Marcus J. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathema...

Marcus J.

£18 - £20 /hr

Studying: Mathematics (Masters) - Exeter University

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About me

I'm a high achieving Master of Mathematics student at the University of Exeter. With a excitement for all things mathematics. I have helped teach at many different levels in the past 8 years primarily in one to one sessions.

I'm a high achieving Master of Mathematics student at the University of Exeter. With a excitement for all things mathematics. I have helped teach at many different levels in the past 8 years primarily in one to one sessions.

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About my sessions

The sessions will be primarily guided by what you want covered and your experience with mathematics. Understanding why is much more important than just how to plug in the numbers and I will not only teach the applications but how they can be derived ( within reason, no need to stress over learning PhD level proofs!), but, most importantly help you to think like a mathematician! What now? If you have any questions feel free to message me and don't be afraid to book a free 'Meet the Tutor' session! If you could also let me know the exam board and any specific areas you are struggling with I would be very grateful! Look forward to hearing from you!  

The sessions will be primarily guided by what you want covered and your experience with mathematics. Understanding why is much more important than just how to plug in the numbers and I will not only teach the applications but how they can be derived ( within reason, no need to stress over learning PhD level proofs!), but, most importantly help you to think like a mathematician! What now? If you have any questions feel free to message me and don't be afraid to book a free 'Meet the Tutor' session! If you could also let me know the exam board and any specific areas you are struggling with I would be very grateful! Look forward to hearing from you!  

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Enhanced DBS Check

06/10/2017

Qualifications

SubjectQualificationGrade
MathematicsA-level (A2)A*
Further MathsA-level (A2)A
English LiteratureA-level (A2)B

General Availability

Before 12pm12pm - 5pmAfter 5pm
mondays
tuesdays
wednesdays
thursdays
fridays
saturdays
sundays

Subjects offered

SubjectQualificationPrices
Further MathematicsA Level£20 /hr
MathsA Level£20 /hr
Further MathematicsGCSE£18 /hr
MathsGCSE£18 /hr
Maths13 Plus£18 /hr
Maths11 Plus£18 /hr

Questions Marcus has answered

How do we differentiate y=a^x when 'a' is an non zero real number

Firstly we must change it into a form we can deal with. To do this we take the natural log (ln) of both sides.

ln(y)=ln(ax

ln(y)=x(ln(a))         using our rules of logs

From here we differentiate. The differential of ln(f(x)) is [(d/dx)f(x)]/f(x)

(dy/dx)/y=ln(a)            

differentiating from above rule and ln(a) is just a constant so d/dx xln(a)= ln(a)

dy/dx=yln(a)        times both sides by y

dy/dx=(ax)(ln(a))  

subbing in y=ato get dy/dx in terms of x

Firstly we must change it into a form we can deal with. To do this we take the natural log (ln) of both sides.

ln(y)=ln(ax

ln(y)=x(ln(a))         using our rules of logs

From here we differentiate. The differential of ln(f(x)) is [(d/dx)f(x)]/f(x)

(dy/dx)/y=ln(a)            

differentiating from above rule and ln(a) is just a constant so d/dx xln(a)= ln(a)

dy/dx=yln(a)        times both sides by y

dy/dx=(ax)(ln(a))  

subbing in y=ato get dy/dx in terms of x

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2 years ago

798 views

If (m+8)(x^2)+m=7-8x has two real roots show that (m+9)(m-8)<0 where m is an arbitrary constant

For this we are going to test our knowledge of discriminats and factorisation.
Firstly we will format the equation as (m+8)x2+8x+(m-7)=0

From here we can see it takes the form ax2+bx+c, and as we know the equation has two real roots we know that the discriminant D is greater than 0. Therfore b2-4ac>0

a=(m+8)        b=8          c=(m-7)

82-4(m+8)(m-7)>0       Pluggin in a,b,c

64-4(m2+m-54)>0       expanding brackets and squaring 8

16-(m2+m-54)>0         dividing both sides by a factor of 4

0>(m2+m-54)-16         moving left handside to right handside by addition / subtraction

0>m2+m-72                 collecting terms

0>(m+9)(m-8)             factorising

We have now shown that (m+9)(m-8)<0 for the above equation when it has two real roots.

For this we are going to test our knowledge of discriminats and factorisation.
Firstly we will format the equation as (m+8)x2+8x+(m-7)=0

From here we can see it takes the form ax2+bx+c, and as we know the equation has two real roots we know that the discriminant D is greater than 0. Therfore b2-4ac>0

a=(m+8)        b=8          c=(m-7)

82-4(m+8)(m-7)>0       Pluggin in a,b,c

64-4(m2+m-54)>0       expanding brackets and squaring 8

16-(m2+m-54)>0         dividing both sides by a factor of 4

0>(m2+m-54)-16         moving left handside to right handside by addition / subtraction

0>m2+m-72                 collecting terms

0>(m+9)(m-8)             factorising

We have now shown that (m+9)(m-8)<0 for the above equation when it has two real roots.

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2 years ago

735 views

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