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DSC1501: Introduction to Decision Sciences
OCT/NOV Examination 2026
Comprehensive Revision Guide: Covering 2023 to 2025 Past Papers
⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆
Decision Sciences | Quantitative Methods | UNISA
Exam Revision Guide
DSC1501
Module Code:
Introduction to Decision Sciences
Module Name:
OCT/NOV Examination 2026
Paper / Exam:
OCT/NOV 2023, 2024 & 2025 Past Papers
Covers:
100
Total Marks:
2 Hours
Duration:
Use this guide to revise thoroughly. Focus on understanding, not memorisation. All
questions are answered in full.
Exam Revision Notes | DSC1501 | 2026
,DSC1501 | Exam Revision OCT/NOV Examination 2026
Question 1 [20 marks]
(a) [4 marks]
Question: Classify each of the following numbers by writing it under the most specific
set to which it belongs (Natural numbers N, Integers Z, Rational numbers Q, Irrational
numbers, Real numbers R):
√
(i) −7 (ii) 5 (iii) 34 (iv) 0
Answer:
Key Concept
The number sets are nested: N ⊂ Z ⊂ Q ⊂ R. Irrational numbers are real numbers
√
that cannot be written as pq (e.g. 2, π).
• (i) −7: An Integer (Z). It is negative so not a natural number, but it is a whole number
(no fractional part).
√ p
• (ii) 5: An Irrational number. It cannot be expressed as q for integers p, q; its decimal
expansion is non-terminating and non-repeating.
• (iii) 34 : A Rational number (Q). It is expressed as a ratio of two integers with non-zero
denominator.
• (iv) 0: A Natural number (in the inclusive convention N0 ) and also an Integer. In
UNISA’s DSC1501, 0 is accepted as an integer; the most specific classification is an in-
teger (Z).
(b) [4 marks]
Question: Simplify the following, showing all steps:
5 3 1 2 4
(i) + − (ii) ÷
6 4 3 3 9
Answer:
(i) Find the lowest common denominator (LCD) of 6, 4, and 3. The LCD is 12.
5 3 1 10 9 4 10 + 9 − 4 15 5
+ − = + − = = = = 1 41
6 4 3 12 12 12 12 12 4
Page 2 of 30
,DSC1501 | Exam Revision OCT/NOV Examination 2026
(ii) To divide by a fraction, multiply by its reciprocal:
2 4 2 9 18 3
÷ = × = = = 1 21
3 9 3 4 12 2
Exam Tip
When dividing fractions, flip the second fraction and multiply. Never divide numerators
and denominators separately. Always simplify to lowest terms.
(c) [4 marks]
Question: A clothing store increases the price of a jacket by 15% and then later offers a
10% discount on the new price. If the original price was R800, find the final selling price.
Is the final price higher or lower than the original, and by how much?
Answer:
Step 1: Apply 15% increase.
New price = R800 × (1 + 0.15) = R800 × 1.15 = R920
Step 2: Apply 10% discount.
Final price = R920 × (1 − 0.10) = R920 × 0.90 = R828
Step 3: Compare to original.
Difference = R828 − R800 = R28 (higher)
The final price is R828, which is R28 higher than the original R800. This is a net increase
of 28
800 × 100 = 3.5%.
Watch Out
A 15% increase followed by a 10% decrease does NOT result in a 5% net increase. The
percentages apply to different base values. Always work through each step separately.
Page 3 of 30
,DSC1501 | Exam Revision OCT/NOV Examination 2026
(d) [4 marks]
Question: Express the following in the required form:
(i) Write 0.000 045 3 in scientific notation.
(ii) Write 3.72 × 104 as an ordinary number.
(iii) Round 47.86 to 2 decimal places.
7
(iv) Express 8 as a percentage.
Answer:
• (i) Move the decimal 5 places to the right: 0.0000453 = 4.53 × 10−5
• (ii) Move the decimal 4 places to the right: 3.72 × 104 = 37 200
• (iii) 47.86 = 47.866 . . . ≈ 47.87 (the third decimal digit is 6 ≥ 5, so round up)
7
• (iv) × 100% = 87.5%
8
(e) [4 marks]
Question: A business divides its monthly profit of R180 000 among three partners A, B,
and C in the ratio 3:5:7. How much does each partner receive?
Answer:
Step 1: Find the total number of parts.
3 + 5 + 7 = 15 parts
Step 2: Find the value of one part.
R180 000
1 part = = R12 000
15
Step 3: Compute each partner’s share.
A = 3 × R12 000 = R36 000
B = 5 × R12 000 = R60 000
Page 4 of 30
, DSC1501 | Exam Revision OCT/NOV Examination 2026
C = 7 × R12 000 = R84 000
Check: 36 000 + 60 000 + 84 000 = 180 000 ✓
Page 5 of 30
]]
DSC1501: Introduction to Decision Sciences
OCT/NOV Examination 2026
Comprehensive Revision Guide: Covering 2023 to 2025 Past Papers
⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆ ⋄ ⋆
Decision Sciences | Quantitative Methods | UNISA
Exam Revision Guide
DSC1501
Module Code:
Introduction to Decision Sciences
Module Name:
OCT/NOV Examination 2026
Paper / Exam:
OCT/NOV 2023, 2024 & 2025 Past Papers
Covers:
100
Total Marks:
2 Hours
Duration:
Use this guide to revise thoroughly. Focus on understanding, not memorisation. All
questions are answered in full.
Exam Revision Notes | DSC1501 | 2026
,DSC1501 | Exam Revision OCT/NOV Examination 2026
Question 1 [20 marks]
(a) [4 marks]
Question: Classify each of the following numbers by writing it under the most specific
set to which it belongs (Natural numbers N, Integers Z, Rational numbers Q, Irrational
numbers, Real numbers R):
√
(i) −7 (ii) 5 (iii) 34 (iv) 0
Answer:
Key Concept
The number sets are nested: N ⊂ Z ⊂ Q ⊂ R. Irrational numbers are real numbers
√
that cannot be written as pq (e.g. 2, π).
• (i) −7: An Integer (Z). It is negative so not a natural number, but it is a whole number
(no fractional part).
√ p
• (ii) 5: An Irrational number. It cannot be expressed as q for integers p, q; its decimal
expansion is non-terminating and non-repeating.
• (iii) 34 : A Rational number (Q). It is expressed as a ratio of two integers with non-zero
denominator.
• (iv) 0: A Natural number (in the inclusive convention N0 ) and also an Integer. In
UNISA’s DSC1501, 0 is accepted as an integer; the most specific classification is an in-
teger (Z).
(b) [4 marks]
Question: Simplify the following, showing all steps:
5 3 1 2 4
(i) + − (ii) ÷
6 4 3 3 9
Answer:
(i) Find the lowest common denominator (LCD) of 6, 4, and 3. The LCD is 12.
5 3 1 10 9 4 10 + 9 − 4 15 5
+ − = + − = = = = 1 41
6 4 3 12 12 12 12 12 4
Page 2 of 30
,DSC1501 | Exam Revision OCT/NOV Examination 2026
(ii) To divide by a fraction, multiply by its reciprocal:
2 4 2 9 18 3
÷ = × = = = 1 21
3 9 3 4 12 2
Exam Tip
When dividing fractions, flip the second fraction and multiply. Never divide numerators
and denominators separately. Always simplify to lowest terms.
(c) [4 marks]
Question: A clothing store increases the price of a jacket by 15% and then later offers a
10% discount on the new price. If the original price was R800, find the final selling price.
Is the final price higher or lower than the original, and by how much?
Answer:
Step 1: Apply 15% increase.
New price = R800 × (1 + 0.15) = R800 × 1.15 = R920
Step 2: Apply 10% discount.
Final price = R920 × (1 − 0.10) = R920 × 0.90 = R828
Step 3: Compare to original.
Difference = R828 − R800 = R28 (higher)
The final price is R828, which is R28 higher than the original R800. This is a net increase
of 28
800 × 100 = 3.5%.
Watch Out
A 15% increase followed by a 10% decrease does NOT result in a 5% net increase. The
percentages apply to different base values. Always work through each step separately.
Page 3 of 30
,DSC1501 | Exam Revision OCT/NOV Examination 2026
(d) [4 marks]
Question: Express the following in the required form:
(i) Write 0.000 045 3 in scientific notation.
(ii) Write 3.72 × 104 as an ordinary number.
(iii) Round 47.86 to 2 decimal places.
7
(iv) Express 8 as a percentage.
Answer:
• (i) Move the decimal 5 places to the right: 0.0000453 = 4.53 × 10−5
• (ii) Move the decimal 4 places to the right: 3.72 × 104 = 37 200
• (iii) 47.86 = 47.866 . . . ≈ 47.87 (the third decimal digit is 6 ≥ 5, so round up)
7
• (iv) × 100% = 87.5%
8
(e) [4 marks]
Question: A business divides its monthly profit of R180 000 among three partners A, B,
and C in the ratio 3:5:7. How much does each partner receive?
Answer:
Step 1: Find the total number of parts.
3 + 5 + 7 = 15 parts
Step 2: Find the value of one part.
R180 000
1 part = = R12 000
15
Step 3: Compute each partner’s share.
A = 3 × R12 000 = R36 000
B = 5 × R12 000 = R60 000
Page 4 of 30
, DSC1501 | Exam Revision OCT/NOV Examination 2026
C = 7 × R12 000 = R84 000
Check: 36 000 + 60 000 + 84 000 = 180 000 ✓
Page 5 of 30
