9390 A Level questions

Simplify 3log(x^2)+4log(y^3)

Using rules of logarithms: 3log(x^2)+4log(y^3)=log((x^2)^3)+log((y^3)^4) =log(x^6)+log(y^12) =log((x^6)(y^12)
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Answered by Alexander, tutor with MyTutor

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Draw the electric field lines produced by a negative point charge and calculate the electric field strength at a distance of 50mm from a point charge of size -30nC.

The diagram should show a negative point charge with the electric field lines pointing towards the point charge. The separation of the lines should decrease as you get closer to the point charge. The lines should be straight and perpendicular to the equipotential lines which circle the point charge.

In order to calculate the electric field strength, the equation for the force on a charge due to Coulomb's law and the equation for the electric field strength must be combined to give an equation for the electric field strength in terms of the size of the point charge;
F = Q1 Q2 / 4πε0 r2
E = F / Q1
E = Q2 / 4πε0 r2

Q2 should be recognised as the size of the point charge and this should be changed should be changed into Coulombs (nC = 1 x 10-9 C).
r should be recognised as the distance from the point charge and this should be changed into metres (mm = 1 x 10-3 m).
These numbers and the constants should be substituted into the final equation to give an electric field strength of -1.08 x 105 C (3 significant figures).
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Answered by Jemima, tutor with MyTutor

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Explain how an Act of Parliament is passed (12 marks)

The first stage in passing an Act of Parliament involves introducing a Green Paper (this contains tentative proposals for new law). The next stage is a White Paper (which contains firm proposals for a new piece of legislation. There then follows the drafting stage, where draftsmen write the Bill (including a preamble explaining what the Bill intends to do). There will also be definition sections in the Draft version of the Bill. After this follows the First Reading (where the Bill is read out and Parliament is familiarised with the general scope of the Bill. It can be introduced into either House of Parliament. Once this has occurred the Second Reading follows where there are votes on the Bill and any amendments to it can be put forward. The Committee Stage occurs after this with an ad hoc Select Committee set up to review the Bill and its proposals. The findings of this Committee are then announced to Parliament in the Report Stage. There is then a Third Reading and another vote on whether to pass the Bill. It then passes to the other House of Parliament (to the Commons if it originated in the House of Lords or vice versa). Once the other House has voted to pass the Bill, it goes to the monarch to be signed into law and receive the Royal Assent (and thus becomes an Act of Parliament.
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Answered by Maxim, tutor with MyTutor

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Describe the sequence of events in DNA transcription

An enzyme called DNA helicase breaks the hydrogen bonds holding the complimentary base pairs together in a double stranded DNA molecule. This causes the DNA helix to unwind, exposing the unpaired bases. Another enzyme called RNA polymerase binds to a 'promotor' region on the exposed DNA strand and moves downstream, attaching free complementary mRNA nucleotides to the exposed DNA bases. This strand of mRNA is released to form a strand of pre-mRNA. The non-coding regions called introns are removed via RNA 'splicing', resulting in a strand of coding mRNA.

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Answered by Ellie, tutor with MyTutor

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How do I find the equation of the normal to the curve y=x^2 at the point (x1,y1)? Where x1=2 and y1=4 .

I would get the student to draw a diagram of the situation.. so draw the curve y=x^2, the tangent at (2,4) and then the normal. Then I would highlight to them that the equation we want is the equation of a straight line.. with the form y=mx+c. Then we would need m and c. So, m first, let's use the fact that the tangent gradient multiplied by the normal gradient must be minus 1. So we can find the gradient of the tangent to the curve using differentiation, and then utilise that result to find m for the normal. Now we need c... so we know a point the curve passes through (2,4).. now all we need to do is to plug those x and y values that satisfy the equation we want to find and plug in the m value from before into the general equation y=mx+c. From which we can find c. So c and m have both been found. Hence we have found the equation we are looking for.
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Answered by Mr, tutor with MyTutor

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What does differentiation actually do?

Differentiation allows you to find the rate of change of a variable relative to another, which is basically the gradient. So if you had a speed-time graph, finding the amount that speed changes over a given time will get you acceleration.
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Answered by Kourosh, tutor with MyTutor

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Find the equation of the tangent to the circle x^2 + y^2 + 10x + 2y + 13 = 0 at the point (-3, 2)

First, what is a tangent? A line which touches a circle (or ellipse) at just one point. In our case (-3,2)
As it touches the line at one point, it is perpendicular the radius at (-3,2). Which implies that the gradient of the tangent is the negative reciprocal of the gradient of the the radius at (-3,2).
To work out the gradient of the radius at (-3,2) we need to know the centre point of the circle.
Rearrange the equation of the circle into square form yielding, centre as (-5,-1)
With two points on the same line we can work out the gradient of the radius at (-3,2). It's 3/2
So gradient of the tangent is the negative reciprocal of 3/2 which is -2/3.
We now have a point on the tangent line (-3,2) and the gradient of the line, hence we can work out the equation of the tangent. Solving yields 2x+3y=0
NOTE: I will draw a diagram on the whiteboard and do the arithmetic in the session also
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Answered by Patrick, who has applied to tutor with MyTutor

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Why do I need to do a risk assessment?

The risk assessment lets the examiners know how much thought you have put into both the planning and the execution of your project. While the risk assessment doesn't go into the main body of your project, it is a very important part that can be attached as an appendix and spoken about in your verbal presentation.
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Answered by Anastasia, tutor with MyTutor

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