Intersection Skills Math: Graphs & Functions

A 36-page Senior Secondary Mathematics resource with 23 progressively challenging practice questions on graph intersections, variation tables, approximate roots, function composition, derivatives, absolute-value equations, trigonometric functions, and solution counting. Includes a Quick Reference & Skill Guide and detailed worked solutions.
Full Description Develop the skill of counting solutions through mathematical reasoning.
This resource focuses on Intersection, a fundamental problem-solving skill that allows students to determine the number of solutions of an equation by interpreting graphs, variation tables, and relationships between functions.
Rather than relying only on direct algebraic manipulation, students learn to transform equations into forms that can be interpreted graphically and analyzed systematically.
The resource includes a Quick Reference & Skill Guide followed by 23 practice questions and a complete set of detailed worked solutions.
Students practise:
-Counting intersections between graphs
-Reading and interpreting variation tables
-Determining the number of real solutions
-Using approximate roots
-Working with sign charts
-Analyzing f(f(x))f(f(x))
-Applying derivative-based reasoning
-Solving absolute-value equations through intersections
-Working with f(sin⁡x)f(\sin x) and f(cos⁡x)f(\cos x)
-Applying tracing / spiral techniques
-Solving more advanced function and parameter problems
The later questions progressively increase the level of reasoning, including problems involving composite functions, polynomial graphs, trigonometric inputs, and parameter relationships.
Resource includes
35 pages
-1 Quick Reference & Skill Guide
-23 practice questions
-Student workspace
-Detailed worked solutions
-Answer key
The solutions section demonstrates multiple approaches, including variation-table methods, approximate-root methods, graphical intersection methods, and tracing/spiral techniques.
**Suitable for: **Senior Secondary Mathematics, Functions, Calculus , Graphs, Exam Preparation, Mathematical Problem Solving