Maths year 11 book 1 4.5 / 5 MathematicsWork done end of year 10 - start of year 11GCSEEdexcel Created by: NicoleCaitlinCreated on: 28-12-14 16:29 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 1 of 15 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) 2 of 15 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 3 of 15 Distance, Speed, Time Distance = Speed x Time Speed = Distance / Time Time = Distance / Speed D S T 4 of 15 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 5 of 15 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 6 of 15 Surds Practice Questions √32 = √16 x √2 = 4√2 √128 = √64 x √2 = 8√2 √50 = √25 x √2 = 5√2 √7 x √7 = 7 √100 / √10 = √10 √2 + √2 = 2√2 3√5 - 2√5 = √5 √2 + √3 = unsimplifyable 7 of 15 Rationalising the Denominator Practice Questions 1/√2 x √2/√2 = √2/2 11/√18 x √2/√2 = 11√2/6 6/√500 x √3/√3 = 6√3/30 = 2√3/10 = √3/5 4/3√10 x √10/√10 = 4√10/30 = 2√10/15 8 of 15 The Rules of Congruency SSS = side, side, side AAS = angle, angle, side SAS = side, angle, side RHS = right angle, hypotenuse, side 9 of 15 Scale factors Area Scale Factor ASF = (length scale factor)^2 Volume Scale Factor VSF = (length scale factor)^3 10 of 15 Scale factors Area Scale Factor ASF = (length scale factor)^2 Volume Scale Factor VSF = (length scale factor)^3 11 of 15 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 12 of 15 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) 13 of 15 Cones and Spheres - Surface Area Cone Curved surface area = Πrl Total surface area = Πr^2 + Πrl Sphere Total surface area = 4Πr^2 14 of 15 Frustums Definition - cone or pyramid with the top cut off Volume of Frustum whole volume - cut piece volume = frustum volume 15 of 15

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