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Cambridge IGCSE Mathematics practice

exam practice - 1. Utilize and understand graphs in real-world contexts, including estimating and interpreting the gradient of a tangent at a specific point, as well as working with travel and conversion graphs. 2. Create graphs based on provided data. 3. Use the concept of rate of change in basic kinematics, focusing on distance-time and speed-time graphs, including acceleration and deceleration. 4. Determine the distance traveled by calculating the area under a speed-time graph, considering only linear segments of the graph. - Graphs in practical situations

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Graphs in practical situations

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Paper 2Core or Extended Mathematics4 marks

A cyclist's speed-time graph for a 10-second interval is shown. The graph consists of two linear segments: from 0 to 5 seconds, speed increases from 0 to 12 m/s; from 5 to 10 seconds, speed decreases from 12 m/s to 4 m/s.

Diagram Description

Speed-Time Graph

Speed (m/s) on vertical axis, time (seconds) on horizontal axis. First segment: straight line from (0,0) to (5,12). Second segment: straight line from (5,12) to (10,4).

Time (s)Speed (m/s)
00
512
104
  1. a

    Calculate The total distance traveled by the cyclist during the 10 seconds.

    Aim for approximately 4 distinct marking points.

    [4]

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  • Topic focus: Graphs in practical situations.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
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Paper 2 structured question: Graphs in practical situations

Paper 2Core or Extended Mathematics3 marks

Diagram Description

Distance-Time Graph

The graph shows distance (in km) on the vertical axis and time (in hours) on the horizontal axis. The curve starts at the origin (0,0), rises steeply at first, then the slope decreases gradually.

Time (hours)Distance (km)
00
160
2100
3120
  1. a

    Calculate Estimate the speed of the car at t = 2 hours by finding the gradient of the tangent to the curve at that point.

    Aim for approximately 3 distinct marking points.

    [3]