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Core Mathematics Formulas and Methods

30 flashcards on essential algebra, functions, geometry, calculus and statistics formulas. Practice material written for study, not the official test.

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Quadratic pq-formula
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Nationella prov (Sweden) mock tests →
1
Quadratic pq-formula
For x^2 + px + q = 0, roots are x = -p/2 +- sqrt((p/2)^2 - q).
2
Difference of squares
a^2 - b^2 = (a - b)(a + b).
3
First squaring rule (binomial theorem)
(a + b)^2 = a^2 + 2ab + b^2.
4
Second squaring rule
(a - b)^2 = a^2 - 2ab + b^2.
5
Exponent multiplication rule
a^m * a^n = a^(m + n).
6
Exponent division rule
a^m / a^n = a^(m - n).
7
Power of a power rule
(a^m)^n = a^(m * n).
8
Negative exponent rule
a^(-n) = 1 / a^n for a != 0.
9
Fractional exponent rule
a^(m/n) = n-th root of (a^m).
10
Logarithm product rule
log_a(x * y) = log_a(x) + log_a(y).
11
Logarithm quotient rule
log_a(x / y) = log_a(x) - log_a(y).
12
Logarithm power rule
log_a(x^k) = k * log_a(x).
13
Arithmetic sequence n-th term
a_n = a_1 + (n - 1)d, where d is the common difference.
14
Arithmetic series sum formula
S_n = n * (a_1 + a_n) / 2.
15
Geometric sequence n-th term
a_n = a_1 * r^(n - 1), where r is the common ratio.
16
Geometric series sum formula
S_n = a_1 * (r^n - 1) / (r - 1) for r != 1.
17
Infinite geometric series sum
S = a / (1 - r) for |r| < 1.
18
Straight line equation (slope-intercept)
y = kx + m, where k is the slope (gradient) and m is the y-intercept.
19
Slope formula between two points
k = (y_2 - y_1) / (x_2 - x_1).
20
Perpendicular lines slope condition
k_1 * k_2 = -1 (the slopes are negative reciprocals).
21
Distance formula in Cartesian plane
d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2).
22
Midpoint coordinates formula
M = ((x_1 + x_2) / 2, (y_1 + y_2) / 2).
23
Circle equation centered at (a, b)
(x - a)^2 + (y - b)^2 = r^2, where r is the radius.
24
Triangle area theorem (sine formula)
Area = (1/2) a b * sin(C).
25
Law of sines
a / sin(A) = b / sin(B) = c / sin(C).
26
Law of cosines
c^2 = a^2 + b^2 - 2ab * cos(C).
27
Fundamental trigonometric identity
sin^2(x) + cos^2(x) = 1.
28
Power rule for differentiation
d/dx [x^n] = n * x^(n - 1).
29
Equation of tangent line at x_0
y - y_0 = f'(x_0) * (x - x_0), where y_0 = f(x_0).
30
Combinations formula (order does not matter)
C(n, k) = n! / (k! * (n - k)!).

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