Trigonometry
Probability and statistics
Calculus
Functions
Financial
100

cot2x + 1 = _____

cosec2x

100

Define 'sample space'

The set of all possible outcomes for an experiment

100

True or false: acceleration is the double derivative of displacement

True

100

True or false: a piecewise function is a function made up of three or more functions defined on different domains

False.

A piecewise function is a function made up of TWO or more functions defined on different domains

100

What is the formula for compound interest?

A = P(1 + r)n​

FV = PV(1 + r)n

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200

What is the domain and range of the tan function?

(100 points for correct domain, 100 points for correct range)

Range: (-∞, ∞)

Domain: (-∞, ∞), except for odd multiples of 90°

200

P(A | B) 

What does this notation mean?

Conditional probability: probability of Event A occurring given Event B has occurred

200

Give two formulas for determining gradient 

(100 points for each formula)

m = rise/run

m = (y2 - y1)/(x2 - x1)

200

How do you find the y-intercept and the x-intercept?

(100 points for each correct answer)

y-intercept: let x = 0

x-intercept: let y = 0

200

What does the 'P' in the formula A = P(1 + r)n stand for?

Principal

300

Define 'angle of elevation'

The angle of elevation is the angle measured upwards from the horizontal

300

Define 'continuous random variable' and give two examples

(100 points for correct definition, 100 points for each correct example)

Continuous random variable: measured along a continuous scale

Examples: diameter, weight, height, time, age, temperature

300

Differentiate y = x2ex, factorising your answer

dy/dx = xex(x + 2)

300

Give the domain and range for f(x) = x2

(100 points for correct domain values, 100 points for correct range values, 100 points for correct brackets)

Domain: (-∞, ∞)

Range: [0, ∞)

300

Describe what an annuity and give one example of one

An annuity is a form of investment that involves regular contributions of money. Interest compounds at the end of each period before the next contribution of money is made.

Example: superannuation

400

x/sin(53) = 3.5sin(75)

Solve for x

x = 2.89 units

400

True or False:

Var(X) = E(x2) - μ2

Variance is a measure of central tendency

σ = Var(X)2

The sample mean symbol is x̄

(100 points for each correct answer)

1. True: equation is correct

2. False: variance is a measure of spread

3. False: σ2 = Var(X), variance is the square of standard deviation

4. True: x̄ is sample mean, μ is population mean

400

What does the 'n' in the trapezoidal rule represent?

The number of trapeziums (or subintervals)
400

Describe the symmetry and test for odd and even functions

(100 points for each correct symmetry and test)

Even function: symmetry across the y-axis. Even if f(x) = f(-x)

Odd function: point symmetry around the origin. Odd if f(-x) = -f(x)

400

Describe a what a reducing-balance loan is and give three examples.

A loan, the value of which decreases over time as it is paid off

Examples: car (or any other) loan, mortgage, credit card

500

y = ksin(a(x + b)) + c

Identify each of the transformations

(100 points for each correct transformation)

(100 points for identifying the equation to find period)

k: amplitude

a: period

b: phase shift (left or right)

c: vertical shift (up or down)

Period = 2π/a or 2π/n

500

List five ways of displaying data

(100 points for each correct answer)

Sector graph (pie chart), two-way tables, bar graph, column graph, pareto chart

500

Integrate x4 - 4x3 + 9x2 - 6x + 5

Integral: x5/5 - x4 + 3x3 - 3x2 + 5x +c

500

Solve 2(x - 1)3 -5 = 0 for x

x = 3√ (5/2) + 1

x = 2.357 . . .

500

Find the amount that will be in the bank after one year if $10000 is invested at 4.5% p.a. with interest paid montly.

FV = $10459.20

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