Reach for the Star | GCSE Mathematics

L085: Functions pathway

Objective

Interpret functions at the appropriate tier.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Functions pathway
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for functions pathway.

Core practice

If f(x)=x²+2x, find f(−3) and solve f(x)=0.

Reasoning

Let f(x)=2x+1 and g(x)=x². Compare f(g(3)) and g(f(3)).

Exam-style

Solve an exam-style problem involving functions pathway. Show working, include a check and interpret your answer.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L085: Functions pathway

Objective: Interpret functions at the appropriate tier.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.

Even Better If (EBI)

I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.

Stretch and deep challenge

Stretch: If f(x)=x²+2x, find f(−3) and solve f(x)=0.

Deep challenge: Let f(x)=2x+1 and g(x)=x². Compare f(g(3)) and g(f(3)).