JAMB and WAEC Mathematics questions: Loci

31 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· JAMB

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

   • Aa semicircle of radius 2 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

3. Question 3· Loci· JAMB

   The locus of points equidistant from two parallel lines is

   • Aa line parallel to them, midway between them
   • Ba circle
   • Ca line perpendicular to them
   • Da single point

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   Explanation and discussion

4. Question 4· Loci· JAMB

   A circle of radius r rolls round the outside of a fixed circle of radius R. The locus of the centre of the rolling circle is

   • Aa circle of radius r
   • Ba circle of radius R − r
   • Ca straight line
   • Da circle of radius R + r with the same centre as the fixed circle

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   Explanation and discussion

5. Question 5· Loci· JAMB

   The locus of points at a fixed distance d from a straight line is

   • Athe line itself
   • Ba circle of radius d
   • Ca single line perpendicular to it
   • Da pair of lines parallel to it, each at distance d

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   Explanation and discussion

6. Question 6· Loci· JAMB

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

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

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   Explanation and discussion

7. Question 7· Loci· JAMB

   The locus of points equidistant from A(0, 0) and B(4, 0) is the line

   • Ay = 2
   • Bx = 2
   • Cx = 4
   • Dy = x

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   Explanation and discussion

8. Question 8· 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

9. Question 9· Loci· JAMB

   The locus of points less than 5 cm from a fixed point P is

   • Athe region inside a circle of radius 5 cm centred at P
   • Ba circle of radius 5 cm only
   • Cthe region outside the circle
   • Da straight line through P

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   Explanation and discussion

10. Question 10· 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

11. Question 11· Loci· JAMB

    The locus of points equidistant from the parallel lines y = 2 and y = 6 is the line

    • Ay = 8
    • By = 4
    • Cx = 4
    • Dy = 3

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    Explanation and discussion

12. Question 12· Loci· JAMB

    The locus of points 3 cm from a fixed point O is

    • Atwo parallel lines
    • Ba straight line through O
    • Ca square with centre O
    • Da circle with centre O and radius 3 cm

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    Explanation and discussion

13. Question 13· 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

14. Question 14· 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

15. Question 15· 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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16. Question 16· Loci· JAMB

    A point moves so that it is always 3 units from the x-axis. Its locus is

    • Aa circle of radius 3
    • Bthe line y = 3 only
    • Cthe line x = 3
    • Dthe pair of lines y = 3 and y = −3

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17. Question 17· 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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    Explanation and discussion

18. Question 18· 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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    Explanation and discussion

19. Question 19· Loci· JAMB

    The locus of points equidistant from two intersecting straight lines is

    • Aa circle through the point of intersection
    • Bthe pair of lines bisecting the angles between them
    • Ca line parallel to one of them
    • Dthe perpendicular from one line to the other

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20. Question 20· Loci· JAMB

    The locus of points equidistant from three points that are not in a straight line is

    • Aa single point
    • Ba straight line
    • Ca circle
    • Dtwo parallel lines

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    Explanation and discussion