IB MYP Extended Math Mock Test 3– 2026 Edition
IB MYP Extended Math Mock Test 3 – April/May 2026 Exam
IB MYP Extended Math Mock Test 3: Prepare for the MYP exams with subject-specific Prediction questions, model answers. All topics covered.
Prepared by MYP teachers: Access our IB MYP Extended Math Mock Test 3 Mock with model answer. Students: Practice with exam-style papers for MYP Exam
Question 1: Function [6 marks]
Find the domain and range from the graph of a function.
We can plot the graph of \( y = f(x) \) and determine the domain and range of the functions by analysing its coordinates.
a Question 1a [3 marks] – Domain and Range from Graph
Write down the domain and range of the function f shown in the graph below.
Graph description:
y-axis from -9 to 5, x-axis from -5 to 11. The function f appears as a curve starting around (-4,-8), peaking near (3,4), and ending around (10,-6).
▶️Answer/Explanation
Step 1: Determine Domain (x-values)
The graph starts at approximately x = -4 and ends at x = 10. The function is defined for all x-values in this interval.
Domain: \( -4 \leq x \leq 10 \)
Step 2: Determine Range (y-values)
The lowest point is around y = -8 and the highest point is near y = 4.
Range: \( -8 \leq y \leq 4 \)
Step 3: Verification
All points on the graph fall within these x and y boundaries, confirming our answer.
Final Answer:
Domain: \( -4 \leq x \leq 10 \)
Range: \( -8 \leq y \leq 4 \)
b Question 1b [3 marks] – Trigonometric Functions Domain and Range
The graphs of trigonometric functions, \( y = \sin x \) and \( y = \cos x \) are shown below. Show that the domain and range of the given trigonometric functions, \( y = \sin x \) and \( y = \cos x \) are equal.
▶️Answer/Explanation
Step 1: Domain of sin(x) and cos(x)
Both sine and cosine functions are defined for all real numbers.
Domain for both: \( x \in \mathbb{R} \) (all real numbers)
Step 2: Range of sin(x) and cos(x)
The output values of both functions oscillate between -1 and 1.
Range for both: \( -1 \leq y \leq 1 \)
Step 3: Graphical Verification
From the graphs (not shown here but referenced in the question):
- Both functions continue infinitely in both x-directions (same domain)
- Both have maximum value of 1 and minimum of -1 (same range)
- Both are periodic with period \( 2\pi \)
Step 4: Conclusion
Since both functions share identical domain and range, we’ve shown they are equal.
Final Answer:
Both \( y = \sin x \) and \( y = \cos x \) have:
Domain: All real numbers (\( x \in \mathbb{R} \))
Range: \( -1 \leq y \leq 1 \)
Syllabus Reference
Unit 3: Function
- Domain and range
- Graphing trigonometric functions
- Representation and shape of more complex functions
Assessment Criteria: A (Knowing and understanding), C (Communication)