UNISA MIP1502 MASTER TEST BANK
EXAM AND ASSIGNMENT MCQS WITH
DETAILED RATIONALES
This comprehensive question multiple-choice study bank is explicitly
tailored for UNISA's MIP1502 module, covering essential algebraic
functions, pattern expansions, geometric transformations, and core
pedagogical theories. Each practice question includes the correct
answer along with a bolded, step-by-step mathematical rationale to
ensure rapid concept mastery and independent correction. It serves
as a premium, high-converting revision resource perfect for students
preparing for final portfolio submissions and academic examinations.
Q1. A printing shop charges a fixed fee of R50 and R8 per page.
Which algebraic expression represents the total cost C(x) for printing
x pages?
A) C(x) = 50x + 8
B) C(x) = 8x + 50
C) C(x) = 58x
D) C(x) = 8x - 50
Answer: B
Rationale: The total cost consists of a variable component that
depends on the number of pages (8x) and a constant fixed setup fee
(50). Combining these gives C(x) = 8x + 50.
Q2. If a student sells handmade bookmarks for R15 each, and the
materials cost a fixed R120 plus R3 per bookmark, what is the profit
equation P(x) for x bookmarks sold?
A) P(x) = 12x - 120
B) P(x) = 18x - 120
,C) P(x) = 15x - 120
D) P(x) = 12x + 120
Answer: A
Rationale: Profit is Revenue minus Cost. Revenue is 15x and Cost is
3x + 120. Therefore, P(x) = 15x - (3x + 120) = 12x - 120.
Q3. Using the profit formula P(x) = 6x - 90, what is the minimum
number of items a school tuck shop must sell to break even?
A) 10 items
B) 12 items
C) 15 items
D) 20 items
Answer: C
Rationale: To break even, profit must equal zero. Setting 6x - 90 = 0
leads to 6x = 90, which simplifies to x = 15.
Q4. Consider the geometric visual pattern where Stage 1 has 3
triangles, Stage 2 has 7 triangles, and Stage 3 has 11 triangles. How
many triangles will be in Stage 10?
A) 33
B) 39
C) 41
D) 43
Answer: B
Rationale: The pattern increases by a constant difference of 4. The
general formula for this arithmetic sequence is \(T_n = 4n - 1\). For
Stage 10, T₁₀ = 4(10) - 1 = 39.
Q5. In the context of the South African CAPS curriculum, at which Van
Hiele level do Intermediate Phase learners primarily operate when
they analyze geometric shapes by their properties?
A) Level 0: Visualization
B) Level 1: Analysis
C) Level 2: Informal Deduction
D) Level 3: Formal Deduction
Answer: B
,Rationale: Learners at Van Hiele Level 1 (Analysis) can identify and
describe the properties of geometric figures rather than just
identifying them by their holistic visual appearance.
Q6. Solve for x in the linear equation: 3(x - 4) = 2x + 5
A) x = 1
B) x = 9
C) x = 17
D) x = -7
Answer: C
Rationale: Expanding the equation gives 3x - 12 = 2x + 5. Subtracting
2x from both sides gives x - 12 = 5. Adding 12 to both sides gives x =
17.
Q7. Which type of assessment is most appropriate when a teacher
wants to identify specific mathematical misconceptions in multi-step
fraction addition before planning the next unit?
A) Summative assessment
B) Diagnostic assessment
C) Evaluative assessment
D) Benchmark assessment
Answer: B
Rationale: Diagnostic assessments are explicitly designed to uncover
gaps in knowledge, learning difficulties, and specific procedural
misconceptions before or during instruction.
Q8. A linear function passes through the points (2, 5) and (4, 11). What
is the gradient (m) of this line?
A) m = 2
B) m = 3
C) m = 4
D) m = 6
Answer: B
Rationale: The gradient formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values yields \(m = \frac{11 - 5}{4 - 2} = \frac{6}{2} =
3\).
, Q9. What is the value of the y-intercept for the function defined by f(x)
= -4x + 12?
A) -4
B) 3
C) 12
D) 0
Answer: C
Rationale: The y-intercept occurs where x = 0. Substituting zero gives
f(0) = -4(0) + 12 = 12.
Q10. Simplify the algebraic expression completely: 2(3a - 5b) - 3(a -
2b)
A) 3a - 4b
B) 3a - 16b
C) 3a + 4b
D) 5a - 4b
Answer: A
Rationale: Distribute the constants: (6a - 10b) - (3a - 6b) = 6a - 10b - 3a
+ 6b. Grouping like terms results in 3a - 4b.
Q11. Which mathematical property is illustrated by the statement: \(a
\times (b + c) = (a \times b) + (a \times c)\)?
A) Associative Property
B) Commutative Property
C) Distributive Property
D) Identity Property
Answer: C
Rationale: The distributive property shows how multiplication
operations distribute over addition or subtraction inside brackets.
Q12. A pattern of squares is built using matchsticks. Stage 1 requires
4 sticks, Stage 2 requires 7 sticks, and Stage 3 requires 10 sticks.
Find the general rule \(T_{n}\) for this pattern.
A) \(T_n = 4n\)
B) \(T_n = 3n + 1\)
C) \(T_n = 3n - 1\)
EXAM AND ASSIGNMENT MCQS WITH
DETAILED RATIONALES
This comprehensive question multiple-choice study bank is explicitly
tailored for UNISA's MIP1502 module, covering essential algebraic
functions, pattern expansions, geometric transformations, and core
pedagogical theories. Each practice question includes the correct
answer along with a bolded, step-by-step mathematical rationale to
ensure rapid concept mastery and independent correction. It serves
as a premium, high-converting revision resource perfect for students
preparing for final portfolio submissions and academic examinations.
Q1. A printing shop charges a fixed fee of R50 and R8 per page.
Which algebraic expression represents the total cost C(x) for printing
x pages?
A) C(x) = 50x + 8
B) C(x) = 8x + 50
C) C(x) = 58x
D) C(x) = 8x - 50
Answer: B
Rationale: The total cost consists of a variable component that
depends on the number of pages (8x) and a constant fixed setup fee
(50). Combining these gives C(x) = 8x + 50.
Q2. If a student sells handmade bookmarks for R15 each, and the
materials cost a fixed R120 plus R3 per bookmark, what is the profit
equation P(x) for x bookmarks sold?
A) P(x) = 12x - 120
B) P(x) = 18x - 120
,C) P(x) = 15x - 120
D) P(x) = 12x + 120
Answer: A
Rationale: Profit is Revenue minus Cost. Revenue is 15x and Cost is
3x + 120. Therefore, P(x) = 15x - (3x + 120) = 12x - 120.
Q3. Using the profit formula P(x) = 6x - 90, what is the minimum
number of items a school tuck shop must sell to break even?
A) 10 items
B) 12 items
C) 15 items
D) 20 items
Answer: C
Rationale: To break even, profit must equal zero. Setting 6x - 90 = 0
leads to 6x = 90, which simplifies to x = 15.
Q4. Consider the geometric visual pattern where Stage 1 has 3
triangles, Stage 2 has 7 triangles, and Stage 3 has 11 triangles. How
many triangles will be in Stage 10?
A) 33
B) 39
C) 41
D) 43
Answer: B
Rationale: The pattern increases by a constant difference of 4. The
general formula for this arithmetic sequence is \(T_n = 4n - 1\). For
Stage 10, T₁₀ = 4(10) - 1 = 39.
Q5. In the context of the South African CAPS curriculum, at which Van
Hiele level do Intermediate Phase learners primarily operate when
they analyze geometric shapes by their properties?
A) Level 0: Visualization
B) Level 1: Analysis
C) Level 2: Informal Deduction
D) Level 3: Formal Deduction
Answer: B
,Rationale: Learners at Van Hiele Level 1 (Analysis) can identify and
describe the properties of geometric figures rather than just
identifying them by their holistic visual appearance.
Q6. Solve for x in the linear equation: 3(x - 4) = 2x + 5
A) x = 1
B) x = 9
C) x = 17
D) x = -7
Answer: C
Rationale: Expanding the equation gives 3x - 12 = 2x + 5. Subtracting
2x from both sides gives x - 12 = 5. Adding 12 to both sides gives x =
17.
Q7. Which type of assessment is most appropriate when a teacher
wants to identify specific mathematical misconceptions in multi-step
fraction addition before planning the next unit?
A) Summative assessment
B) Diagnostic assessment
C) Evaluative assessment
D) Benchmark assessment
Answer: B
Rationale: Diagnostic assessments are explicitly designed to uncover
gaps in knowledge, learning difficulties, and specific procedural
misconceptions before or during instruction.
Q8. A linear function passes through the points (2, 5) and (4, 11). What
is the gradient (m) of this line?
A) m = 2
B) m = 3
C) m = 4
D) m = 6
Answer: B
Rationale: The gradient formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values yields \(m = \frac{11 - 5}{4 - 2} = \frac{6}{2} =
3\).
, Q9. What is the value of the y-intercept for the function defined by f(x)
= -4x + 12?
A) -4
B) 3
C) 12
D) 0
Answer: C
Rationale: The y-intercept occurs where x = 0. Substituting zero gives
f(0) = -4(0) + 12 = 12.
Q10. Simplify the algebraic expression completely: 2(3a - 5b) - 3(a -
2b)
A) 3a - 4b
B) 3a - 16b
C) 3a + 4b
D) 5a - 4b
Answer: A
Rationale: Distribute the constants: (6a - 10b) - (3a - 6b) = 6a - 10b - 3a
+ 6b. Grouping like terms results in 3a - 4b.
Q11. Which mathematical property is illustrated by the statement: \(a
\times (b + c) = (a \times b) + (a \times c)\)?
A) Associative Property
B) Commutative Property
C) Distributive Property
D) Identity Property
Answer: C
Rationale: The distributive property shows how multiplication
operations distribute over addition or subtraction inside brackets.
Q12. A pattern of squares is built using matchsticks. Stage 1 requires
4 sticks, Stage 2 requires 7 sticks, and Stage 3 requires 10 sticks.
Find the general rule \(T_{n}\) for this pattern.
A) \(T_n = 4n\)
B) \(T_n = 3n + 1\)
C) \(T_n = 3n - 1\)
