Exam (elaborations)
TMS3725 SUPP EXAM 2024
- Course
- TMS3725 (TMS3725)
- Institution
- University Of South Africa (Unisa)
TMS3725 SUPP EXAM 2024
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JAN/FEB SUPPEXAM2024TMS3725
TEACHING Tms3725 supp
exam 2024
MATHEMATICS IN
FET PHASE100
MARKS 3 HOURS 30
1.1 Explain what it means to do mathematics. (4)
, Question 1
1.1Explain what it means to do mathematics. (4)
Doing mathematics refers to the act of using logical reasoning and problem-solving skills to study
and understand patterns, relationships, and structures within the realm of numbers, quantities,
shapes, and space. It involves using methods such as calculations, proofs, and deductions to solve
problems and explore concepts in areas such as algebra, geometry, calculus, and statistics.
Additionally, doing mathematics involves the ability to communicate findings and insights through
written and verbal explanations. Overall, doing mathematics is about exploring and applying the
principles and techniques of the discipline to make sense of the world around us.
1.2 The quality of mathematics that learners learn depends on the mathematical tasks/activities
they are exposed to. Routine and non-routine problems are often used in mathematics classrooms.
These tasks play a role in teaching mathematics for understanding. In your classroom, you intend
using the following tasks:
Task 1: Find the 26th term of the sequence 2; 5; 8; 11
Task 2: Find the arithmetic sequence if the 4th term is 3 and the 8th term is -13
In Task 1, you are asked to find the 26th term of the sequence 2, 5, 8, 11. This task involves finding
the pattern or rule that governs the sequence and using it to determine the desired term.
To find the pattern in this sequence, we can observe that each term is obtained by adding 3 to the
previous term. So, the pattern can be described as adding 3 repeatedly to the initial term of 2.
To find the 26th term, we can use the formula for the nth term of an arithmetic sequence:
𝑎_𝑛 = 𝑎_1 + (𝑛 - 1)𝑑
where 𝑎_𝑛 is the nth term, 𝑎_1 is the first term, 𝑛 is the position of the term, and 𝑑 is the common
difference.
In this case, 𝑎_1 = 2, 𝑛 = 26, and 𝑑 = 3. Plugging these values into the formula, we get:
𝑎_26 = 2 + (26 - 1) * 3
= 2 + 25 * 3
= 2 + 75
= 77
Therefore, the 26th term of the sequence 2, 5, 8, 11 is 77.
In Task 2, you are asked to find the arithmetic sequence given the 4th term is 3 and the 8th term is -
13. This task involves finding the common difference and using it to generate the sequence.
We can start by using the formula for the nth term of an arithmetic sequence:
𝑎_𝑛 = 𝑎_1 + (𝑛 - 1)𝑑
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