Formulae used in the exams

## Formulae used in the exams

### Algebra:

{Higher} Quadratic formulae: x = frac(-b +- sqrt(b^2 - 4ac))(2a)

If b^2 - 4ac is negative, then there will be no real answers. The rest of the time there will be two answers, although the two answers may be the same.

### Geometry:

Circumference of a circle: C = 2pir text( or ) pid (diameter is 2 x radius))

Area of a circle: A = pir^2

Area of a rectangle: A = bh

{Higher} Area of any triangle: text(Area ) = frac(1)(2)bc sin C

Area of a parallelogram: A = bh where h is the vertical height

Area of a triangle: A = frac(1)(2)bh where h is the vertical height

Area of a trapezium: A = frac(a + b)(2)h where h is the vertical height

Volume of a right prism: V = Ah where A is the cross-sectional area

### Trigonometry:

Pythagoras's theorem: a^2 + b^2 = c^2 text( where c is the hypotenuse)

Sin: sin x = frac(text(Opposite))(text(Hypotenuse))

Cos: cos x = frac(text(Adjacent))(text(Hypotenuse))

Tan: tan x = frac(text(opposite))(text(Adjacent))

For Sin, Cos and Tan, the Opposite side is the side opposite the angle being calculated, and the Hypotenuse is the longest side.

{Higher} Sin rule: frac(a)(sin A) = frac(b)(sin B) = frac(c)(sin C)

{Higher} Cosine rule: c^2 = a^2 + b^2 - 2bc cos C

### Ratio:

{Higher} Compound Interest: A = P(1 + frac(r)(100))^(t) where A is the calculated amount, P is the starting amount (Principal), r is the interest rate and t is the number of periods.

text(speed) = frac(text(distance))(text(time))

text(density) = frac(text(mass))(text(volume))

text(pressure) = frac(text(force))(text(area))

### Probability:

{Higher} Probability Or: P(A or B) = P(A) + P(B) - P(A-B)

{Higher} Probability And: P(A and B) = P(A given B)P(B))

### Geometry:

Curved surface area of a cone: A = pirl where l is the sloping length

Surface area of a cone: A = pirl + pir^2 where r is the radius of the base

Volume of a cone: V = pir^2frac(h)(3) where h is the vertical height

Surface area of a sphere: A = 4pir^2

Volume of a sphere: V = frac(4)(3)pir^3

### Kinematics:

v=u+at

s=ut + frac(1)(2)at^2

v^2 = u^2+2as

where u is starting velocity, v is final velocity, s is displacement, a is acceleration and t is time.

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