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.
Sample questions
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1.The line segment joining the points M (5, 7) and N (-3, 2) is intersected by the y-axis at point L. What is the ratio in which L divides MN, and what are the coordinates of L?
- A.Ratio = 3 : 5, L = (0, 29/4)
- B.Ratio = 5 : 3, L = (0, 29/4)
- C.Ratio = 5 : 3, L = (0, 4)
- D.Ratio = 2 : 1, L = (0, 23/4)
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2.Find the centroid of the triangle whose vertices are A $(x_1, y_1)$, B $(x_2, y_2)$ and C $(x_3, y_3)$. Which of the following represents the coordinates of the centroid?
- A.$\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right)$
- B.$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$
- C.$\left(\frac{x_1 + x_2 + x_3}{2}, \frac{y_1 + y_2 + y_3}{2}\right)$
- D.$\left(x_1 + x_2 + x_3, y_1 + y_2 + y_3\right)$
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3.In the given diagram, the centre of a circle is labelled C at $(-2, 3)$ and one end of diameter PQ is labelled P at $(2, -4)$. What are the co-ordinates of the point labelled Q?
- A.(-6, 10)
- B.(0, -1)
- C.(-4, 7)
- D.(6, -10)
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4.A point $P$ is at a distance of $\sqrt{10}$ units from the point $A(4, 3)$. Find the coordinates of $P$, it being given that its ordinate is twice its abscissa.
- A.(1, 2)
- B.(2, 4)
- C.(3, 6)
- D.(5, 10)
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5.Show that the points A (7, 10), B (-2, 5) and C (3, -4) are the vertices of an isosceles right-angled triangle. Which of the following correctly describes the triangle and its area?
- A.AB = BC = √106, AB² + BC² = AC², and area = 53 square units
- B.AB = AC = √106, AB² + AC² = BC², and area = 26.5 square units
- C.BC = AC = √106, BC² + AC² = AB², and area = 106 square units
- D.AB = BC = √53, AB² + BC² = AC², and area = 53 square units
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