ICSE Class 10

ICSE Class 10 Section Formula and Mid-point — Mock Test (2027)

Free online mock test for Section Formula and Mid-point (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 Section Formula and Mid-point 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.

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Sample questions

  1. 1.A (6, y), B (-4, 4) and C(x, -1) are the vertices of $\Delta$ABC whose centroid is the origin. What are the values of $x$ and $y$?
    • A.x = -2, y = -3
    • B.x = 2, y = 3
    • C.x = -2, y = 3
    • D.x = 2, y = -3
  2. 2.In what ratio does the y-axis divide the line segment joining the points P(-4, 5) and Q(3, -7)? Also, identify the coordinates of the point of intersection. img-10.jpeg
    • A.Ratio 3:4, point (0, -1)
    • B.Ratio 4:3, point (0, -13/7)
    • C.Ratio 2:3, point (0, -5/3)
    • D.Ratio 5:2, point (0, -11/7)
  3. 3.Find the ratio in which the join of (-4, 7) and (3, 0) is divided by the y-axis. Also, determine the co-ordinates of the point of intersection.
    • A.Ratio = 3 : 4, Point of intersection = (0, 4)
    • B.Ratio = 4 : 3, Point of intersection = (0, 3)
    • C.Ratio = 2 : 1, Point of intersection = (0, 5)
    • D.Ratio = 1 : 1, Point of intersection = (0, 7/2)
  4. 4.Construct a right-angled triangle PQR, in which ∠Q = 90°, hypotenuse PR = 8 cm and QR = 4·5 cm. Draw the bisector of angle PQR and let it meet PR at point T. Why is T equidistant from PQ and QR?
    • A.T lies on the angle bisector of ∠PQR, so it is equidistant from PQ and QR.
    • B.T divides PR into two equal segments, making it equidistant from PQ and QR.
    • C.T is the midpoint of PR, so it is equidistant from all sides of the triangle.
    • D.T lies on QR extended, so it is equidistant from PQ and QR.
  5. 5.Find the co-ordinates of the point C which divides the join of A $(4, -3)$ and B $(9, 7)$ in the ratio $3:2$.
    • A.$(7, 3)$
    • B.$(6.2, 1.8)$
    • C.$(5.5, -0.2)$
    • D.$(8, 5)$

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