GCSE - Numeracy and Mathematics
Topic: Constructing and using
Tier: Higher
A*/A
tangents to estimate the gradient.
Starter:
Work out the change in y and change
in x for this pair of coordinates.
Top Tips!
To find the gradient of a line you divide the change in y by the
change in x.
𝑐ℎ𝑎𝑎𝑎𝑎 𝑖𝑖 𝑦
(3 , 7 ) and ( 5 , 11 )
𝑐ℎ𝑎𝑎𝑎𝑎 𝑖𝑖 𝑥
=
Skills:
1) Plot these to points, draw a line
between them and find its
gradient. (1,5) and (5,7)
2) What is the gradient of the line
between (-4,7) and (1,12)
3) What is the gradient of the line
between (-6,3) and (3,-9)
4) Find the gradient here.
(Gradient = velocity
on a distance-time graph)
Grade:
4
2
=2
For curves the gradient changes
so it is only possible to estimate
the gradient at one point by
drawing a tangent (straight line
that touches at one point) and
finding its gradient.
This is useful when looking at
velocity-time graphs because the
gradient is the acceleration at
that point.
Examination Question:
2015 Summer Linear P1 Higher Q18a
A scientist records the velocity, v m/s, of a particle from time t = 0 to
t = 9 seconds. only His results are shown in the graph below.
(a) Use the graph to estimate the acceleration of the particle at
t = 1·5. Give your answer to one decimal place.
Assessment for Learning
Video / QR code
GCSE - Numeracy and Mathematics
Topic: Constructing and using
Tier: Higher
A*/A
tangents to estimate the gradient.
Starter:
Work out the change in y and change
in x for this pair of coordinates.
Top Tips!
To find the gradient of a line you divide the change in y by the
change in x.
𝑐ℎ𝑎𝑎𝑎𝑎 𝑖𝑖 𝑦
(3,7) and (5,11):
y change = 4, x change = 2
𝑐ℎ𝑎𝑎𝑎𝑎 𝑖𝑖 𝑥
=
Skills:
1) Plot these to points, draw a line
between them and find its
gradient. (1,5) and (5,7)
Gradient = (7-5)/(5-1) = 2/4 = 1/2
2) What is the gradient of the line
between (-4,7) and (1,12)
Gradient = (12-7)/(1- -4) = 5/5 = 1
3) What is the gradient of the line
between (-6,3) and (3,-9)
Gradient = (-9 - 3)/(3 - -6)
= -12/9 = -4/3
4) Find the gradient here.
(Gradient = velocity
on a distance-time graph)
Grade:
4
2
=2
For curves the gradient changes
so it is only possible to estimate
the gradient at one point by
drawing a tangent (straight line
that touches at one point) and
finding its gradient.
This is useful when looking at
velocity-time graphs because the
gradient is the acceleration at
that point.
Examination Question:
2015 Summer Linear P1 Higher Q18a
A scientist records the velocity, v m/s, of a particle from time t = 0 to
t = 9 seconds. only His results are shown in the graph below.
(140-20)/(9-4) = 120/5 = 24 m/s
Assessment for Learning
(a) Use the graph to estimate the acceleration of the particle at
t = 1·5. Give your answer to one decimal place.
Tangent at t = 1.5 correct method and a reasonable answer
Video / QR code