Maths year 11 book 1

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Mutually Exclusive Events/Conditional Probabaility

Mutually Exclusive Events

Two events are mutually exclusive when they cannot occur at the same time

Conditional Probability

Two events are independent if they have no effect whatsoever on each other

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The Equation of a circle

Recipricol - y=1/x

Expodential - y=a^x

X-cubed - y=x^3/ y=-x^3+...

Negative recipricol - y=-1/x

Negative expodential - y=a^-x

General equation - y^2+x^2=r^2 (r=radius)

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Volume and Capacity Units/Fraction hours

1m^3 = 1,000,000 cm^3

1l = 1000cm^3

30 mins = 1/2 hour 15 mins = 1/4 hour

45 mins = 3/4 hour 20 mins = 1/3 hour

40 mins = 2/3 hour 10 mins = 1/6hour

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Distance, Speed, Time

Distance = Speed x Time

Speed = Distance / Time

Time = Distance / Speed

    D

S T

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Upper and Lower bounds

Practice Question

The length of a rectangle is measured as 8.3cm to the nearest mm and its width is 3.6cm to the mearest mm

Upper bound (length) = 8.35 cm

Lower bound (length) = 8.25 cm

Upper bound (width) = 3.65 cm

Lower bound (width) = 3.55 cm

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Recurring Decimals to Fractions

Practice Question 

0.3 recurring as a fraction

x = 0.33333... (x10)

10x = 3.33333...

10x - x = 9x = 3

x = 3/9

x = 1/3

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Surds

Practice Questions

  1. √32 = √16 x √2 = 4√2
  2. √128 = √64 x √2 = 8√2
  3. √50 = √25 x √2 = 5√2
  4. √7 x √7 = 7
  5. √100 / √10 = √10
  6. √2 + √2 = 2√2
  7. 3√5 - 2√5 = √5
  8. √2 + √3 = unsimplifyable
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Rationalising the Denominator

Practice Questions 

  1. 1/√2 x √2/√2 = √2/2
  2. 11/√18 x √2/√2 = 11√2/6
  3. 6/√500 x √3/√3 = 6√3/30 = 2√3/10 = √3/5
  4. 4/3√10 x √10/√10 = 4√10/30 = 2√10/15
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The Rules of Congruency

SSS = side, side, side

AAS = angle, angle, side

SAS = side, angle, side

RHS = right angle, hypotenuse, side

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Scale factors

Area Scale Factor

ASF = (length scale factor)^2

Volume Scale Factor

VSF = (length scale factor)^3

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Scale factors

Area Scale Factor

ASF = (length scale factor)^2

Volume Scale Factor

VSF = (length scale factor)^3

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Pyramids and Cones

Equation

(Area of base x height) / 3

Great Pyramid of Giza (Practice question)

755 x 755 = 570,025

570,025 + 480 = 273,612,000

273,612,000 / 3 = 91,204,000 cubic ft

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Volume of Spheres and Complex Shapes/Area of a Cyl

Equation

Volume of a sphere = 4/3Πr^3

Area of a Cylinder

Πr^2 + Πr^2  + 2Πrh

2Πr^2 + 2Πrh

2Πr (r+h)

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Cones and Spheres - Surface Area

Cone

Curved surface area Πrl

Total surface area Πr^2 + Πrl

Sphere

Total surface area = 4Πr^2

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Frustums

Definition - cone or pyramid with the top cut off

Volume of Frustum

whole volume - cut piece volume = frustum volume


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