MIP1502 MATHEMATICS FOR INTERMEDIATE PHASE
TEACHERS II: ASSIGNMENT 4 PRACTICE EXAM 2026-
2027 QUESTIONS AND 100% CORRECT VERIFIED
ANSWERS WITH DETAILED RATIONALES PLUS
ANSWER KEY GRADED A+ GOOD LUCK!!!
Question 1
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
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.
Question 2
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
Profit is Revenue minus Cost. Revenue is 15x and Cost is 3x + 120. Therefore, P(x) =
15x - (3x + 120) = 12x - 120.
Question 3
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
To break even, profit must equal zero. Setting 6x - 90 = 0 leads to 6x = 90, which
simplifies to x = 15.
Question 4
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
The pattern increases by a constant difference of 4. The general formula for this
arithmetic sequence is Tn = 4n - 1. For Stage 10, T10 = 4(10) - 1 = 39.
Question 5
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 (Deduction)
Answer: B
Intermediate Phase learners typically operate at Van Hiele Level 1 (Analysis),
where they can identify and describe properties of shapes but may not yet
understand formal proofs or logical relationships between properties .
Question 6
What is the next term in the sequence 5, 12, 19, 26, ...?
A. 31
B. 33
C. 35
D. 37
Answer: B
The sequence has a constant difference of 7 (12 - 5 = 7, 19 - 12 = 7). Therefore, the
next term is 26 + 7 = 33.
Question 7
A car rental company charges R300 per day plus R5 per kilometer driven. Identify
the independent and dependent variables.
A. Independent: Total cost; Dependent: Kilometers driven
B. Independent: Kilometers driven; Dependent: Total cost
C. Independent: R300; Dependent: R5
D. Independent: Total cost; Dependent: Days
Answer: B
The total cost depends on the number of kilometers driven. The number of
kilometers driven is the input (independent variable), and the total cost is the
output (dependent variable).
Question 8
What is the gradient (slope) of the linear function passing through the points (2, 5)
and (4, 11)?
A. m = 2
B. m = 3
, C. m = 4
D. m = 6
Answer: B
The gradient formula is m = (y₂ - y₁) / (x₂ - x₁). Substituting the values yields m = (11
- 5) / (4 - 2) = 6/2 = 3.
Question 9
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
The y-intercept occurs where x = 0. Substituting zero gives f(0) = -4(0) + 12 = 12.
Question 10
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
Distribute the constants: (6a - 10b) - (3a - 6b) = 6a - 10b - 3a + 6b. Grouping like
terms results in 3a - 4b.
Question 11
Which mathematical property is illustrated by the statement: a × (b + c) = (a × b) +
(a × c)?
A. Associative Property
B. Commutative Property
C. Distributive Property
D. Identity Property
Answer: C
TEACHERS II: ASSIGNMENT 4 PRACTICE EXAM 2026-
2027 QUESTIONS AND 100% CORRECT VERIFIED
ANSWERS WITH DETAILED RATIONALES PLUS
ANSWER KEY GRADED A+ GOOD LUCK!!!
Question 1
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
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.
Question 2
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
Profit is Revenue minus Cost. Revenue is 15x and Cost is 3x + 120. Therefore, P(x) =
15x - (3x + 120) = 12x - 120.
Question 3
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
To break even, profit must equal zero. Setting 6x - 90 = 0 leads to 6x = 90, which
simplifies to x = 15.
Question 4
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
The pattern increases by a constant difference of 4. The general formula for this
arithmetic sequence is Tn = 4n - 1. For Stage 10, T10 = 4(10) - 1 = 39.
Question 5
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 (Deduction)
Answer: B
Intermediate Phase learners typically operate at Van Hiele Level 1 (Analysis),
where they can identify and describe properties of shapes but may not yet
understand formal proofs or logical relationships between properties .
Question 6
What is the next term in the sequence 5, 12, 19, 26, ...?
A. 31
B. 33
C. 35
D. 37
Answer: B
The sequence has a constant difference of 7 (12 - 5 = 7, 19 - 12 = 7). Therefore, the
next term is 26 + 7 = 33.
Question 7
A car rental company charges R300 per day plus R5 per kilometer driven. Identify
the independent and dependent variables.
A. Independent: Total cost; Dependent: Kilometers driven
B. Independent: Kilometers driven; Dependent: Total cost
C. Independent: R300; Dependent: R5
D. Independent: Total cost; Dependent: Days
Answer: B
The total cost depends on the number of kilometers driven. The number of
kilometers driven is the input (independent variable), and the total cost is the
output (dependent variable).
Question 8
What is the gradient (slope) of the linear function passing through the points (2, 5)
and (4, 11)?
A. m = 2
B. m = 3
, C. m = 4
D. m = 6
Answer: B
The gradient formula is m = (y₂ - y₁) / (x₂ - x₁). Substituting the values yields m = (11
- 5) / (4 - 2) = 6/2 = 3.
Question 9
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
The y-intercept occurs where x = 0. Substituting zero gives f(0) = -4(0) + 12 = 12.
Question 10
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
Distribute the constants: (6a - 10b) - (3a - 6b) = 6a - 10b - 3a + 6b. Grouping like
terms results in 3a - 4b.
Question 11
Which mathematical property is illustrated by the statement: a × (b + c) = (a × b) +
(a × c)?
A. Associative Property
B. Commutative Property
C. Distributive Property
D. Identity Property
Answer: C
