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KCSE Mathematics Formulae and Rules

Key KCSE mathematics formulae for geometry, algebra, sequences, statistics, logarithms and calculus, one card per formula.

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Area of a circle
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1
Area of a circle
pi x r^2, where r is the radius.
2
Circumference of a circle
2 x pi x r, or pi x d.
3
Volume of a cylinder
pi x r^2 x h.
4
Volume of a cone
One third x pi x r^2 x h.
5
Volume of a sphere
Four thirds x pi x r^3.
6
Surface area of a sphere
4 x pi x r^2.
7
Pythagoras theorem
In a right-angled triangle, hypotenuse squared = the sum of the squares of the other two sides.
8
Quadratic formula
For ax^2 + bx + c = 0, x = (-b plus or minus root(b^2 - 4ac)) / 2a.
9
Gradient of a line
(y2 - y1)/(x2 - x1).
10
Equation of a straight line
y = mx + c, where m is the gradient and c the y-intercept.
11
Sum of an arithmetic progression
S = n/2 [2a + (n - 1)d].
12
nth term of an arithmetic progression
T = a + (n - 1)d.
13
Sum of a geometric progression
S = a(r^n - 1)/(r - 1) for r greater than 1.
14
Compound interest
A = P(1 + r/100)^n.
15
Sine rule
a / sin A = b / sin B = c / sin C.
16
Cosine rule
a^2 = b^2 + c^2 - 2bc cos A.
17
Area of a triangle using sine
1/2 x a x b x sin C.
18
Area of a trapezium
1/2 x (a + b) x h, where a and b are the parallel sides.
19
Sum of interior angles of a polygon
(n - 2) x 180 degrees.
20
Exterior angle of a regular polygon
360 / n degrees.
21
Determinant of a 2 by 2 matrix
For rows (a b) and (c d), the determinant is ad - bc.
22
Mean of grouped data
The sum of frequency x midpoint, divided by the total frequency.
23
Probability of independent events A and B
P(A and B) = P(A) x P(B).
24
Area of a sector
(angle / 360) x pi x r^2.
25
Arc length
(angle / 360) x 2 x pi x r.
26
Area scale factor of similar figures
The square of the linear scale factor.
27
Volume scale factor of similar solids
The cube of the linear scale factor.
28
Logarithm rule for a product
log (xy) = log x + log y.
29
Logarithm rule for a power
log (x^n) = n log x.
30
Derivative of x^n
n x^(n - 1).
31
Integral of x^n
x^(n + 1)/(n + 1) + c, for n not equal to -1.
32
Standard form
A number written as a x 10^n with 1 less than or equal to a less than 10.

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