[TYPE THE COMPANY NAME]
MIP1502 Assignment 1
(COMPLETE ANSWERS)
2026 - DUE 21 April 2026
NO PLAGIARISM
[Pick the date]
[Type the abstract of the document here. The abstract is typically a short summary of the contents of
the document. Type the abstract of the document here. The abstract is typically a short summary of
the contents of the document.]
,Exam (elaborations)
MIP1502 Assignment 1 (COMPLETE
ANSWERS) 2026 (636464) - DUE 21 April
2026
MIP1502 Assignment 1 (COMPLETE ANSWERS) 2026 (636464) - DUE 21 April
2026; 100% TRUSTED Complete, trusted solutions and explanations.
An engineer is designing a steel truss for a bridge using metal beams
arranged in triangles. Figure 1: 1 triangle is formed using 3 beams. Figure 2:
2 triangles are formed in a row pointing up and down using 5 beams. Figure
3: 3 triangles are formed in a row using 7 beams. Draw or visualise figure 4.
How many beams would be needed? Determine the general rule Tn for the
number of beams in terms of n, the number of triangles. Your formula will
likely include multiplication by 2. Explain what this 2 represents physically in
the construction of the bridge, showing how many beams are added for each
new triangle and how many are shared. Calculate which figure number n
would require exactly 87 beams. A student plots this pattern on a Cartesian
plane and connects the points with a solid straight line. Critique this
representation and state whether the data is continuous or discrete. Explain
why drawing a solid line is not correct in this context, for example what a
value such as n equals 1.5 would mean. If the engineer adds 2 extra vertical
support beams, one at the start and one at the end, explain how the rule Tn
would change. 1.1 Algebra is often introduced in primary school through
patterns, number sentences, and symbolic reasoning. Critically evaluate the
rationale for introducing algebraic thinking in the Foundation and
Intermediate Phases. In your response: 1.1.1 Discuss at least two
pedagogical benefits of early algebra exposure. (4) 1.1.2 Identify one
common misconception learners may develop and explain how it can be
addressed. (3) 1.1.3 Justify how early algebra supports progression into
formal algebra in later grades. (3) 1.2 Many learners struggle with the
concept of multiplying negative numbers. Design a mini-lesson (not just
explanations) that includes: 1.2.1 A real-world context (2) 1.2.2 A visual
model (2) 1.2.3 A pattern-based reasoning approach (2) 1.2.4 Explain how
each method supports conceptual understanding. (4) [20] Question 2 2.1
Translate the following real-world scenarios into algebraic expressions or
equations. Then solve them. 2.1.1 A machine depreciates in value by 15%
annually. If it was worth R120,000 initially, what is its value after 3 years? (4)
2.1.2 A recipe calls for 2 parts flour, 3 parts sugar, and 5 parts water. If you
have 1.2 kg of sugar, how much flour and water are needed to maintain the
ratio?. (4) 2.1.3 A plumber charges a call-out fee and an hourly rate. A 3-hour
job costs R870, and a 5-hour job costs R1,250. Determine the call-out fee
and hourly rate. (6) 2.2 Create a real-world context for the equation: 0.75
, This question requires you to move beyond simply solving mathematical
problems. The study guide distinguishes between an unknown in a number
sentence and a variable in a functional relationship. Consider the following
two mathematical statements: Statement A: 5k − 10 = 25 Statement B: y =
5k − 10 Explain the conceptual difference in the role of the symbol k in
statement A compared to statement B. Which statement represents a
specific value, and which statement represents a domain of input values?
You are observing a Grade 6 class. A learner, Sam, writes the equation P + S
= 20 to represent the sentence that there are 20 people in the room
consisting of professors and students. However, when asked to represent the
sentence that there are six times as many students as professors, Sam
writes 6S = P. Explain why Sam’s logic is flawed. Consider the inequality 5 −
3x ≥ −4. Solve for x, ensuring you explicitly show the inverse operations.
Represent the solution using correct set-builder notation. A learner looks at
the solution and asks if x is less than or equal to 3, then the biggest number
is 3 and whether the next biggest number is 2. Refute this claim using the
property of density in real numbers and give an example of a number
between 2 and 3 that satisfies the condition. Explain why the expression 5
divided by x minus 3 is undefined if x equals 3 and relate this to the inverse
relationship between multiplication and division. Algebra evolved from
describing problems in sentences to using symbols. Translate the rhetorical
problem into a single symbolic equation: I am thinking of a number. If I
square it and subtract five times the number, the result is negative six. Solve
the equation algebraically. Explain why it is necessary to set the equation
equal to zero to solve it effectively and explain the zero product principle. A
learner, Lerato, attempts to simplify the expression 5(2a · 3). Her work is
shown. Identify the specific property she applied incorrectly and explain why
it is not applicable. Solve the expression correctly and name the property
that allows regrouping of numbers. Provide a simple arithmetic
counterexample to show that her method changes the value. Using the
distributive property, prove that x · 0 = 0. A student claims that division is
associative like multiplication. Disprove this claim by calculating (24 ÷ 6) ÷ 2
and comparing it to 24 ÷ (6 ÷ 2). Mr Jola is organising transport for a Grade
7 field trip using identical minibuses. If he places 12 learners in each
minibus, 5 learners are left. If he places 13 learners in each minibus, there
are 2 empty seats in the last minibus. Define your variables clearly.
Construct two linear equations representing the total number of learners for
both scenarios. Solve the system to determine the number of minibuses and
total learners. Explain how you would verify your answer without using a
memo. The Student Representative Council is organising a concert and
needs to generate R6000 from ticket sales. Let x be the price of a ticket and
y the number of people attending. The situation is represented by xy = 6000.
If the ticket price is lowered by R10, 20 more people will attend, and revenue
remains R6000. Set up a system of two equations. Substitute one variable
into the other to show it results in a quadratic equation of the form x² − 10x
− 3000 = 0. Solve for the original ticket price and explain why the negative
MIP1502 Assignment 1
(COMPLETE ANSWERS)
2026 - DUE 21 April 2026
NO PLAGIARISM
[Pick the date]
[Type the abstract of the document here. The abstract is typically a short summary of the contents of
the document. Type the abstract of the document here. The abstract is typically a short summary of
the contents of the document.]
,Exam (elaborations)
MIP1502 Assignment 1 (COMPLETE
ANSWERS) 2026 (636464) - DUE 21 April
2026
MIP1502 Assignment 1 (COMPLETE ANSWERS) 2026 (636464) - DUE 21 April
2026; 100% TRUSTED Complete, trusted solutions and explanations.
An engineer is designing a steel truss for a bridge using metal beams
arranged in triangles. Figure 1: 1 triangle is formed using 3 beams. Figure 2:
2 triangles are formed in a row pointing up and down using 5 beams. Figure
3: 3 triangles are formed in a row using 7 beams. Draw or visualise figure 4.
How many beams would be needed? Determine the general rule Tn for the
number of beams in terms of n, the number of triangles. Your formula will
likely include multiplication by 2. Explain what this 2 represents physically in
the construction of the bridge, showing how many beams are added for each
new triangle and how many are shared. Calculate which figure number n
would require exactly 87 beams. A student plots this pattern on a Cartesian
plane and connects the points with a solid straight line. Critique this
representation and state whether the data is continuous or discrete. Explain
why drawing a solid line is not correct in this context, for example what a
value such as n equals 1.5 would mean. If the engineer adds 2 extra vertical
support beams, one at the start and one at the end, explain how the rule Tn
would change. 1.1 Algebra is often introduced in primary school through
patterns, number sentences, and symbolic reasoning. Critically evaluate the
rationale for introducing algebraic thinking in the Foundation and
Intermediate Phases. In your response: 1.1.1 Discuss at least two
pedagogical benefits of early algebra exposure. (4) 1.1.2 Identify one
common misconception learners may develop and explain how it can be
addressed. (3) 1.1.3 Justify how early algebra supports progression into
formal algebra in later grades. (3) 1.2 Many learners struggle with the
concept of multiplying negative numbers. Design a mini-lesson (not just
explanations) that includes: 1.2.1 A real-world context (2) 1.2.2 A visual
model (2) 1.2.3 A pattern-based reasoning approach (2) 1.2.4 Explain how
each method supports conceptual understanding. (4) [20] Question 2 2.1
Translate the following real-world scenarios into algebraic expressions or
equations. Then solve them. 2.1.1 A machine depreciates in value by 15%
annually. If it was worth R120,000 initially, what is its value after 3 years? (4)
2.1.2 A recipe calls for 2 parts flour, 3 parts sugar, and 5 parts water. If you
have 1.2 kg of sugar, how much flour and water are needed to maintain the
ratio?. (4) 2.1.3 A plumber charges a call-out fee and an hourly rate. A 3-hour
job costs R870, and a 5-hour job costs R1,250. Determine the call-out fee
and hourly rate. (6) 2.2 Create a real-world context for the equation: 0.75
, This question requires you to move beyond simply solving mathematical
problems. The study guide distinguishes between an unknown in a number
sentence and a variable in a functional relationship. Consider the following
two mathematical statements: Statement A: 5k − 10 = 25 Statement B: y =
5k − 10 Explain the conceptual difference in the role of the symbol k in
statement A compared to statement B. Which statement represents a
specific value, and which statement represents a domain of input values?
You are observing a Grade 6 class. A learner, Sam, writes the equation P + S
= 20 to represent the sentence that there are 20 people in the room
consisting of professors and students. However, when asked to represent the
sentence that there are six times as many students as professors, Sam
writes 6S = P. Explain why Sam’s logic is flawed. Consider the inequality 5 −
3x ≥ −4. Solve for x, ensuring you explicitly show the inverse operations.
Represent the solution using correct set-builder notation. A learner looks at
the solution and asks if x is less than or equal to 3, then the biggest number
is 3 and whether the next biggest number is 2. Refute this claim using the
property of density in real numbers and give an example of a number
between 2 and 3 that satisfies the condition. Explain why the expression 5
divided by x minus 3 is undefined if x equals 3 and relate this to the inverse
relationship between multiplication and division. Algebra evolved from
describing problems in sentences to using symbols. Translate the rhetorical
problem into a single symbolic equation: I am thinking of a number. If I
square it and subtract five times the number, the result is negative six. Solve
the equation algebraically. Explain why it is necessary to set the equation
equal to zero to solve it effectively and explain the zero product principle. A
learner, Lerato, attempts to simplify the expression 5(2a · 3). Her work is
shown. Identify the specific property she applied incorrectly and explain why
it is not applicable. Solve the expression correctly and name the property
that allows regrouping of numbers. Provide a simple arithmetic
counterexample to show that her method changes the value. Using the
distributive property, prove that x · 0 = 0. A student claims that division is
associative like multiplication. Disprove this claim by calculating (24 ÷ 6) ÷ 2
and comparing it to 24 ÷ (6 ÷ 2). Mr Jola is organising transport for a Grade
7 field trip using identical minibuses. If he places 12 learners in each
minibus, 5 learners are left. If he places 13 learners in each minibus, there
are 2 empty seats in the last minibus. Define your variables clearly.
Construct two linear equations representing the total number of learners for
both scenarios. Solve the system to determine the number of minibuses and
total learners. Explain how you would verify your answer without using a
memo. The Student Representative Council is organising a concert and
needs to generate R6000 from ticket sales. Let x be the price of a ticket and
y the number of people attending. The situation is represented by xy = 6000.
If the ticket price is lowered by R10, 20 more people will attend, and revenue
remains R6000. Set up a system of two equations. Substitute one variable
into the other to show it results in a quadratic equation of the form x² − 10x
− 3000 = 0. Solve for the original ticket price and explain why the negative
