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Facts currently selected by your teacher · 74 facts · questions only
Algebra
02
Quadratic formula
03
The factor theorem
04
The remainder theorem
23
Laws of logarithms
Trigonometry
05
The sine rule
06
The cosine rule
07
Area of a triangle using two sides and the included angle
10
Sketch the graph of y = sin x in degrees and radians
11
Sketch the graph of y = cos x in degrees and radians
12
Sketch the graph of y = tan x in degrees and radians
13
Special values of sin, cos and tan (in both degrees and radians)
14
Arc length when the angle is in radians
15
Area of a sector when the angle is in radians
16
Identity linking tan θ, sin θ and cos θ
17
The Pythagorean trigonometric identity
18
Identity linking tan² θ and sec² θ
19
Identity linking cot² θ and cosec² θ
20
Double-angle formula for sin 2θ
21
Three forms of the double-angle formula for cos 2θ
22
Double-angle formula for tan 2θ
56
Small-angle approximations for sin θ, cos θ and tan θ
Coordinate geometry
08
Equation of a circle
09
Equation of a straight line with gradient m passing through (x₁, y₁)
Graphs
24
Sketch the graph of y = x²
25
Sketch the graph of y = x³
26
Sketch the graph of y = 1/x
27
Sketch the graph of y = √x
28
Sketch the graph of y = aˣ
29
Sketch the graph of y = logₐ x
30
Transformation y = f(x) + a
31
Transformation y = f(x + a)
32
Transformation y = af(x)
33
Transformation y = f(ax)
34
Transformation y = −f(x)
35
Transformation y = f(−x)
Calculus
36
Nature of stationary points from the second derivative
37
Definitions of concave and convex
43
Chain rule for y = (stuff)ⁿ
44
Chain rule for e to the power of stuff
45
Chain rule for a to the power of stuff
46
Chain rule for y = ln(stuff)
47
Chain rule for y = sin(stuff)
48
Chain rule for y = cos(stuff)
49
Chain rule for y = tan(stuff)
50
Product rule for differentiation
51
Quotient rule for differentiation
52
What partial-fraction form would you use for two distinct linear factors?
53
What partial-fraction form would you use for a repeated linear factor?
54
What partial-fraction form would you use for an irreducible quadratic factor?
Sequences
38
nth term of an arithmetic sequence
39
Sum of the first n terms of an arithmetic sequence
40
nth term of a geometric sequence
41
Sum of the first n terms of a geometric sequence
42
Sum to infinity of a geometric sequence
59
Sum of the first n positive integers
60
Sum of the first n squares
61
Sum of the first n cubes
Matrices
62
Matrix for reflection in the x-axis
63
Matrix for reflection in the y-axis
64
Matrix for reflection in y = x
65
Matrix for reflection in y = −x
66
Matrix for anticlockwise rotation through θ about O
67
Matrix for stretches parallel to the axes
68
Matrix for a shear with the x-axis invariant
69
Matrix for a shear with the y-axis invariant
70
Determinant of a 2×2 matrix
71
Inverse of a 2×2 matrix
72
Geometric significance of the determinant of a matrix
Polynomials
73
Vieta’s relations for ax² + bx + c = 0
74
Vieta’s relations for ax³ + bx² + cx + d = 0
75
Vieta’s relations for ax⁴ + bx³ + cx² + dx + e = 0
Complex numbers
76
Modulus of a product of two complex numbers
77