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Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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18 questions

SA-9709-P1-CG-0053 marksL1 FoundationCalculatorEquation
State the centre and radius of the circle (x−3)2+(y+2)2=49(x-3)^2+(y+2)^2=49.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0041 markL1 FoundationCalculatorProperties
Where is the point (6,2)(6,2) relative to the circle (x−2)2+(y+1)2=25(x-2)^2+(y+1)^2=25?
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0071 markL1 FoundationCalculatorProperties
A circle has centre (3,−5)(3,-5) and touches the xx-axis. State its radius.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-G013 marksL1 FoundationCalculatorEquation
A circle has centre (2,−3)(2,-3) and radius 44. Its equation can be written x2+y2+ax+by+c=0x^2+y^2+ax+by+c=0. Find aa, bb and cc.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-Q011 markL1 FoundationCalculatorEquation
The radius of the circle x2+y2=49x^2+y^2=49 is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-Q021 markL1 FoundationCalculatorProperties
ABAB is a diameter of a circle and PP is another point on the circle. Angle APBAPB is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0013 marksL2 StandardCalculatorExpanded form
Find the centre and radius of the circle x2+y2−6x+2y−15=0x^2+y^2-6x+2y-15=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0023 marksL2 StandardCalculatorExpanded form
Find the centre and radius of the circle x2+y2+8x=9x^2+y^2+8x=9.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0033 marksL2 StandardCalculatorProperties
A(−1,2)A(-1,2) and B(5,10)B(5,10) are the ends of a diameter of a circle. Find the centre and the radius.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0052 marksL2 StandardCalculatorEquation
A circle with centre (3,4)(3,4) passes through the origin. Its equation is x2+y2−6x−8y+c=0x^2+y^2-6x-8y+c=0. Find cc.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0063 marksL2 StandardCalculatorProperties
Find the xx-coordinates of the points where the circle (x−1)2+(y−2)2=20(x-1)^2+(y-2)^2=20 meets the xx-axis.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG-Q021 markL2 StandardCalculatorEquation
The centre of the circle x2+y2+4x−6y−3=0x^2+y^2+4x-6y-3=0 is
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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG-0064 marksL3 ExamCalculatorEquation
Find the centre and radius of the circle x2+y2+10x−8y+5=0x^2+y^2+10x-8y+5=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG-0074 marksL3 ExamCalculatorEquation
A circle has centre (1, 2)(1,\,2) and passes through (4, 6)(4,\,6). Its equation can be written x2+y2−2x−4y+c=0x^2+y^2-2x-4y+c=0. Find the radius and the value of cc.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0083 marksL3 ExamCalculatorExpanded form
x2+y2−4x+6y+k=0x^2+y^2-4x+6y+k=0 is the equation of a circle. The set of possible values of kk is k<ak<a. Find aa.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0094 marksL3 ExamCalculatorProperties
A circle passes through O(0,0)O(0,0), B(6,0)B(6,0) and C(0,8)C(0,8). Find its centre and radius.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG-0126 marksL4 ChallengingCalculatorEquation
A(2, 1)A(2,\,1) and B(8, 9)B(8,\,9) are the ends of a diameter of a circle. (a) Find the centre and radius. (b) The point C(1, k)C(1,\,k), where k>5k>5, lies on the circle. Find kk, and hence explain why angle ACB=90∘ACB=90^\circ.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-CG3-0105 marksL5 ExtensionCalculatorEquation
A circle passes through (1,1)(1,1) and (5,1)(5,1), and its centre lies on the line y=xy=x. Find the centre and r2r^2.

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Salam Academy Original Practice · Proposed mark scheme