STEP Prep Thread 2021

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What grade roughly is 2 full solutions. (With potential flaws.)
- And Q3 where part 1 was fine but for part 2 I showed J(n) < 1/n+1((1+tanb)^n-cos^nb) not 1/n.
- And Q6 where only the differentiation and rearranging to find g(X) as the logarithm of trig functions was right.
- And like 2-3 marks in Q2.
Many thanks

Reply 581

Junkmaniac

Here's Q3 of the paper, on integration:
Q3:

Spoiler

My solution:

Spoiler

(edited 2 years ago)

Reply 582

neca322

I u

Original post by Junkmaniac

Here's Q3 of the paper, on integration:
Q3:

Spoiler

My solution:

Spoiler

I used am gm inequalities for the

[latex]J_{n+1}+J_{n-1}

result, but otherwise that's how I did the question also

Reply 583

gitHappens

Original post by Junkmaniac

Indeed---the parametric question was quite a gift, because there wasn't much requirement for inspiration until the last part, where you had to find the perpendicular distance and the equation of the curve.

I think the perpendicular distance wasn't really inspiration needed, but the curve was (I did all but that in the problem)

Reply 584

neca322

Original post by gitHappens

I think the perpendicular distance wasn't really inspiration needed, but the curve was (I did all but that in the problem)

I think the distance was 1 right?

Reply 585

Junkmaniac

Original post by gitHappens

I think the perpendicular distance wasn't really inspiration needed, but the curve was (I did all but that in the problem)

Ah, it took me a while to get that one. Fortunately, there's no working involved, so I doubt it could be worth more than two marks.

Reply 586

Junkmaniac

The other two questions I could recall:

Q2:

Spoiler

Mfw matrices is added into the specification to fuel a question on inequalities

Q11:

Spoiler

It is exhausting to typeset solutions so I guess I'll just leave these hanging for now. Do correct me if any details are wrong because its terribly hard to recollect all of that from memory

(edited 2 years ago)

Reply 587

_gcx

Study Forum Helper

Original post by Junkmaniac

The other two questions I could recall:

Q2:

Spoiler

Mfw matrices is added into the specification to fuel a question on inequalities

Q11:

Spoiler

It is exhausting to typeset solutions so I guess I'll just leave these hanging for now. Do correct me if any details are wrong because its terribly hard to recollect all of that from memory

that Q11 looks like a gift. nicest question on the paper?

Reply 588

Junkmaniac

Original post by _gcx

that Q11 looks like a gift. nicest question on the paper?

Would still give it to Q1. Q1 was relatively straightforward algebra with no tricks. I think some thinking is still required for Q11.

Reply 589

_gcx

Study Forum Helper

Original post by Junkmaniac

Would still give it to Q1. Q1 was relatively straightforward algebra with no tricks. I think some thinking is still required for Q11.

What was Q1 on?

Reply 590

Junkmaniac

Original post by _gcx

What was Q1 on?

Hm, they first gave a set of parametric equations (trigo related) and asked to find the equation of thenormal at the parameter

t=\theta

.

Then, they asked to prove that this line is a tangent to

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4

at the point

(8cos^3 \theta , 8sin^3 \theta )

, or something.

Next part was another set of parametric equations. Again, asked to find the equation of the normal.

Next, find perpendicular distance from the normal to the origin (its 1)

Hence, find a Cartesian equation free of t that this normal is a tangent to. (Since the normal is 1 unit from the origin, it is tangent to the unit circle.)

Reply 591

_gcx

Study Forum Helper

Original post by Junkmaniac

Hm, they first gave a set of parametric equations (trigo related) and asked to find the equation of thenormal at the parameter

t=\theta

.

Then, they asked to prove that this line is a tangent to

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4

at the point

(8cos^3 \theta , 8sin^3 \theta )

Just sounds like a standard calculus exercise - hopefully gave a relatively confident starter.

Reply 592

Junkmaniac

Original post by _gcx

Just sounds like a standard calculus exercise - hopefully gave a relatively confident starter.

Indeed.

Reply 593

bos0n

Original post by Junkmaniac

Hm, they first gave a set of parametric equations (trigo related) and asked to find the equation of thenormal at the parameter

t=\theta

.

Then, they asked to prove that this line is a tangent to

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4

at the point

(8cos^3 \theta , 8sin^3 \theta )

How many marks do you think finding the distance was worth?

Reply 594

Junkmaniac

Original post by bos0n

How many marks do you think finding the distance was worth?

Together with the hence part, maybe 5 marks?

(edited 2 years ago)

Reply 595

gitHappens

Lmao I did 11 I think perfectly but actually had trouble on 1 and got the distance wrong somehow lmao so I think 11 was the better gift.

Reply 596

gitHappens

How many marks would proving that the matrices had determinant 0 be worth?

Reply 597

bos0n

Original post by gitHappens

How many marks would proving that the matrices had determinant 0 be worth?

yeah thats worrying me as well bc I didn't really explain it...

Reply 598

bos0n

and the final inequality? would you guess it to be more than 5 marks?

Reply 599

Junkmaniac

Original post by bos0n

and the final inequality? would you guess it to be more than 5 marks?

I doubt so--- actually it can be done in one line, because a/(b+c) + b/(a+c) + c/(a+b) > a/(a+b+c) + b/(a+b+c) + c/(a+b+c)=1.

The inequality is quite weak, a stronger bound would be
a/(b+c) + b/(a+c) + c/(a+b) >= 3/2, by Nesbitt's inequality. (https://en.m.wikipedia.org/wiki/Nesbitt%27s_inequality)

Unfortunately for me I didn't see the way to go for the last part so I kinda ended up quoting the inequality--doubt that will give me any marks haha