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ZIMSEC O-Level Analytical geometry — practice questions

Explore 5 free Analytical geometry questions in ZIMSEC O-Level Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Analytical geometry questions and exercises with answers

Showing questions 1–5 of 5.

What does the gradient of a line measure?Read the answer and worked solution →Which quadrilateral has exactly one pair of opposite sides parallel?Read the answer and worked solution →A line passes through the points (2, 3) and (6, 11). What is its gradient?Read the answer and worked solution →The gradient of a straight line is equal to which value of its angle of inclination?Read the answer and worked solution →A straight line has a negative gradient. What angle does it make with the positive horizontal direction?Read the answer and worked solution →

Worked practice questions

What does the gradient of a line measure?

  1. How long it is
  2. How steep it is
  3. How thick it is
  4. How near it is
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Correct answer: B. How steep it is

1. Two points are enough to fix a straight line. 2. Gradient describes the slope or steepness of the line joining those two points. 3. Steepness is found by comparing the vertical change with the horizontal change. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 4: Analytical geometry_

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Which quadrilateral has exactly one pair of opposite sides parallel?

  1. A rhombus
  2. A rectangle
  3. A pentagon
  4. A trapezium
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Correct answer: D. A trapezium

1. A quadrilateral is a closed shape made of four straight line segments. 2. A trapezium is a quadrilateral with one pair of opposite sides parallel. 3. A rhombus and a rectangle are both parallelograms, so each has two such pairs. 4. A pentagon has five sides, so it is not a quadrilateral at all. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 4: Analytical geometry_

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A line passes through the points (2, 3) and (6, 11). What is its gradient?

  1. It is 2
  2. It is 4
  3. It is 8
  4. It is 3
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Correct answer: A. It is 2

1. Gradient is the ratio of vertical change to horizontal change. 2. The vertical change is 11 minus 3, which is 8. 3. The horizontal change is 6 minus 2, which is 4. 4. Dividing 8 by 4 gives a gradient of 2. 5. Answering 8 stops at the vertical change and never divides by the horizontal change. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 4: Analytical geometry_

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