TOTAL
MARKS
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label here
INTERNATIONAL SECONDARY CERTIFICATE EXAMINATION
NOVEMBER 2023
FURTHER STUDIES MATHEMATICS (STANDARD): PAPER I
EXAMINATION NUMBER
Time: 2 hours 200 marks
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 20 pages and an Information Booklet of 4 pages (i–iv).
Please check that your question paper is complete.
2. Answer ALL the questions on the question paper and hand it in at the end of
the examination. Remember to write your examination number in the space
provided.
3. Non-programmable and non-graphical calculators may be used, unless otherwise
indicated.
4. All necessary calculations must be clearly shown and writing must be legible.
5. Diagrams have not been drawn to scale.
6. Round off your answers to 2 decimal digits, unless otherwise indicated.
7. ONE blank page (page 20) is included at the end of the question paper. If you run
out of space for an answer, use this page. Clearly indicate the number of your answer
should you use this extra space.
FOR OFFICE USE ONLY: MARKER TO ENTER MARKS
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Total
Mark
Marker
Initial
Moderated
Mark
Moderator
Initial
Question
38 12 10 22 18 14 12 12 12 10 24 16 /200
Total
IEB Copyright © 2023 PLEASE TURN OVER
,INTERNATIONAL SECONDARY CERTIFICATE: FURTHER STUDIES MATHEMATICS (STANDARD): PAPER I Page 2 of 20
QUESTION 1
1.1 Solve:
(a) In (2 + e − x ) = 2. Leave your answer in the form x = In(….)
(8)
(b) 2x + 3 = 3 x + 4
(6)
IEB Copyright © 2023
, INTERNATIONAL SECONDARY CERTIFICATE: FURTHER STUDIES MATHEMATICS (STANDARD): PAPER I Page 3 of 20
1.2 Give, in standard ax 4 + bx 3 + cx 2 + dx + e = 0 form, a quartic equation which has
x = 2 + 3 and 2 − i as roots. The values of a, b, c, d and e must be rational.
(8)
1.3 Determine positive real values of a and b if:
(a + bi )(b + i ) = (2b + a)i
(8)
IEB Copyright © 2023 PLEASE TURN OVER
MARKS
Please paste the barcoded
label here
INTERNATIONAL SECONDARY CERTIFICATE EXAMINATION
NOVEMBER 2023
FURTHER STUDIES MATHEMATICS (STANDARD): PAPER I
EXAMINATION NUMBER
Time: 2 hours 200 marks
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 20 pages and an Information Booklet of 4 pages (i–iv).
Please check that your question paper is complete.
2. Answer ALL the questions on the question paper and hand it in at the end of
the examination. Remember to write your examination number in the space
provided.
3. Non-programmable and non-graphical calculators may be used, unless otherwise
indicated.
4. All necessary calculations must be clearly shown and writing must be legible.
5. Diagrams have not been drawn to scale.
6. Round off your answers to 2 decimal digits, unless otherwise indicated.
7. ONE blank page (page 20) is included at the end of the question paper. If you run
out of space for an answer, use this page. Clearly indicate the number of your answer
should you use this extra space.
FOR OFFICE USE ONLY: MARKER TO ENTER MARKS
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Total
Mark
Marker
Initial
Moderated
Mark
Moderator
Initial
Question
38 12 10 22 18 14 12 12 12 10 24 16 /200
Total
IEB Copyright © 2023 PLEASE TURN OVER
,INTERNATIONAL SECONDARY CERTIFICATE: FURTHER STUDIES MATHEMATICS (STANDARD): PAPER I Page 2 of 20
QUESTION 1
1.1 Solve:
(a) In (2 + e − x ) = 2. Leave your answer in the form x = In(….)
(8)
(b) 2x + 3 = 3 x + 4
(6)
IEB Copyright © 2023
, INTERNATIONAL SECONDARY CERTIFICATE: FURTHER STUDIES MATHEMATICS (STANDARD): PAPER I Page 3 of 20
1.2 Give, in standard ax 4 + bx 3 + cx 2 + dx + e = 0 form, a quartic equation which has
x = 2 + 3 and 2 − i as roots. The values of a, b, c, d and e must be rational.
(8)
1.3 Determine positive real values of a and b if:
(a + bi )(b + i ) = (2b + a)i
(8)
IEB Copyright © 2023 PLEASE TURN OVER
