UEC HSC MATHS 2U

This was my UEC for my 2U HSC exam last year. It might not help but meh.

UEC (Ultimate Error Correction)

Golden Rules
- Look at how many marks and answer accordingly
- Change calculator to rads or deg accordingly
- Remember units
- Domain must always be in your head
- If unsure of answer, go back to it later
- In exam, WRITE ALL STEPS
- When about to round off, write exact answer first, then write the rounded off places in brackets

Arithmetic
- When you see 8 and 6, use CALCULATOR to find the fraction
- When you see 4 and 6, use CALCULATOR to find the fraction
- When forming quadratics, the sum of roots has a negative sign.

Integration:
- Remember +C
- When finding Area under the curve, Remember UNITS
- When asked to find a primitive, remember +C
- When finding volume, SQUARE before integrating
- When finding volume remember the π

Series and Applications:
- Nth term of GP given by: arn-1
- When finding i.e. x,4,y,9 when u want to find first term or common difference/ratio, use Tn=arn-1 or Tn=a+(n-1)d as opposed to simultaneous equations
- To prove limiting sum, absolute value of r must be less than 1
- To do ∑ questions, write out series then say it is an AP/GP with first term X, and common difference/ratio Y
- With the above case, the top is the last term and the bottom is the first term
- Read questions and do not assume it goes twice or once for a trip i.e. the truck going back and forth question
- When finding formula for Arithmetic Sequence, - Prove its arithmetic, with a=X and d=Y, Write out formula Tn=a+(n-1)d, sub in a and d, then expand and simplify

Locus and Parabola
- Sketch the locus before answering
- When its concave down or side left, then remember negative sign on the formula
- When squaring both sides, must SQUARE the CONSTANT

Absolute Values and Inequalities
- When dividing/multiplying by negatives in inequality, remember to change the direction of sign as well as the NEGATIVE SIGN
- When doing absolute values equality where one side has abs and the other doesn’t, MUST CHECK SOLUTION
- When throwing logs to other side, use calculator to check if + or – and change inequality sign accordingly
- Turning point only required in equality when there is a LONELY CONSTANT and in inequality when there is an ABSOLUTE VALUE ON ONE SIDE ONLY

Differentiation
- When u see acceleration-velocity , think differentiation
- When doing y d or y dd table, sub in points
- When doing y dd to y d questions, DO ALL STEPS
- For differentiation show questions, remember UNITS

Trigonometry
- For cosine rule: remember to square root answer when finding the side
- When doing area of a sector and finding the larger sector, consider reflex angle
- When domain has a π, answer must be in RADIANS
- When there is a quadratic, take into account acuteness to restrict domain
- When using sin rule to find an angle there are 2 cases, obtuse or acute.
- Area of sector: 1/2rrq
- Bearing must be in 3 digits
- Write exact ratios in non-rationalised form

Geometry
- “matching” not “corresponding”
- Because midpoints are the same for both diagonals, they bisect each other
- When giving radius of circle, remember units
- Similar triangles – NO SAS. Only : one angle equal and sides about equal angle are equal
- Dotted line when it is <>

Probability
- ALWAYS DRAW TREE DIAGRAMS WHEN UNSURE
- When it is a non-replacement question, remember to subtract from the total
- DRAW TABLE WHEN DOING DICE QUESTIONS