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Vocabulary > Maths Properties/Tricks > Flashcards

Maths Properties/Tricks Flashcards

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1
Q

Triangle Inequality

A

The sum of any two sides of a triangle must be bigger than the third side

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2
Q

30-60-90 triangles

A

Also called the 1-2-squ(3) triangle

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3
Q

30-60-90 triangles

A

Special nature of these right triangles is their abililty to yield exact answers instead of decimal approximations when dealing with trigo functions

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4
Q

Circle property I

A

If two inscribed angles in the same circle intercept the same arc/chord, then the two inscribed angles are equal

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5
Q

Finding out about Prime numbers

A

If a number less than 100 is not divisible by 2, 3 or 5 or 7, then it is prime (NB: sun the digits to check for divisibility)

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6
Q

Generalized Pythagorean Theorem

A
  • a2 + b2 = c2 then the angle opposite c is a right triangle
  • a2 + b2 90•)
  • a2 + b2
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7
Q

Sum of a sequence

A

Sum = (n*(n-1))/2

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8
Q

remainder/dividend rule

A

If dividend

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9
Q

2/3

A

0.6666

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10
Q

4/3

A

1.3333

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11
Q

3/4

A

0.75

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12
Q

4/5

A

0.8

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13
Q

5/6

A

0.8333

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14
Q

9/8

A

1.125

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15
Q

30-60-90 triangle’s sides

A

Hypothenus: x * square root of 3

Side I: 1

Side II: 2

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16
Q

Area of an equilateral triangle

A

(Square root of 3)/4 * (side^2)

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17
Q

2/3

A

0.6666

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18
Q

4/3

A

1.3333

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19
Q

3/4

A

0.75

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20
Q

4/5

A

0.8

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21
Q

5/6

A

0.8333

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22
Q

9/8

A

1.125

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23
Q

30-60-90 triangle’s sides

A

Hypothenus: x * square root of 3

Side I: 1

Side II: 2

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24
Q

Area of an equilateral triangle

A

(Square root of 3)/4 * (side^2)

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25
Q

Solve by elimination

A

Multiply both sides of the equation by chosen nbs, then add them to cancel one of the two variables

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26
Q

Solve by substitution

A

Solve one of the two equations for one of the variables, then we replace y in the other equation with this expression for y, finally we solve for x

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27
Q

Permutation vs. Combination

A

Permutation: order of the selection matters
Combination: only the result matters, not the order of selection

28
Q

Fundamental Counting Principle

A

If task #1 can happen inm ways, task #2 can happen in n ways, and task #3 can happen in p ways, and if all three tasks are independent, then the nb of outcome is nmp

29
Q

In how many ways can 5 books be ordered on a shelf

A

Permutation! 5! = 5x4x3x2x1 = 120

30
Q

nCr

A

The nb of combination of r things that can be selected from a pool of n things

31
Q

p is a factor of q

A

p and q are positive integers and there’s another positive integer k such that p*k=q.
You can multiply p by some positive integer and get q

32
Q

Divisibility rule

A

A number is divisible by k iif the sum of the digits is also a nb divisible by k

33
Q

Inclusive counting

A

(End) - (Start) + 1

34
Q

Multiple of every positive integer

A

0

35
Q

Factor pairs

A

The pairs of factors that, when multiplied together, yield the integer (eg. 1&60 2&30…)

36
Q

Large nb divisible by 4

A

If the last two digits are divisible by 4 then the whole nb is divisible by 4

37
Q

Order of Operations

A 
PEMDAS
Parentheses
Exponents
Multiplication&Division
Addition&Substraction
38
Q

Greatest Common Factor

A

Found by finding the common factor in the prime factorisations of the nbs

39
Q

Rounding Rule

A

We look only at the single digit in the next smallest place (if 4 or less -> round down, if 4 or more -> round up)

40
Q

LCM

A

Useful in adding two fractions bc the LCM is identical to the LCD

41
Q

Percent change

A

((New) - (Original)) / (Original) * 100

42
Q

Percent change

A

((New) - (Original)) / (Original) * 100

43
Q

1/6

A

0.16666

44
Q

Ratio vs. Proportion

A

Ratio: single fraction
Proportion: an equation of the form fraction equal fraction

45
Q

Mixed numeral

A

One way of writing a fraction greater than 1 (eg. 6 (3/5) )

46
Q

Area of a trapeze

A

(b1 + b2)/2 * h

47
Q

Slope of perpendicular lines in the x-y plane

A

They are opposite (+-) reciprocals (x/ 1/x)

48
Q

Rhombus

A

A quadrilateral with four equal sides. The angle of tilt can be anything.

49
Q

Three different sets of three lengths that satisfy the Pythagorean Theorem

A
  • (3, 4, 5)
  • (5, 12, 13)
  • (8, 15, 17)
50
Q

Length of a circular arc

A

Arc length/2pir =. Arc angle/360

51
Q

Moribund

A

At the point of death OR in terminal decline; lacking vitality or vigour

52
Q

Keen

A

Sharp or penetrating

53
Q

Uncanny

A

Strange and mysterious

54
Q

Volume of a cube

A

s^3

55
Q

Nb of positive factors a particular integer has

A
  1. Find the prime factorisation of N
  2. Collect the set of exponents of the prime factors
  3. Add one to every member of this set
  4. Find the product of every nb in the set
56
Q

nCr (shortcut)

A

n(n-1) / r

57
Q

Normal distribution; mean; standard deviation

A
  • between mean and 1d: 34.1%

- between 1d and 2d: 13.6%

58
Q

Volume of a cylinder

A

pi * r^2 * h

59
Q

Reflecting a point over y=-x

A

Reversing the coordinates and giving each thr opposite sign

60
Q

Find two numberd’ LCM

A
  1. Find the prime factorisation of the two numbers
  2. Multiply the multiples
    (E.g. 9 and 15 => 335=45)
61
Q

Prime factorisation

A

Expresses the number as a product of prime numbers

62
Q

Cylinder lateral area

A

2 * pi * r * h

63
Q

Cylinder: total area

A

2pirh + 2pi*r^2

64
Q

Amount of solute =

A

(Concentration)*(Volume of Solution)

65
Q

Doubling and halving trick

A

88*25

44*50

22*100 = 2200

Vocabulary (2 decks)

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