[3ex] A = \{2, 3, 5, 7, 11, 13, 17, 19\} \\[3ex] B = \{1, 2, 3, 4, 5, 6, 10, 12, 15, 20\} \\[5ex] (i.) \\[3ex] A = \{2, 3, 5, 7, 11, 13, 17, 19\} \\[5ex] (ii.) \\[3ex] A \cap B = \{2, 3, 5\} \\[5ex] (iii.) \\[3ex] B' = \{7, 8, 9, 11, 13, 14, 16, 17, 18, 19\} \\[3ex] A \cap B' = \{7, 11, 13, 17, 19\} $
