Your learning journey
Calculate circle circumference and area, arc length and sector area, distinguishing curved length from the full sector perimeter.
Follow the task-specific calculator guidance in Apply. Keyboard - means the same as −. Attempt before opening a scaffold or intentional practice explanation.
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Connect & Check
Radius: centre to circumference. Diameter: chord through centre. Chord: joins two circumference points. Tangent: line touching at one point. Arc: curved boundary portion. Sector: enclosed by two radii and an arc. Segment: enclosed by chord and arc.
Intentional practice feedback after your attempt
10 cm.
Twice radius.
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1/4.
90÷360.
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36.
6×6.
Present
Every circle has circumference divided by diameter equal to π, so C=πd=2πr. Rearranging narrow sectors approaches a rectangle with height r and width πr, explaining area πr². A central angle θ covers θ/360 of a whole circle, so arc=(θ/360)2πr and sector area=(θ/360)πr². A sector perimeter adds two radii to its arc.
Mark radius versus diameter. Decide whether the question asks for length or area. Use the central-angle fraction, retain π or full calculator precision, then round once at the end. Check units and that a minor part is smaller than the whole.
Optional scaffold
Do not double a diameter again.
Intentional practice feedback after your attempt
10π cm.
Use πd.
Optional scaffold
Halve diameter first.
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16π cm².
Radius 4; square it.
Optional scaffold
Use θ/360.
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4π cm.
One third of 12π.
Optional scaffold
Keep length and area separate.
Intentional practice feedback after your attempt
12π cm²; 4π+12 cm.
Area one third of 36π; perimeter adds two radii.
Apply
Optional scaffold
Use fractions of circumference.
Intentional practice feedback after your attempt
8π, 4π, 2π cm.
Whole, half, quarter.
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16π cm²; 4π+16 cm.
Quarter of area and circumference; add radii.
Optional scaffold
Use the π key, not 3.14.
Intentional practice feedback after your attempt
31.4 m; 78.5 m².
10π and 25π; round only final values.
Calculator required for A3 only; other tasks use exact π forms. Enter 10×π and π×5², retaining full precision until rounding to 1 decimal place. Numeric retrieval asks for coefficients of π, not the full symbolic answer.
Apply and extend
Intentional practice feedback after your attempt
Circumference doubles; area quadruples because (2r)²=4r².
Use formulas or a counterexample.
Intentional practice feedback after your attempt
3π is curved arc only; include diameter 6, total 3π+6 m.
Trace the closed boundary.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
A prism has the same cross-section throughout. Volume equals cross-sectional area times perpendicular length; for a cylinder the cross-section is a circle. Use cubic units.
Retrieve F1 again in one week. Bring your working and one question.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
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Optional extension activities
Allow 10–15 minutes if the main practice is secure. Show your method, explain a check and justify your conclusion.
Stretch
Reveal a worked check after attempting
Arc=80/360×18π=4π cm; area=80/360×81π=18π cm².
Deep challenge
Reveal a worked check after attempting
5π is curved arc only; full perimeter includes diameter 10, so 5π+10 cm.