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STEM Schools Problem-Solving Formulas and Patterns

Flashcards with the rates, percentages, geometry formulas and reasoning patterns used in STEM school admission tests. Original study material.

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Percentage change

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Percentage change

\frac{new - old}{old} \times 100

Distance, speed, time

d = v t

Convert km/h to m/s

Divide by 3.6

Average speed for equal distances at

v_{1}

and

v_{2}

\frac{2 v _{1} v _{2}}{v _{1} + v _{2}}

Time for two workers taking

a

and

b

hours working together

\frac{ab}{a + b}

Circumference and area of a circle

2 π r

and

π r^{2}

Volume of a cylinder, cone and sphere

π r^{2} h

\frac{1}{3} π r^{2} h

\frac{4}{3} π r^{3}

Surface area of a cuboid

2 (ab + b c + c a)

Sum of the interior angles of an

n

-sided polygon

(n - 2) \times 18 0^{\circ}

Number of diagonals of an

n

-sided polygon

\frac{n ( n - 3 )}{2}

Number of handshakes among

n

people

\frac{n ( n - 1 )}{2}

n

th term of an arithmetic sequence

a + (n - 1) d

n

th term of a geometric sequence

a r^{n - 1}

Sum of the first

n

natural numbers

\frac{n ( n + 1 )}{2}

Triangular numbers

1, 3, 6, 10, 15, 21, ...

Units digit patterns of powers of 2

2, 4, 8, 6 repeating every 4 powers

Angle between clock hands at

h

m

∣30 h - 5.5 m ∣

(take the smaller of the angle and 360° minus it)

Painted cube of side

n

: cubes with 3 painted faces

Painted cube of side

n

: cubes with 1 painted face

6 (n - 2)^{2}

Painted cube of side

n

: cubes with no painted face

(n - 2)^{3}

Days of the week after

k

days

Find

k

mod 7 and count on from today

Mixture of two solutions

\frac{c _{1} v _{1} + c _{2} v _{2}}{v _{1} + v _{2}}

Compound growth

A = P (1 + r)^{t}

Density

ρ = \frac{m}{V}

Syllogism: all A are B and all B are C

Then all A are C

Pythagorean triples to recognise

3-4-5, 5-12-13, 8-15-17, 7-24-25

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