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.A(-4, 2), B(0, 2) and C(-2, -4) are vertices of a triangle ABC. P, Q and R are mid-points of sides BC, CA and AB respectively. Which of the following statements about the centroids of triangles PQR and ABC is true?
- A.The centroid of ΔPQR is (-2, 0) and it coincides with the centroid of ΔABC.
- B.The centroid of ΔPQR is (-3, -1) and it differs from the centroid of ΔABC.
- C.The centroid of ΔABC is (-2, 0) but the centroid of ΔPQR is (0, 2).
- D.The centroid of ΔPQR is (-1, -1) and it lies on side BC of ΔABC.
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2.Let $P(6, -1)$, $Q(1, 3)$ and $R(p, 8)$ be three points given in such a way that $PQ = QR$. Find the value of $p$.
- A.5 or -3
- B.3 or -5
- C.4 or -4
- D.6 or -2
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3.In the given diagram of parallelogram ABCD, the vertices A $(-1, 0)$, B $(3, 1)$, and C $(2, 2)$ are labelled in order. Identify the coordinates of the fourth vertex D from the options below.
- A.(-2, 1)
- B.(0, 3)
- C.(1, -1)
- D.(4, 3)
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4.Calculate the ratio in which the line joining the points (-3, -1) and (5, 7) is divided by the line x = 2. Also, determine the co-ordinates of the point of intersection. Which of the following options correctly represents the ratio and the point of intersection?
- A.Ratio = 3 : 5, Point of intersection = (2, 4)
- B.Ratio = 5 : 3, Point of intersection = (2, 4)
- C.Ratio = 2 : 1, Point of intersection = (2, 3)
- D.Ratio = 5 : 2, Point of intersection = (2, 5)
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5.In the given figure, chords AB and CD intersect each other externally at point P. Given PA = 16 cm, PB = 6 cm, PC = 4 cm, find CD.
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