Kara  V. GCSE Maths tutor, GCSE Science tutor, A Level Maths tutor, A...

Kara V.

£18 - £20 /hr

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Studying: Evolutionary Anthropology (Masters) - Durham University

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About me

About me:

I am currently at Durham studying for a Masters in Anthropology, after just completing my Masters in Physics at the University of York.

I am looking to teach a bit of maths and science to GCSE and A level student of all abilities. I am the oldest of about 15 cousins, and have tutored most of them at some point or another, for that final exam where they needed that C, or sometimes for just a confidence boost, to get them on the right track again. I think that my patience, reassuring attitude and my terrible humour has really helped me with this. 

I think that because maths and science can be seen as such difficult subjects, a lot of students give up so readily that they can miss out on the opportunity of discovering how interesting and satisfying they can be to study. I really hope that my tutoring can help to spark that interest, particularly for girls who might not otherwise think about persuing science and maths at higher levels. 

About me:

I am currently at Durham studying for a Masters in Anthropology, after just completing my Masters in Physics at the University of York.

I am looking to teach a bit of maths and science to GCSE and A level student of all abilities. I am the oldest of about 15 cousins, and have tutored most of them at some point or another, for that final exam where they needed that C, or sometimes for just a confidence boost, to get them on the right track again. I think that my patience, reassuring attitude and my terrible humour has really helped me with this. 

I think that because maths and science can be seen as such difficult subjects, a lot of students give up so readily that they can miss out on the opportunity of discovering how interesting and satisfying they can be to study. I really hope that my tutoring can help to spark that interest, particularly for girls who might not otherwise think about persuing science and maths at higher levels. 

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Qualifications

SubjectQualificationGrade
PhysicsDegree (Masters)1st
MathsA-level (A2)A*
PhysicsA-level (A2)A
Further MathsA-level (A2)B

Subjects offered

SubjectQualificationPrices
MathsA Level£20 /hr
PhysicsA Level£20 /hr
ChemistryGCSE£18 /hr
MathsGCSE£18 /hr
PhysicsGCSE£18 /hr
ScienceGCSE£18 /hr

Questions Kara has answered

Two points have coordinates (1,-6) and (-2,3). Find the equation of the line which joins them, and their midpoint.

To find the line's equation, you need the gradient and the y-intercept. The gradient is found using:

(y2-y1)/(x2-x1)

Or simply (change in y direction)/(change in x direction)

In this case, the gradient =(3+6)/(-2-1)=9/-3=-3

and so the equation of the line is in the form 

y=-3x+c

We now need to find the y-intercept, or 'c' in the equation above.

All points on this line will follow this equation. This includes the two points in the question, so we can sub in the x and y values and rearrange to find c. We can choose either of the points. Lets start with (1,-6)

x=1, y=-6

y=-3x + c

-6=-3*1 +c

-6=-3 +c

c=-3

Therefore:

y=-3x-3

We can check this by using the other coordinate:

(-2,3) 

x=-2, y=3

3=-3*-2  -3

3=6-3

3=3

As for finding the midpoint of the two points, we just need to find middle of the 2 x-coordinates and the middle of the 2 y-coordinates (need some diagrams here)

To do this, we can just find the averages.

x - coordinates: 1 and -2

x midpoint = (1+ -2)/2 = -0.5

y - coordinates: -6 and 3

y midpoint = (-6+3)/2 =-1.5

So our midpoint coordinate is (-0.5, -1.5)

To find the line's equation, you need the gradient and the y-intercept. The gradient is found using:

(y2-y1)/(x2-x1)

Or simply (change in y direction)/(change in x direction)

In this case, the gradient =(3+6)/(-2-1)=9/-3=-3

and so the equation of the line is in the form 

y=-3x+c

We now need to find the y-intercept, or 'c' in the equation above.

All points on this line will follow this equation. This includes the two points in the question, so we can sub in the x and y values and rearrange to find c. We can choose either of the points. Lets start with (1,-6)

x=1, y=-6

y=-3x + c

-6=-3*1 +c

-6=-3 +c

c=-3

Therefore:

y=-3x-3

We can check this by using the other coordinate:

(-2,3) 

x=-2, y=3

3=-3*-2  -3

3=6-3

3=3

As for finding the midpoint of the two points, we just need to find middle of the 2 x-coordinates and the middle of the 2 y-coordinates (need some diagrams here)

To do this, we can just find the averages.

x - coordinates: 1 and -2

x midpoint = (1+ -2)/2 = -0.5

y - coordinates: -6 and 3

y midpoint = (-6+3)/2 =-1.5

So our midpoint coordinate is (-0.5, -1.5)

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2 years ago

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