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Jack has been tutoring my 12 year old son for about 2 months now and is really beginning to improve his confidence and mathematical ability. The lessons are fun and very thorough, often reinforcing a topic covered in classwork or tricky homework, leaving him confident and ready to move on to the next one. Unlike in school, during sessions with Jack my son is never afraid to say when he doesn't fully understand something, ensuring 100% confidence in a topic. Jack has been very flexible with the timings of our sessions and has endless patience. This is a great way to sign up to a tutor and if you are lucky enough to have Jack you will not be disappointed.

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Usually we cover both subject knowledge and exam technique, although that can change depending on each individual student. Then we go through diagrams, and they ask questions, and we go from there.

Lots of students say that the classes are too big in school, or that they don't have time to ask teachers after lessons. In my tutorials, we take time to explore things in a little in a bit more detail.

I always look up the board my students are taking so the lessons are really relevant. Then we go through past papers or set texts, whatever the student finds helpful.

I use the shared whiteboard. We make diagrams together and label them, and often the student prints it off because they know it's right and they completely understand it.

After tutoring one girl went and told all her friends the new explanation I gave her. And she was so excited about what she wrote in the exam she emailed me immediately afterwards.

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y=3x+2
x^2+y^2=20
x^2+(3x+2)^2=20
x^2+(3x+2)(3x+2)=20
x^2+(9x^2+6x+6x+4)=20
x^2+(9x^2+12x+4)=20
10x^2+12x+4=20
10x^2+12x-16=0
5x^2+6x-8=0
(5x-4)(x+2)=0
5x-4=0, x+2=0
x=4/5=0.8, x=-2
y=3x+2, y=3x+2
y=3(0.8)+2, y=3(-2)+2
y=4.4, y=-4
When x=0.8, y = 4.4
When x=-2, y=-4

Answered by Daniela C.

Studies History at Warwick

By using the quadratic quation, it can be deduced that x = 1.22 or x = -3.55

Answered by Miranda S.

Studies German and Spanish with Management at Exeter

We have to use the chain rule here. If we set u to the inside of the bracket, u = x^2 + 3 and differentiating we get du/dx = 2x.
Now the original expression becomes y = u^2. Differentiating this with respect to x, dy/dx = du/dx * dy/du using the chain rule.
dy/du = 2u and du/dx is 2x so the final answer dy/dx = 2x*2(x^2 + 3) = 4x(x^2 + 3).

Answered by Matthew H.

Studies Computer Science and Maths at Exeter

When simplifying surd expressions we want to look for square numbers that are factors of the number inside the square root. If we list the square numbers (which are numbers that are the result of squaring another number) up to 48 we have 1, 4, 9, 16, 25 and 36 (1^2, 2^2, ... 6^2). Now we see that 1, 4 and 16 are all factors of 48. Choosing the highest we know that 16 x 3 = 48 so the surd becomes sqrt(16x3).
Next, we know that the square root of 16 is 4 so we can apply this and take it outside of the square root giving 4*sqrt(3) (read as 4 root 3). This 4 comes from square rooting 16. As 3 cannot be split up into any more square factors, 4 root 3 is the final answer.

Answered by Matthew H.

Studies Computer Science and Maths at Exeter

First of all, you need to read the question really carefully and look at how many marks it is worth.
The question is worth two marks and it is asking you to do two things: firstly, you need to â€˜rationalise the denominatorâ€™, and then you need to â€˜simplifyâ€™ your answer.
So, what do we mean by rationalising the denominator? Well, the denominator is the number below the line in a fraction. Rationalising means to change a number from being irrational to being rational. An irrational number is a number that cannot be expressed using integers (whole numbers); it goes on and on in a random pattern beyond the decimal point.
Letâ€™s look at the fraction in the question: 10/3âˆš5. What weâ€™re aiming for is the denominator to be an integer. To do this, we need to multiply by a number that will âˆš5 rational. So, we would choose to multiply by âˆš5 because âˆš5 X âˆš5 = 5. (âˆš5 is the same as 5^0.5, so we could write this as 5^0.5 X 5^0.5 = 5^1) Remember that whatever we do to the denominator, we have to do to the numerator (top of the fraction) as well.
Letâ€™s tackle the numerator and denominator separately. The numerator is 10 and we are multiplying that by âˆš5. 10 X âˆš5 = 10âˆš5. Now, for the denominator. The denominator is 3âˆš5, which we could also write as 3 X âˆš5. So, we are multiplying 3 X âˆš5 X âˆš5. This would give us 3 X 5 which would equal 15. Now to combine these two parts, we have 10âˆš5/15.
Now for the second part of the question: simplifying. We could write our fraction as (10 X âˆš5)/15 and then (10/15) X âˆš5. We cannot simplify âˆš5, but we can simplify 10/15. 5 is both a factor of 10 and 15: 5 goes in to 10 twice and 5 goes into 15 three times. Overall, we have (2/3) X âˆš5, but this looks much neater in the form 2âˆš5/3.

Answered by Megan P.

Studies History at Exeter

4x+5=6x-13. Take 4x from both sides
5= 6x-4x-13
5=2x-13. On the right hand side, you have -13 value. Add 13, to make 0. Adding thirteen on right also adds thirteen on left.
5 + 13 = 2x - 13 + 13
18=2x.
2 times 'x' is 18. You might automatically know that 2 times 9 is 18, but it is good practice to use algebra here, as you will not always get a full number and may end up with fractions. If you divide by 2 on both sides, you get 2x/2 = 18/2
x=9.
Always show your working, so the examiner knows what you are trying to do and can give you marks for at least showing your algebra skills.

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