Reach for the Star | GCSE Mathematics

L090: Circle equations pathway

Objective

Connect circle and coordinate geometry at the appropriate tier.

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

Visual model for Circle equations 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 circle equations pathway.

Core practice

A circle has equation x²+y²=49. Find y-values when x=0 and when x=5.

Reasoning

Can (7,7) lie on the circle x²+y²=49? Justify by substitution.

Exam-style

Use a labelled diagram to calculate the missing value. State the theorem or formula and include units where needed.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L090: Circle equations pathway

Objective: Connect circle and coordinate geometry 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 selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: A circle has equation x²+y²=49. Find y-values when x=0 and when x=5.

Deep challenge: Can (7,7) lie on the circle x²+y²=49? Justify by substitution.