Wiki Page, HSC Mathematics 2 unit advanced: 2016 term 4 archives

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2017-02-08T22:13:58-07:00

Last term's (term 3) Prelim exam: 2016 Yearly Exam.pdf

Answers to the above exam: 2016 Preliminary Yearly Mathematics Exam - Answers.pdf

Week / Date | Lesson 1 | Lesson 2
1 / 10 Oct | Tom Cartwright's Life Coaching | Introduction to W(R)ong Maths

2 / 17 Oct

Going through the preliminary exam (part 1).

Homework: start Chapter 1

(Geometry revision)

Start writing your summary notes, especially those formulae not on the formula sheet.

Remember to revise those notes 24 hours after you write them, and then every week after that.

Going through the preliminary exam (part 2).

Homework: finish Chapter 1

By the end of this week, you have mastered:

plane geometry

parallel lines

congruent triangle

similar tirangles

ratio of intercepts

area and volume formulae

coordinate geometry:

distance,

midpoint,

gradient,

equation of a straight line

parallel lines

perpendicular lines

perpendicular distance

3 / 24 Oct

The semantics of Calculus:

Differentiation: (ex. 2.1)

Describing the gradient of a curve:

increasing

stationary

decreasing

Describing the types of Stationary Points (S.P.)

minimum turning point (T.P.)

maximum T.P.

point of horizontal inflection / inflexion

f'(x) = 0

The TABLE method (gradient left of the T.P. and right of the T.P.) was taught in ex. 2.2

Second, third, fourth, ..., etc. derivatives (ex. 2.3)

The second derivative as a test for concavity change. (ex. 2.4)

f''(x) = 0

The TABLE method (concavity left of the Point of Inflection (P.o.I.) and right of the P.o.I.) must be used to verify that the P.o.I. is really a P.o.I.

4 / 31 Oct

The language of the second derivative as a rate of change (ex 2.5)

http://jcsites.juniata.edu/faculty/kruse/ma103/topic03.htm was handed out in class.

Using the second derivative to check if a S.P. is a min. / max. T.P. (ex 2.6)

Graphing polynomial functions (ex. 2.7)

5 / 7 Nov

Finding Maximum and Minimum values on a function, especially when the domain is restricted. (ex. 2.8)

The difference between a relative and absolute min. / max. value.

Problems involving min. / max. values: Using SIMULTANEOUS EQUATIONS techniques (SUBSTITUTION) to create an equation / function with only 1 letter. (ex. 2.9)

First deriving the equation of ex. 2.9, then proving that it is a min. / max. T.P., and finding the actual min. / max. value at that point. (ex. 2.10)

We then learnt that finding the Primitive Function is the same as Indefinite Integrals. (ex. 2.11)

By the end of this week, you have mastered:

The first derivative = 0 finds stationary points

The second derivative = 0 finds potential points of inflection.

There are 2 ways to find if a point is a min. / max. T.P.

The table method MUST be used to prove a potential P.o.I.

min. / max. problems have exactly the same procedure even though there are a lot more words in the question.

we anti-differentiate to find the original function given the gradient function f'(x)

6 / 14 Nov

Indefinite integrals are the same process as finding primitive functions. The 'rule' of integration. (ex. 3.4)

Indefinite integrals have no limits and need +C.

Definite integrals have an upper and lower limit and the number that you calculate from F(b) - F(a) represents the NET area that is under a curve. (ex. 3.3)

Integrating the chain rule (ex. 3.5)

The relationship between the integral and the area under the curve (ex. 3.6 deals with the x-axis)

7 / 21 Nov

Areas enclosed by the y-axis (ex. 3.7)

Combinations of areas under multiple curves. (ex. 3.8)

Volumes of areas rotated around the x - or y - axis. (ex. 3.9)

8 / 28 Nov

The Trapezoidal approximation area formula (ex. 3.1)

Simpson's Rule approximation area formula (ex. 3.2)

Revision (past HSC questions)

9 / 5 Dec

!!! EXAM !!!

Don't you dare miss this lesson otherwise you are getting an N letter if you have no valid reason. There is no opportunity to sit for a catch up exam, obviously, because your last day is Wednesday.

General celebration and ecstasy that the term has finished and you survived 2 unit maths relatively unscathed with no scar tissue. Bring your X-box and gifts to Richard on this day. (Dress up in your basketball gear and we will explore the parabolic motion of basketballs)

Start your revision on these past HSC questions, which have been assembled according to topic.

Probably better to work in reverse order, because they are the most recent exams.

HSC 2U Applications of Differentiation.pdf (the print quality is not good because my printer at home is not good).

HSC 2U Integration.pdf (this file has lots (!) of questions you can't do now because we haven't done logs, exponentials, trig.). Just do the questions that don't look strange.