ICSE Class 10 Locus — Mock Test (2027)
Free online mock test for Locus (ICSE Class 10 Mathematics) — 20 competency-based questions based on the latest CISCE 2027 syllabus, with instant marking. Try the samples below, then take the full test free.
What to expect: This mock test covers key concepts from the Locus chapter — including application-based and competency-focused questions aligned with how ICSE actually sets the paper.
Tip: Attempt without notes first to identify gaps, then review explanations for any wrong answers. Retake after a few days for best retention.
Sample questions
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1.Geometry made by a locus of a swimmer maintaining the same distance from a pole in water is:
- A.Circle
- B.Triangle
- C.Rectangle
- D.Square
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2.Using ruler and compass only, construct a quadrilateral ABCD where AB = 6.5 cm, AD = 4 cm, and ∠DAB = 75°. Point C is equidistant from sides AB and AD and also equidistant from points A and B. How is point C located in the construction?
- A.At the intersection of AB and AD
- B.At the intersection of the angle bisector of ∠DAB and the perpendicular bisector of AB
- C.At the midpoint of AB
- D.At the intersection of AD and the perpendicular bisector of AB
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3.A point P moves such that its distance from a fixed line AB is always the same. Which of the following best describes the path travelled by P?
- A.A single line parallel to AB at the fixed distance.
- B.Two lines parallel to AB, each at the fixed distance from AB.
- C.A circle centered on AB with radius equal to the fixed distance.
- D.A parabola with AB as its directrix.
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4.Let a point P move in such a way that its distance from a fixed line AB is always equal to $d$ cm. The diagram below shows the fixed line AB and the path traced by P. Which labelled part represents the locus of the moving point P?
- A.A single straight line parallel to AB at a distance of $d$ cm from it.
- B.A pair of straight lines CD and EF, each parallel to AB at a distance of $d$ cm from it.
- C.A circle centered on AB with radius $d$ cm.
- D.A single straight line perpendicular to AB at a distance of $d$ cm from it.
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5.On a graph paper, draw the lines $x = 3$ and $y = -5$. Now, on the same graph paper, what is the locus of the point which is equidistant from the given lines?
- A.The pair of lines $y = x - 2$ and $y = -x - 2$
- B.The single line $y = x + 2$
- C.The pair of lines $x = -5$ and $y = 3$
- D.The single line $y = -x + 2$
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