Maths revision

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  • Created by: Robster
  • Created on: 08-02-16 16:30

Upper and lower bounds (P3)

With upper and lower bounds you have a chance to get a question like this:

a) Work out the greatest length of this rectangle?

Area = 379cm2 rounded to the nearest cm2

width = 13.4 cm rounded to the nearest 1dp

So you would have to do the UB of the area divided by the LB of the width.

UB: of area: 379.5

LB: of width: 13.35

378.5 divide 13.35 = 30.7

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squares and cubes

Sometimes you might get a factions such as:

(3/4)squared = 3squared and 4squared... = 9/16

Or

(3/5)cubed = 3cubed and 5cubed... = 27/125

Formula:

Cubed = b x b x b

Squared = b x b 

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Converting

You also have to convert various numbers,

To convert km into metres you have to (x 1000)

To change hoursx into seconds you have to (divide 3600)

To change hours to minutes you have to (divide 600)

a) Convert 72km/h to m/s.

72km = km (x 1000) = 72,000.

72,000 m/h = h into seconds (divide 3600) = 20

Put the units on = 20 m/s

In the paper the units should already be there but incase they arn't make sure you write them.

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Upper and lower bounds (P1)

Upper and lower bounds can be confusing but when you understand it, it is the most easiest thing you might get asked to do...

a) Write down the upper and lower bounds for each measurement.

A swimming pool is 25m long, to the nearest metre.

The nearest metre is the key part because to find an upper and lower bound all you have to do is half the rounded to number and add or minus the number of the origanal number. 1/2 of the nearest number is 0.5 so.

LB: 24.5   UB: 25.5

A glass contains 170ml of milk, to the nearest 10ml.

LB: 165ml  UB: 175ml

Elena's reaction time is 0.20 seconds, correct to 2 dp (think of 1, 1/2 1 = 0.5 :D)

LB: 0.15  UB: 0.25

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DMV Triangles

DMV triangles are simula to DST triangles. The difference is the letters and the triangle order:

M = Mass

D = Density

V = Volume

The M goes at the top of the triangle and the D and V goes at the bottom.

M divide D   M divide V  M x D

a) 250ml of cooking oil has a mass of 230g. Calculate the density of coking oil in g/cm3?

230 divide 250 = 0.92    M divide V = D

Answer is: 0.92g/cm3

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DST triangles

There is a triangle which is D = Distance S = Speed T = Time

in the triangle it is D in the top and s and t at the bottom which means:

D divide T

D divide S

T x S 

a) A car travels 200km in 5 hours. Work out the average speed.

200km is the D = Distance and 5 hours is the T = Time

200 divide 5 = 40. The units is km and hours so = 40km/h

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Standard Form

Standard form makes numbers easier to understand and read. The number has to be between 1 - 10 for it to work. If you are working with decimal numbers the power above the ten has to be -ve whereas if the number is a whole number then the power above the 10 is +ve.

a) 215,000,000: 2.15 x 10

b) 234,500: 2.345 x 10 

C) 0.00054: 5.4 x 10 -4

d) 0.1234: 1.234 x 10 -1

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squares and cubes

Sometimes you might get a factions such as:

(3/4)squared = 3squared and 4squared... = 9/16

Or

(3/5)cubed = 3cubed and 5cubed... = 27/125

Formula:

Cubed = b x b x b

Squared = b x b 

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Surds

You can get many different questions types including surds: Area of a circle, Area, Simplifying surds. Surds are numbers which are in root form but can't be rooted.

This will cover Hypotenuse surds and Simplifying surds.

Simplifying surds:

a) root 20 = root 4 root 5 = root 4 is not a surd therefore can be put into 2 = 2 root 5. This is your answer = 2 root 5

b) root 48 = root 4 root 12 = 2 root 12 = root 12 can be simplified into root 4 root 3 which can turned into 2 x 2 root 3 which then gives us the answer of = 4 root 3.

Hypotenuse surds:

a) one side is 5 the other is 3 root 10 = in hypotenuse you have to square the sides which would be 3 x 3 x root 10 x root 10. = 90 and 5 x 5 is root 25 = then add the numbers = root 115/

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Reciprocals

When it comes to doing reciprocals the easiest thing to do is just flip the fraction round: 

a) 8/5  = 5/8                                b) 6/2 = 2/6

When it comes to whole numbers no fractions just a plain number put a 1 ontop of it:

a) 8 = 1/8                                    b) 9 = 1/9

When you have mixed numbers you have to turn the mixed fraction into a improper fraction:

a) 3 1/2 =  3 x 2 + 1 = 7 = 7/2  =  2/7 is the reciprocal.

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Harder standard form

Sometimes you might get standard form questions like:

a) (1.2 x 10 2) x (3 x 10 3)   1.2 x 3 = 3.6   2 + 3 = 5 = 3.6 x 10 5

b) 8 x 10 5

   2 x 10 3   = 8/2 = 4   5 - 3 = 2             = 4 x 10

c) 5.1 x 10 8 + 1.45 x 10 8  = 6.55 x 10 8

5.1 + 1.45 = 6.55    

d) 9.6 x 10 -7 - 6.3 x 10 -7  = 3.3 x 10 -7

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Fractional powers and roots

Squares, cubes, square roots and cube roots can be written in a difficult way. In way you might not undrstand:

a) 8 2/3 this means cube root and square the answer. The denominator is the root and the numerator is the square or cube. = 8 cube rooted is 2 and square is 4.

b) 9/100 3/2 = 100 square rooted = 10   9 square rooted = 3 and cube it all... 27/100

c) 49 -1/2 = 1/49 qhen you have a - fraction you have to make it a reciprocal and add a one or flip the fraction round. So 1/49 = square root = 1/7 which is 7

d) 64/125 -1/3 = 125/64 1/3 = cube root it = 5/4

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