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.Two parallel lines $l$ and $s$ are 4 cm apart. In the diagram below, which labelled line represents the locus of a point that is always equidistant from both the given lines?
- A.A line parallel to $l$ and $s$, 2 cm from each
- B.A line parallel to $l$ and $s$, 4 cm from line $l$
- C.A line perpendicular to $l$ and $s$ at their midpoints
- D.A line coinciding with either $l$ or $s$
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2.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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3.Using ruler and compasses only, the diagram below shows the construction of a rhombus ABCD whose diagonals AC and BD are 8 cm and 6 cm long respectively. A point P is found by construction such that it is equidistant from AB, AD and also equidistant from C and D.
Which labelled part in the diagram represents the point P that satisfies the given conditions?- A.The intersection of diagonal AC and the perpendicular bisector of CD
- B.The intersection of diagonals AC and BD
- C.The midpoint of diagonal AC
- D.The intersection of side AB and the angle bisector of angle BAD
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4.A point $Q$ is always at the distance of 4 units from (3, 2). Equation of locus of a point $Q$, will be
- A.$x^{2} + y^{2} + 6x + 4y - 3 = 0$
- B.$x^{2} + y^{2} + 6x - 4y - 3 = 0$
- C.$x^{2} + y^{2} - 6x - 4y - 3 = 0$
- D.$x^{2} + y^{2} - 6x - 4y + 3 = 0$
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5.A circle with centre O and radius $r$ cm is the locus of a point which moves in a plane in such a way that its distance from the fixed point O is always equal to $r$ cm. What does the concept of locus represent in this context?
- A.The locus is the fixed point O itself, as it remains stationary while the point moves.
- B.The locus is the path traced by the moving point, which forms a circle since every point on it is at a constant distance $r$ cm from O.
- C.The locus is the radius $r$ cm, as it defines the distance from O to the moving point.
- D.The locus is the set of all possible distances from O, varying continuously as the point moves.
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