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 A(2, 3) and B(6, -5) is intercepted by the x-axis at the point K. The ordinate of the point K is 0. In what ratio does K divide AB, and what are the coordinates of K?
- A.Ratio = 3 : 5, K = (13/4, 0)
- B.Ratio = 5 : 3, K = (7/2, 0)
- C.Ratio = 2 : 3, K = (4, 0)
- D.Ratio = 3 : 2, K = (5, 0)
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2.A(-8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP:PB = 3:5 and AQ:QC = 3:5. Which of the following correctly verifies the relationship between PQ and BC?
- A.PQ = √40, BC = 16, so PQ = (3/8) BC
- B.PQ = √10, BC = 8, so PQ = (3/4) BC
- C.PQ = 2√10, BC = 8, so PQ = (1/4) BC
- D.PQ = √40, BC = 8, so PQ = (5/8) BC
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3.In the given diagram
, the point where the perpendicular bisectors of the sides of a triangle meet is labelled. What is this point called, and which property does it satisfy with respect to the vertices of the triangle?- A.Orthocentre; it lies on the altitudes of the triangle.
- B.Circumcentre; it is equidistant from all three vertices of the triangle.
- C.Centroid; it divides the medians in a 2:1 ratio.
- D.Incentre; it is equidistant from all three sides of the triangle.
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4.In what ratio is the line joining P(5,3) and Q(-5,3) divided by the Y-axis, and what are the coordinates of the point of intersection?
- A.Ratio 2:1, coordinates (0, 3)
- B.Ratio 1:1, coordinates (0, 3)
- C.Ratio 1:2, coordinates (0, 4)
- D.Ratio 3:1, coordinates (0, 2)
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5.Points P $(a, -4)$, Q $(-2, b)$ and R $(0, 2)$ are collinear. If Q lies between P and R, such that PR = 2QR, which of the following correctly gives the values of $a$ and $b$?
- A.$a = -4$, $b = 0$
- B.$a = 2$, $b = -1$
- C.$a = -2$, $b = 2$
- D.$a = 0$, $b = -4$
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