Math Proof Questions

Can someone write the titles of all of the proof questions that come in Pure 1 and 2? I am specifically talking about ones that prove a formula not like "prove that all even numbers are divisible by 2" for example. I mean proofs like the geometric and arithmetic series formulae.

Reply 1

TSR Jessica

Sorry you've not had any responses about this. :frown:

Are you sure you've posted in the right place? :smile:

Here's a link to our subject forum which should help get you more responses if you post there. :redface:

Reply 2

thegeek888

Original post by joaofelix

The Fundamental Theorem of Calculus. Look on Khan Academy. Bicen Maths.

Reply 3

joaofelix

Original post by thegeek888

The Fundamental Theorem of Calculus. Look on Khan Academy. Bicen Maths.

Thank you! But what are the other ones in the syllabus if you know?

Reply 4

TypicalNerd

Original post by joaofelix

I’ve just had a look at the spec to remind myself which topics come up on P1 and P2 (I assume this is the Edexcel IAL course) and these are what I reckon should be covered, though the P1 proofs are suggestions for your own understanding rather than as required by the spec:

P1:

-Proving the quadratic formula (by completing the square).

-Knowing where the formula y - y1 = m(x - x1) comes from (this is simply rearranging the equation for the gradient, y = change in y/change in x).

-Proving the sine and cosine rules may be helpful.

-Proving the equations s = rθ and A = 1/2 θr^2 for a circle, where θ is in radians (this can be done by using the equations c = πd = 2πr and A = πr^2, then multiplying by 180θ/π° (which is the angle within the sector, converted from radians to degrees) and then dividing by 360° (the total angle at the centre of a full circle)).

-By extension, you could show that if a chord is drawn in a sector in such a way that it forms an isoceles triangle with an angle θ and two sides with a length equivalent to that of the radius, the area of the segment created is 1/2 r^2 (θ - sinθ) (this is simply area of sector - area of triangle, where the a = r, so A = 1/2 θr^2 - 1/2 r^2 sinθ => A = 1/2 r^2(θ - sinθ)).

P2:

-There is a whole topic on general methods of proof (deduction, exhausion and disproof by counterexample), but this isn’t what you were asking for.

-Proving Sn = 1/2 n[2a + (n - 1)d] and equivalent forms for an arithmetic sequence.

-Proving Sn = a(1 - r^n)/(1 - r) for a geometric sequence and knowing why the sum to infinity of a geometric sequence with |r| < 1 is a/(1 - r) (if |r| < 1, then r^n decreases as n increases. As such, when n is large, r^n can be neglected and so Sn simplifies to a/(1 - r)).

-Proving the laws of logs may be useful for your own understanding.

-Knowing how to use the identities sin(θ)/cos(θ) = tan(θ) and sin^2(θ) + cos^2(θ) = 1 to prove all sorts of trig statements comes up, but I think proving these identities may be useful for your own understanding (you can try using right-triangles, the definitions of these functions as per SohCahToa etc).

(edited 4 months ago)

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Math Proof Questions

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