WAEC Mathematics questions: Loci

12 questions with answers and explanations. Tap an option to check yourself.

1. Question 1· Loci· WAEC

   The locus of a point P that moves so that it is always 5 cm from a fixed point O is

   • Aa circle of radius 5 cm centred at O
   • Ba straight line
   • Ca square
   • Dan angle bisector

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   Explanation and discussion

2. Question 2· Loci· WAEC

   In a plane, the locus of a point that is always 5 cm from a fixed point O is

   • Aa circle with centre O and radius 5 cm
   • Ba straight line through O
   • Ca pair of parallel lines
   • Dan arc of radius 10 cm

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   Explanation and discussion

3. Question 3· Loci· WAEC

   A goat is tied to a post with a rope 4 m long. The boundary of the region it can graze is

   • Aa circle of radius 8 m
   • Ba square of side 4 m
   • Ca straight line 4 m long
   • Da circle of radius 4 m centred at the post

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   Explanation and discussion

4. Question 4· Loci· WAEC

   A lamp is to be placed the same distance from two straight roads that cross each other. The possible positions lie on

   • Athe lines bisecting the angles between the roads
   • Ba circle round the crossing
   • Ca line parallel to one road
   • Dthe crossing point only

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   Explanation and discussion

5. Question 5· Loci· WAEC

   In a plane, a point moves so that it is always 3 cm from a straight line AB extended both ways. Its locus is

   • Aa single line parallel to AB
   • Ba circle of radius 3 cm
   • Cthe perpendicular bisector of AB
   • Da pair of lines parallel to AB, 3 cm on either side

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   Explanation and discussion

6. Question 6· Loci· WAEC

   As a wheel turns, a point on its rim traces out, relative to the centre of the wheel,

   • Aa circle
   • Ba straight line
   • Ca square
   • Da parabola

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7. Question 7· Loci· WAEC

   A point P moves so that angle APB = 90°, where A and B are fixed points. The locus of P is

   • Aa straight line through A
   • Bthe perpendicular bisector of AB
   • Ca circle with AB as diameter
   • Da circle with centre A

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8. Question 8· Loci· WAEC

   Two boreholes P and Q are 100 m apart. A tap is to be placed the same distance from both. The possible positions of the tap lie on

   • Aa circle with diameter PQ
   • Bthe line PQ only
   • Ca circle with centre P
   • Dthe perpendicular bisector of PQ

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9. Question 9· Loci· WAEC

   Points equidistant from two parallel lines 8 cm apart lie on

   • Aa line midway between them, 4 cm from each
   • Ba line 8 cm from each
   • Ca circle of radius 4 cm
   • Deither of the two lines

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10. Question 10· Loci· WAEC

    The locus of points inside a circle of radius 5 cm that are 2 cm from its centre is

    • Aa circle of radius 3 cm
    • Ba circle of radius 2 cm with the same centre
    • Ca line 2 cm long
    • Da circle of radius 7 cm

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11. Question 11· Loci· WAEC

    The locus of points in space that are 3 cm from a fixed point P is

    • Aa circle of radius 3 cm
    • Ba sphere of radius 3 cm
    • Ca cylinder of radius 3 cm
    • Da plane 3 cm from P

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    Explanation and discussion

12. Question 12· Loci· WAEC

    A goat is tied to a peg by a rope 4 m long. The region it can graze is

    • Aa square of side 4 m
    • Ba circle of radius 4 m and its inside
    • Ca straight line 4 m long
    • Da circle of radius 2 m

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    Explanation and discussion