GCSE Unit 11 Notes & Examples PDF

Percentages - Repeated 100% + 10% = What is the multiplier to increase by 10%? 110% To turn 110% into 1.10 a decimal divide...

Percentages - Repeated 100% + 10% = What is the multiplier to increase by 10%? 110% To turn 110% into 1.10 a decimal divide by 100 100% + 12% = What is the multiplier to increase by 12%? 112% To turn 112% into 1.12 a decimal divide by 100 If you increase an amount by 10% then another 12%, what is the overall Multiply the two percentage increase? percentage multipliers to help find the overall 1.10 x 1.12 = 1.232 percentage 123.2% increase. Percentages - Compounds Compound Interest = Amount x Compound Measures – What is it? Compound measure are where the units are made up of two measurements.  Compound Measure - Speed Speed = Distance ÷ Time Time = Distance ÷ Speed Distance = Speed x Time Convert hours and minutes to hours. 45 minutes = 0.75 hour 12 minutes = 0.2 hour A plane travels 2000km/hour in 15 minutes. How far does the plane travel? Distance = Speed x Time 15 mins = 0.25 hours  Compound Measure - Density Density is the amount of mass in a volume. It tells you how tightly matter is packed. Density = Mass ÷ Volume Volume = Mass ÷ Density Mass = Density x Volume A piece of metal weighs 40g and has a volume of 4cm3. Density = Mass ÷ Volume What is it’s density? D = M ÷ V = 40 ÷ 4 Density = grams ÷ cm3 D = 10 g/cm3 A block of ice measures 5cm by 2cm by 4cm. Given that it’s density is 6 g/cm3, Find the volume of the cube calculate it’s mass. first V = 2 x 4 x 5 = 40 cm3 Mass = Density x Volume M = D x V = 6 x 40  Compound Measure - Pressure Pressure = Force ÷ Area Area = Force ÷ Pressure Force = Pressure x Area N = Newtons Examples of Pressure units: N/cm2 ,N/m2 , N/km2 This is the units for force. A force of 10 Newtons is applied to an area of 20cm2. How much pressure is produced? State you units. Force = N 1 Area = cm2 0 Therefore Pressure = 20 Pressure N/cm2 = 10 ÷ 20 = 0.5 2 Compound Measure – Converting Measurements Convert 8km/h to mph 1 km = 1.6 miles Convert 18km/h to km/s 1 hour = 3600 seconds Convert 70mph to m/s  What is Direct Proportion? Two sets of values are directly proportional if they have a common multiplier. xµy To be in direct proportion there must be a common multiplier. Direct proportion graphs must - be a straight a line - start at (0,0)  Direct Proportion – without powers yµx y = kx where k is the multiplier y is in direct proportion x y and x are directly proportional. Find a formula for y in terms of y = kx x. Given that when x = 6, y = 18 To find the multiplier you need to do d and t are directly proportional. Find a formula for t in terms of d. Given that d = y = kx 2 when t = 8 To find the multiplier you need to do  Direct Proportion – with powers k is the common multiplier Write an equation for y in terms of x y = kx2 Given that when x = 2, y = 16 and that y is proportional x2 16 = k(2)2 16 = 4k k=4 Don’t forget to write x2 in your final equation and not just x Write an equation for g in terms of f f=k Given that when f = 9, g = 30 and that g is proportional to square root of f. 30 =k 30  Inverse Proportion Two sets of values are said to be inversely or proportional if, one value increases as the other k = common multiplier = yx decreases. y and x are inversely proportional. Write an equation for y in terms of x given that when x = 4, y = 25 k = yx k = 4(25) = 100 Don’t forget to write the value back in the equation y and x are inversely proportional. Write an equation for y in terms of x given that when x = 4, y = 25 A follow up question could be to find y when x is 2.