IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Functions–Linear programming,including inequalities
Topic :Function- Weightage : 21 %
All Questions for Topic : Representation and shape of more complex functions,Transformation of quadratic functions,Rational functions,Graphing trigonometric functions,Linear programming, including inequalities,Networks-edges and arcs, nodes/ vertices, paths,Calculating network pathways,Weighted networks,Domain and range
Question : Coordinate Geometry [6 marks]
Given the functions:
• y = x²
• 2x + y = 12
• x = 5
a Question a [3 marks] – Graph Sketching
Sketch the graphs on the coordinate plane and shade the region satisfying:
y ≤ x², 2x + y ≥ 12, and x ≤ 5
▶️Answer/Explanation
Key Features:
- Parabola y = x² opening upwards
- Line 2x + y = 12 with intercepts at (6,0) and (0,12)
- Vertical line x = 5
- Shaded region: Below parabola, above line, left of x=5
Marking Scheme:
- •1: Correct sketch of y = x²
- •2: Correct sketch of 2x + y = 12 with intercepts
- •3: Correct sketch of x = 5 and correct shaded region
b Question b [3 marks] – Maximum Value
Find the maximum value of the function f(x,y) = x + 2y in the shaded region:
▶️Answer/Explanation
Solution Steps:
- Find vertices of the feasible region:
- Intersection of y=x² and 2x+y=12 → (2,4) and (-3,9)
- Intersection of x=5 and y=x² → (5,25)
- Intersection of x=5 and 2x+y=12 → (5,2)
- Evaluate f(x,y) at vertices:
- f(2,4) = 2 + 8 = 10
- f(-3,9) = -3 + 18 = 15
- f(5,25) = 5 + 50 = 55
- f(5,2) = 5 + 4 = 9
- Maximum value is 55 at (5,25)
Marking Scheme:
- •1: Finds at least two correct vertices
- •2: Evaluates f(x,y) at vertices
- •3: Identifies correct maximum value (55)
Syllabus Reference
Unit 2: Algebra
- Graphical inequalities
- Linear programming
Unit 3: Functions
- Quadratic functions
- Linear functions
Assessment Criteria: B (Investigating Patterns), D (Applying Mathematics in Real-life Contexts)