iGCSE 0580 Maths – The Ultimate Formula Cheat Sheet
An analogy of compound interest is that it can be seen as exponential growth on the principal amount invested.
It is also important to note that, in IGCSE, while n does usually refer to the number of years, it can sometimes also
refer to the number of times interest compounds in a year. For example, if the question gives compound interest at a
rate of 0.1% per month, and the money was invested for 2 years, n would be 24 (since there are 24 months in a year),
rather than 2.
Quadratic equations can also be solved graphically. Sketch the quadratic on a graph, and the roots of the quadratic
(i.e. the solutions) will be the x-coordinates of the point where the graph intersects/touches the x-axis.
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1. Area of a parallelogram is twice the area of a triangle since it can be split into two congruent triangles. Therefore,
since the formula for the area of a triangle is 1/2ab*sin(C), the area of a parallelogram is twice that, which is just
ab * sin (C).
2. The area of a triangle is 1/2*base*height because if there was a rectangle with length, b, and width, h, if you had
any point on the top edge of the rectangle joined to the bottom two corners (to create a triangle), the area of a
triangle would be half that of the area of a rectangle, bh.
3. Knowledge of Heron's formula (i.e. the third formula provided for the area of the triangle) is not needed for the
IGCSE course.
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1. θ/360 is common in both the formula for the area of a sector and the perimeter of a sector. This is because
θ/360 gives the fraction that needs to be dealt with as a whole of the circle (a circle has 360 degrees), since a
sector (perimeter or area) is a fraction of the whole circle.
2. A cone is a specific type of pyramid. This is why the formula for the volume of a cone resembles that of a
pyramid. πr^2 is the base area, and h is the perpendicular height.
3. To derive the curved surface area of the cylinder, visualise the cylinder opening up into a net. The curved surface
area would then be the area of the rectangle that unfolds as part of the net. The length of the rectangle would be
h, and the width would be 2πr, since the circle's perimeter would unfold to become the other side of the rectangle
(visualise on diagram for reference). Therefore, we obtain the curved surface area to be length*width of the
rectangle which is 2πrh.
To work out the total surface area, simply add on the areas of the two circles of the cylinder which would give an
additional 2πr^2. Hence, the total surface area is 2πrh + 2πr^2, which can be factorised as 2πr(h+r)
The diagram shows a net of a cylinder, which can be used to derive the surface area.
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A common application question of similarity is map scales. For example, they will give you the area of a lake on
a map as 5cm2, and they will give you the linear scale factor of the map:actual as 1:240,000. From there, you
need to square this linear scale factor to get the area scale factor, i.e. (1)2:(240,000)2. Then, you will need to
multiply 5 by (240,000)2 to get the actual area of the lake, in cm2.
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1. You can link the circle theorem on bullet-point (BP) 3 given here to the circle theorem listed on
BP 1. Since we know that the angle subtended at the centre is twice that as the angle subtended
at the arc, since AOB is a straight line (it is a diameter of the circle), angle AOB is 180°, and so
angle APB is half of that and therefore it is 90°. This proves that the angle in a semicircle is
always a right angle. This theorem is also known as Thales' theorem.
2. Proof that the exterior angle of a cyclic quadrilateral is equal to the interior opposite angle:
Let p° be the exterior angle (i.e. angle CDE)
Then, since ADE is a straight line, angle CDA = (180-p)°
Since quadrilateral ABCD is cyclic, its opposite angles sum to 180.
Thus, angle ABC = 180 - (180-p) = p°
Therefore, we see that the exterior angle is equal to the interior opposite angle (angle ABC)
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Compiled by Baaz Pathan 9930758555 @ Catalyst International School & Mohd Hilmy
Mnemonic to remember the trigonometric ratios or SOH CAH TOA:
Studying Our Homework Can Always Help To Obtain Achievement
Cosine Rule:
The formula to find the angle when all three sides are given is simply a rearrangement of the formula to find the length
of a side, with cosX as the subject, where X is the angle we are trying to find.
1. The formula to calculate the distance between two points of a line segment is simply a sophisticated formula
of the Pythagorean Theorem, as can be seen on the diagram to the left of it.
2. The slopes of perpendicular lines are negative reciprocals of each other. Negative reciprocal is a key term to
use in exams, and it means that the product of the two gradients is -1.
3. The formula of calculating the midpoint involves half the distance between the two x-coordinates and half the
distance between the two y-coordinates. In essence, what we are doing here is creating a similar triangle to
triangle AXB, where angle AXB = 90°. The similar triangle can, for example, be MYB, where M is the midpoint
and angle MYB = 90°. It could also be represented diagramatically as triangle AYM. Either way, this triangle
has half the side lengths of the original triangle created (AXB), and M is therefore the midpoint of the points A
and B.
The area under a speed-time graph represents the distance traveled because it represents the product of speed and
time. Since speed multiplied by time gives distance (e.g., if an object moves at 10 m/s for 5 seconds, it covers 50
metres), the area beneath the graph shows this calculation visually. Therefore, each small segment of the area beneath
the graph sums to the total distance traveled over a given time period.
KEY TERM: Position vector simply refers to the vector that represents the location of a point relative to the origin, O.
For example, the position vector of point A in the diagram is simply the vector OA, or a.
Similar to calculating the length of a line segment, calculating the magnitude/modulus of a vector is an application of
the Pythagorean theorem.
NB: knowledge of box-and-whisker plots is no longer needed for IGCSE Maths exams from 2025 onwards.