Maths Advanced flashcards

276 HSC Maths Advanced cards across 9 modules (40 definitions, 106 key facts, 49 fill-the-gap, 81 formulas). Each session gives you 20 cards, due cards first. Swipe right for easy, left for hard, down for again. Keyboard: Space to flip, 1 to 4 to rate.

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What this deck covers

Year 11: Introduction to Differentiation (5 cards, 1 dot point)
- Average and instantaneous rates of change for HSC Maths Advanced: the average rate of change as the gradient of a chord (secant) between two points on a curve or in a table, the instantaneous rate of change as the gradient of the tangent at a point, estimating an instantaneous rate with a short chord, reading and interpreting rates from real graphs such as distance-time and cooling curves, and the idea of the derivative as a new function giving the gradient at each point (5)
Year 11: Exponential and Logarithmic Functions (25 cards, 5 dot points)
Year 11: Functions (52 cards, 9 dot points)
Year 11: Trigonometry (33 cards, 6 dot points)
Year 12: Calculus (64 cards, 12 dot points)
Year 12: Financial Mathematics (25 cards, 5 dot points)
Year 12: Functions (14 cards, 4 dot points)
Year 12: Statistical Analysis (33 cards, 6 dot points)
Year 12: Trigonometric Functions (25 cards, 5 dot points)

Sample cards from this deck

Fill the gap
Average and instantaneous rates of change for HSC Maths Advanced: the average rate of change as the gradient of a chord (secant) between two points on a curve or in a table, the instantaneous rate of change as the gradient of the tangent at a point, estimating an instantaneous rate with a short chord, reading and interpreting rates from real graphs such as distance-time and cooling curves, and the idea of the derivative as a new function giving the gradient at each point
A ___ measures how fast one quantity changes as another changes: how fast a tank fills, how fast a hot drink cools, how fast a car covers ground.
A rate of change measures how fast one quantity changes as another changes: how fast a tank fills, how fast a hot drink cools, how fast a car covers ground.
Definition
Exponential and logarithmic graphs for HSC Maths Advanced: the shape of y=a^x and y=log_a x, the horizontal asymptote of an exponential and the vertical asymptote of a logarithm, the reflection in y=x that makes them inverse functions, transformations by translation, reflection and dilation, and stating domain and range
Define Transformations move the graph and its asymptote together
For an exponential, a vertical shift $y = a^x + k$ moves the horizontal asymptote to $y = k$ and the range to $y > k$ ; a horizontal shift leaves them alone. For a logarithm, a horizontal shift $y = \log_a(x - h)$ moves the vertical asymptote to $x = h$ and the domain to $x > h$ ; a vertical shift leaves them alone. Always re-state the asymptote and the domain/range after transforming.
Definition
Algebraic techniques for HSC Maths Advanced: expanding, factoring, simplifying algebraic fractions and solving linear and simultaneous equations
Define Difference of squares (two terms)
If you have a square minus a square, use $A^2 - B^2 = (A + B)(A - B)$ . Sometimes take out a common factor first: $80x^2 - 5y^2 = 5(16x^2 - y^2) = 5(4x - y)(4x + y)$ .
Definition
Right-angled triangle trigonometry for HSC Maths Advanced: the sine, cosine and tangent ratios, finding sides and angles, the exact ratios of 30, 45 and 60 degrees, angles of elevation and depression, and compass and true bearings
Define A back-bearing reverses by $180\degree$
The bearing of $A$ from $B$ is the bearing of $B$ from $A$ plus or minus $180\degree$ (add if the original is under $180\degree$ , subtract if over), because those two north arrows are parallel and the line between the points is a transversal.
Definition
Applications of differentiation: stationary points, inflection, optimisation and related rates
Define First derivative test
Check the sign of $f'(x)$ just before and just after the stationary point.
Fill the gap
Annuities and future value: deriving the formula and applying it to regular savings
In the ___ model used in Maths Advanced, each payment is made at the end of a compounding period, and interest is credited at the same rate per period that compounding occurs.
In the ordinary annuity model used in Maths Advanced, each payment is made at the end of a compounding period, and interest is credited at the same rate per period that compounding occurs.
Fill the gap
Graph transformations: translations, reflections and dilations for HSC Maths Advanced functions
Outside constants do exactly what the arithmetic says; inside constants do the ___ of what they look like, because they act on the input $x$ before $f$ sees it.
Outside constants do exactly what the arithmetic says; inside constants do the opposite of what they look like, because they act on the input $x$ before $f$ sees it.
Definition
Bivariate data: scatter plots, Pearson correlation and least-squares regression for HSC Maths Advanced
Define Direction
Positive (the cloud rises to the right), negative (it falls to the right), or none.
Definition
Graphs of sine, cosine and tangent: amplitude, period, phase shift and vertical shift
Define Amplitude
$= |a|$ . The graph oscillates between $d - |a|$ and $d + |a|$ .
Definition
Radian measure, arcs and sectors for HSC Maths Advanced: the definition of a radian as arc length over radius, converting between degrees and radians with pi rad = 180 deg, the exact radian values of common angles, the arc-length formula L = r theta, the sector-area formula A = half r squared theta, and the area of a segment as a sector minus a triangle, with code-checked numbers and diagrams
Define Arc length: $L = r\theta$ , with $\theta$ in radians
It is the definition $\theta = \dfrac{L}{r}$ rearranged. Always convert a degree angle to radians first; the formula has no degree version.