Variation - By Lisa

Direct variation or direct proportional for inverse.
Given thta y varies directly as x or x varies as y:
y [fish sign] OR y= kx; k is constant

Inverse or indirect variation
y [fish sign] 1/x
y =k/x
If y gets bigger, x gets smaller
If y gets smaller, x gets bigger

EXAMPLES

y=k/x
If x is trebled, y/3 [y=k/3x, move 3 onto other side so dat u get k/x : 3y=k/x]
If x increased by 250%, y * 2/7. [y=k/(7/2)x, move 7/2 on otha side, flip over]

y=k/x^2
x * 3, y/9
x *75%, y*16
y*9, x/3

y=1/[square root of x]
x=3^2, y=12. x=? if y=15

12=k/3
k=36
15=36/[square root of] x
[square root of]x= 36/15
x=36^2/15^2
x=1296/225=5.76

Answers

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Really Useful Maths Notes - By Lisa

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Math’s Topics By Dilshan seneviratna

Math’s Topics By Dilshan seneviratna



NOTHING ELSE WILL BE IN TEST (at least that’s what our teacher said) (no guarantees)

1. Algebra

-expansion
-factorisation
-binomial products
-trinomials
-perfect squares
-difference of perfect squares
-factorisation in groups

1. Consumer Arithmetic

-salary
-wage
-commission
-overtime
-income tax
-best buy
-purchases in instalments
-successive discounts
-NO COMPOUND INTEREST
-simple interest
-Medicare levy

1. Geometry

-angles
-triangles
-Quadrilaterals – all properties
-polygon
-all stuff on angles
-NO SIMILARITY
-proofs
-congruency
-triangle

1. Surds + Indices

-standard notation
-everything, addition, multiplication etc.

1. Graphs in practical situations

-All types of graphs – pie, step, travel etc.
-Rates – filling tanks etc
-variation+inverse variation

1. Equations

-All linear equations
-simultaneous
-changing the subject
-problem solving
-absolute value
-surdic equations

1. Quadratic equations

-Solve by: factorising, completing square, formulae
-How many solutions? i.e. square root b squared minus four a c
-Remember exact value is in surd form

1. Graphing – with asymptotes

-linear
-parabola
-cubic
-exponential
-hyperbole
-circle
-NO SEMI CIRCLES
-absolute value

1. Co – ordinate Geometry

-distance
-midpoint
-gradient
-straight line
-parallel/perpendicular
-lines parallel to x/y axis

1. Trigonometry

-sin cos tan only
-ONLY IN FIRST QUADRANT OF UNIT CIRCLE I.E up to 90 degrees
-bearings
-angles of elevations/depression
-reciprocal ratios
-complimentary ratios
-relationships between trig ratios
- IDENTITIES ARE EXTENTION – NOT IN TEST
-exact values
-Pythagoras
-exact values are only in first quadrant
- No ASTC

1. Measurement

–all units eg. cm, m, km
-prefixes
-sig figs
-rates i.e. Km/h
-perimeter/are in circles
-volume
-surface area of prisms, cylinder, sphere etc.

1. Basic Statistics

-nothing advanced
-NO STANDARD DEVIATION

Thanks a heap for your contributions Dilshan!!!

EZ notes - Maths

Hey guys, this is a new section of the site and was started because of Dilshan, thanks heaps dilshan!!!