Free HSC Mathematics Standard 2 Flashcard Review
Review 20 public cards with spaced repetition. Flip a card, then grade your recall. Cards you miss return today. Your schedule stays in this browser.
Loading your review schedule…
Browse the free cards
Define the gradient of a straight line.
The gradient (slope) is the ratio of the vertical change (rise) to the horizontal change (run) between two points. Formula: m = (y2 - y1)/(x2 - x1).
State the gradient-intercept form of a straight line.
y = mx + b, where m is the gradient and b is the y-intercept (the point where the line crosses the y-axis).
What does a positive gradient indicate?
A positive gradient indicates that as x increases, y increases; the line slopes upward from left to right.
What does a negative gradient indicate?
A negative gradient indicates that as x increases, y decreases; the line slopes downward from left to right.
Describe a horizontal line in terms of gradient.
A horizontal line has a gradient of zero (m = 0), because there is no vertical change as x changes.
Describe a vertical line in terms of gradient.
A vertical line has undefined gradient, because the horizontal change is zero, making division by zero impossible (x2 - x1 = 0).
State the point-gradient form of a line.
y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a known point on the line.
Define linear relationship.
A linear relationship is a relationship between two variables that, when plotted on a coordinate plane, produces a straight line. It has a constant rate of change.
Define exponential growth.
Exponential growth occurs when a quantity increases by a constant percentage or factor over equal time intervals. Formula: A = P(1 + r)ᵗ or A = Peᵏᵗ.
Define exponential decay.
Exponential decay occurs when a quantity decreases by a constant percentage or factor over equal time intervals. Formula: A = P(1 - r)ᵗ or A = Pe-ᵏᵗ.
In the exponential growth/decay formula A = P(1 ± r)ᵗ, what do the variables represent?
A = final amount, P = initial amount (principal), r = rate of growth/decay (as a decimal), t = time period.
What is the Sine Rule?
The Sine Rule states: a/sin A = b/sin B = c/sin C, where a, b, c are side lengths opposite to angles A, B, C respectively in a non-right-angled triangle.
When should the Sine Rule be used?
The Sine Rule is used when you know either two angles and one side (AAS or ASA), or two sides and a non-included angle (SSA).
What is the Cosine Rule?
The Cosine Rule states: c2 = a2 + b2 - 2ab cos C, where c is the side opposite angle C, and a, b are the other two sides.
When should the Cosine Rule be used?
The Cosine Rule is used when you know either three sides (SSS), or two sides and the included angle (SAS).
State the area formula for a non-right-angled triangle using sine.
Area = ½ab sin C, where a and b are two sides of the triangle and C is the included angle between them.
Define bearing in navigation.
A bearing is the direction or angle measured clockwise from north. It is expressed as an angle from 0° to 360°, or as a three-figure bearing (e.g. 045°, 180°, 270°).
What is a true bearing?
A true bearing is an angle measured clockwise from north, expressed as a three-digit number from 000° to 360°.
How do you convert a compass bearing (e.g. S 40° E) to a three-figure bearing?
Measure the angle clockwise from north. For S 40° E: start at south (180°) and measure 40° toward east, giving 180° - 40° = 140°.
Define rate in mathematics.
A rate is a ratio that compares two quantities with different units (e.g. km/h, cost per item, litres per minute). It expresses how one quantity changes relative to another.