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Year 10

Higher

Advanced problem solving with linear graphs

I can use my knowledge of linear graphs to solve problems.

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New

Year 10

Higher

Advanced problem solving with linear graphs

I can use my knowledge of linear graphs to solve problems.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

Knowledge of the geometric properties of shapes can be used here.
Knowledge of ratio can be used here.

Keywords

Tangent (of a circle) - The tangent (of a circle) is a line that intersects the circle exactly once.

Common misconception

P is a point such that AP : PB is in the ratio of 1 : 3 means that point P is a third of the distance of AB from A.

There are 4 equal parts in total, meaning that point P is a quarter of the distance of AB from A.

The feedback slides show where annotations have been added to the given diagram in order to support answering the question. Encourage pupils to annotate any given diagrams with the information they deduce in order to support reaching a solution.

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Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.

Two lines are perpendicular if their gradients are the negative __________ of one another.

gradient

multiplier

product

Correct answer: reciprocal

Q2.

Match each line with a line that is perpendicular to it.

Correct Answer:$$y=3x-8$$,$$y=-{1\over3}x-11$$

$$y=-{1\over3}x-11$$

Correct Answer:$$y={1\over2}x+8$$,$$y=10-2x$$

$$y=10-2x$$

Correct Answer:$$y=7-{2\over3}x$$,$$y={3\over2}x-3$$

$$y={3\over2}x-3$$

Correct Answer:$$y={3\over2}x-10$$,$$y=-{2\over3}x+8$$

$$y=-{2\over3}x+8$$

Q3.

What is the equation of this line?

$$y=1+3x$$

$$y=1+{1\over3}x$$

$$y={1\over3}x-1$$

$$y=-{1\over3}x-1$$

Correct answer: $$y=1-{1\over3}x$$

Q4.

What is the equation of the straight line that goes through the coordinates (-5, -23) and (3, 17)?

$$y=2-5x$$

$$y=2x+5$$

Correct answer: $$y=5x+2$$

$$y=5x-2$$

$$y=2x-5$$

Q5.

Find the coordinates of the point P when AP : PB is in the ratio 1 : 5.

(3, 2)

(2, 3)

(4 3)

Correct answer: (3, 5)

(1, 5)

Q6.

What is the coordinate of C when AB : BC is in the ratio 1 : 2?

(0.5, 1)

(5, -8)

(7, -12)

Correct answer: (11, -20)

(15, -28)

Exit quiz

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6 Questions

Q1.

In a circle, a tangent and a __________ meet at a right angle.

chord

circumference

Correct answer: radius

Q2.

The grid shows a circle, its radius and a tangent which touches the circumference at (3, -4). What is the equation of the tangent line?

$$y=2x+5$$

Correct answer: $$y=2x-10$$

$$y=2x-4$$

$$y={1\over2}x+5$$

$$y={1\over2}x-10$$

Q3.

The grid shows a circle, its radius and a tangent which touches the circumference at (3,-4). The radius is a line segment of the line ...

$$y=-5-2x$$

$$y=-2x-2.5$$

$$y=-{1\over2}x-5$$

$$y=-{1\over2}x+{5\over2}$$

Correct answer: $$y=-{1\over2}x-{5\over2}$$

Q4.

In this graph the radius is a line segment of the line $$y=-{1\over2}x-{5\over2}$$ and the tangent is line $$y=2x-10$$. How can you tell they meet at a right angle?

$$(-4)=-{1\over2}(3)-{5\over2}$$

$$(-4)=2(3)-10$$

$$-{5\over2}\times{10}=-25$$

Correct answer: $$-{1\over2}\times{2}=-1$$

$$-{1\over2}\times{2}=1$$

Q5.

Point P is such that AP : PB is in the ratio 1 : 2. Find the area of triangle OPB.

18 sq units

27 sq units

Correct answer: 36 sq units

54 sq units

Q6.

Point P is such that AP : PB is in the ratio 5 : 1. The area of triangle OAP is square units.

Correct Answer: 45