New
New
Year 11
Higher

Advanced problem solving with real-life graphs

I can use my knowledge of interpreting real-life graphs to solve problems.

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New
New
Year 11
Higher

Advanced problem solving with real-life graphs

I can use my knowledge of interpreting real-life graphs to solve problems.

Link copied to clipboard

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Lesson details

Key learning points

  1. Different speed/time graphs can be interpreted and compared.
  2. The area under the graph can also be interpreted in context.
  3. Circle theorems can be demonstrated using coordinate geometry.

Keywords

  • Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.

  • Tangent - A tangent of a circle is a line that intersects the circle exactly once.

Common misconception

The intersection of two different graphs on a speed-time graph is the point where the faster particle overtakes the slower moving particle.

Remind pupils that this is a speed-time graph and ask, "How do we find the distance travelled on a speed-time graph?". Then, ask pupils to calculate how far each particle has travelled at the point of intersection.


To help you plan your year 11 maths lesson on: Advanced problem solving with real-life graphs, download all teaching resources for free and adapt to suit your pupils' needs...

A powerful starter is to give students a distance-time graph and ask, "How much information can we obtain from this graph? What does it tell us?". Then, do the same activity for a speed-time graph.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
This speed-time graph shows __________ rate of change between time and speed.
An image in a quiz
Correct answer: a constant
an increasing
a decreasing
a fast
Q2.
What speed is this vehicle travelling at after $$10$$ seconds? m/s
An image in a quiz
Correct Answer: 50
Q3.
What distance has this vehicle travelled after $$10$$ seconds? m/s
An image in a quiz
Correct Answer: 250
Q4.
Which equation generalises how far this vehicle has travelled after $$x$$ seconds?
An image in a quiz
$$A={{x^2}\over{2}}$$
$$A=5x$$
$$A=5x^2$$
$$A={{5x}\over{2}}$$
Correct answer: $$A={{5x^2}\over{2}}$$
Q5.
What is the $$y$$-coordinate at the point of intersection of the two linear equations $$y=2x-10$$ and $$y=-{1\over2}x+5$$ ?
Correct Answer: 2, y=2
Q6.
What is the equation of the tangent to the circle at point A?
An image in a quiz
$$y=-{2\over5}x+{34\over5}$$
$$y=-{5\over2}x+1$$
Correct answer: $$y={5\over2}x+1$$
$$y={5\over2}x+11$$
$$y={5\over2}x-{27\over2}$$

6 Questions

Q1.
The __________ to a circle from an external point are equal in length.
radii
Correct answer: tangents
perpendiculars
Q2.
What is the tangent to the circle at A?
An image in a quiz
$$y=4x-14$$
$$y={1\over4}x+{29\over4}$$
Correct answer: $$y=-{1\over4}x+{29\over4}$$
$$y=-{1\over4}x-{29\over4}$$
$$y=-{1\over4}x+{13\over2}$$
Q3.
Find the point of intersection of the tangents to the circle from points A and B.
An image in a quiz
Correct answer: $$(21,2)$$
$$(2,21)$$
$$(19,2)$$
$$(23,2)$$
Q4.
Tangents from A and B meet at point C. To show that AC $$=$$ BC we would use __________.
An image in a quiz
a ruler
Correct answer: Pythagoras theorem
circle theorem
$$A=\pi \times r^2$$
Q5.
How far have these cars travelled between $$0$$ and $$6$$ seconds?
An image in a quiz
Both have travelled $$30$$ metres each
Both have travelled $$90$$ metres each
'a' has travelled $$90$$ metres and 'b' has travelled $$120$$ metres
Correct answer: 'a' has travelled $$90$$ metres and 'b' has travelled $$135$$ metres
'a' has travelled $$250$$ metres and 'b' has travelled $$275$$ metres
Q6.
After how many seconds will car 'a' overtake car 'b'? seconds.
An image in a quiz
Correct Answer: 12