Free SACE Year 11 Mathematics Flashcard Review
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How is gradient calculated?
m = (y₂ − y₁)/(x₂ − x₁), for distinct x coordinates.
Point-gradient form?
y − y₁ = m(x − x₁).
Parallel nonvertical lines?
Equal gradients; distinct lines have different intercepts.
Perpendicular nonvertical gradients?
Their product is −1.
What does the vertical intercept mean?
The output when input is zero, if zero is meaningful in context.
What is an intersection?
An ordered pair satisfying both equations.
What does elimination producing 0 = 0 imply for two linear equations?
The equations are dependent and describe coincident lines.
Inverse proportion rule?
y = k/x, so xy remains constant.
Asymptotes of y = k/x, k ≠ 0?
x = 0 and y = 0.
Circle with centre (a, b) and radius r?
(x − a)² + (y − b)² = r².
Function test?
Each allowed input has exactly one output; apply the vertical line test.
Domain versus range?
Domain contains inputs; range contains achieved outputs.
What is the vertex of a(x − h)² + k?
(h, k).
What does a negative quadratic leading coefficient do?
The parabola opens downwards.
State the quadratic formula.
x = (−b ± √(b² − 4ac))/(2a).
What does a zero discriminant mean?
One repeated real root; the parabola touches the axis.
State the sum and product of quadratic roots.
Sum = −b/a; product = c/a.
Simplify √12.
2√3.
How do you model zeros r and s?
Use y = a(x − r)(x − s), then use another point to find a.
What is a cubic?
A polynomial of degree three.