GCSE Maths GRADE BOOSTER Higher

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1 k 7 % GCSE Maths GRADE BOOSTER Higher Revision Workshop Student Name: Note the resource download link for this workshop:

2 3.2 A Percentages-1 Worked Examples Applying Percentage Change Increase 146 by 32% There are two methods that can be used: Method 1: Find 32% of x 146 = = Method 2: Using a multiplier increasing by 32% means you are finding 132% overall of x 1.32 = Calculating Percentage Change A jumper costing 45 is put into the sale and now costs 28. Find the percentage change = x 100 = 37.78% (2 dp) 45 The jumper has been decreased by 37.78% (2 dp) Reverse Percentages: A jumper is reduced in price by 30% and now costs 70. What was the original cost? = 100 B Applying Percentage Change Following the announcement of Brexit, George the shopkeeper was told there would be a change to the price of some of the items he sells. Calculate the new prices for the following items in George s shop: Item Marmite Ben & Jerry s Pot Noodle Beef Mince Chicken Thighs Shower Gel Percentage Change Original Price New Price 12.5% % % % % % 1.24 C Calculating Percentage Change Write the amount of percentage change on the arrows between the amounts in the boxes shown opposite: GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

3 D Finding Profit and Loss Question Frankie buys and sells items on ebay. She often makes a profit, but sometimes she make a loss. Calculate the total percentage profit/loss that she makes from the following items, giving your answers to 2 decimal places. USB Powered Desk Fan Polaroid Mobile Printer Disney mug Bought 7.40 Bought 125 Bought 27 Sold Sold Sold Reverse Percentages Exam Questions 1 Shops 4 U have labelled a tea cup they are selling with a 45% off label. It now costs What price was the tea cup selling for originally? (Total for Question 1 is 2 marks) 2 Clayton bought some comic books in By 2017 these books had increased in value by 15% and are now worth 230. How much did Clayton spend on comic books in 2012? (Total for Question 1 is 3 marks) 19

4 3.3 Percentages-2 Compound Interest A Compound interest is one way that interest can be calculated, and is a way of calculating repeated percentage change over time. Make sure you also know how to calculate simple interest, as you may be asked to work this out too! Multiplier Match Up You need to know how multipliers work for compound interest. Here s a quick activity to help remind you. Match up the description to the multiplier that would be used in the calculation. Increase by 6% Decrease by 6% Increase by 94% Decrease by 94% Compound Interest Question Ann invests 65,000 at a compound interest rate of 6%. (a) Work out how much she has in her account at the end of: i. 3 years ii. 15 years iii. 6 months (b) How many years until she has 97,000? 20 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

5 B Growth & Decay Another way that repeated percentage change can be applied involves growth and decay. You may be given a model to work from, and asked questions based on this model. During an experiment, Nina discovers the rate at which cells are decreasing in her sample is Cn+1 = 0.81 Cn where Cn is the number of cells after n minutes. (a) If C 0 = 250, calculate: i. C1 ii. C 4 (b) Nina is predicting that after k minutes the number of cells will have decreased to less than 70. Calculate the value of k. Exam Question 1 Here are the interest rates for two accounts which Clare is considering to invest in. Account A 3% per annum compound interest Account B 2% per annum compound interest up to % per annum compound interest on amounts above 1500 Clare has 1800 to invest for 3 years. Which account gives the best return on her investment? (Total for Question 1 is 4 marks) 21

6 3.4 A Speed, and Pressure Formulae You need to know these formulae, which you will not be given in the exam: distance mass force speed = density = pressure = time volume area B Speed, Distance and Time: The Planets Complete the table below by calculating speed, distance and time for the selected planets, giving your answers to a sensible degree of accuracy. Assume that the orbit of each planet is circular around the sun. Exam Question How fast are the planets? Planet Distance from sun (million km) Time for 1 orbit of Sun (days) Speed (km/h) Mercury Mars ,885 Saturn 1,427 10,760 Neptune 60,200 19,557 1 Luke is traveling to Alton Towers from London which is 150 miles to the nearest 5 miles. He travels at an average speed of 65 mph, correct to the nearest 5 mph. Will he arrive at the opening time of 10 am if he leaves London at 7:50 am? (Total for Question 2 is 2 marks) C, Mass and Mass 2.5 kg 375 mm 3 Mass 4.72 g/cm 3 Make your way around the circuit, using the information in the previous 2 boxes to fill in the missing values (give all answers 2 significant figures). Don't forget to write in your units! 46 g/cm 3 Mass g 4 m 3 2 Kg/m 3 Mass 0.84 m 3 Mass kg Mass 250 g 1.3 m 3 Start 8 g/m 3 22 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

7 Exam Question 2 The two wooden boxes shown are being examined. 8cm 6cm 6cm 10cm The density of the cuboid is 1.2 g/cm 3 10cm The mass of the cylinder is 1.89 g Becki says that the cuboid has a higher density than the cylinder. John says that the cylinder weighs more. Who is correct? Show your working clearly and make sure you justify your answer. (Total for Question 2 is 5 marks) D Exam Question 3 Growth & Decay Practice Questions (a) The pressure of a concrete block which covers 220 cm 2 is 150 N/m 2. Calculate the force applied (b) Arlo applies a force of 90 N to a cuboid with 80 cm lengths. Calculate the pressure. The volume of a cube, with sides of length 40 cm, and the cuboid shown are the same. The density of the cuboid is 10 g/m 2. 8cm 40cm 10cm 6cm When the cuboid is put onto it s front face (shaded grey), pressure is put onto it. Find the pressure exerted onto the cuboid. (Total for Question 3 is 5 marks) 23

8 3.5 Direct and Inverse Proportion A Direct or Inverse Identify and circle whether the following equations describe a direct proportion relationship, or inverse proportion relationship. 5 a) y = Direct Inverse d) y Direct Inverse x x = 8 b) y = 5x Direct Inverse e) y = 12x 3 Direct Inverse c) y = 6 x 2 Direct Inverse f) y = 2x 3 Direct Inverse B Proportionality Statements Complete the table below for the statements of proportionality and formule. Proportionality in words Statement of proportionality Formula r is directly proportional to the square of y r is directly proportional to the root of y r is inversely proportional to the cube of y r is inversely proportional to the square of y C Graph Matching Match each graph to the correct relationship, a), b) or c). A B C Relationship a) y y x b) y y yy c) y x y 1 x 24 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

9 D Ordering Activity Sally has brought home an ordering activity she completed in class, but it has become unordered on the way home! Help her to put these into the correct order. y P = kq y y P and Q are directly proportional. If P = 30 when Q = 6, find P when Q = 8 y P = 5Q y y y 30 = k x 6y y y P = 5 x 8y y P Qy y k = 5 y y y P = 40 y y y x = 4.5 y y y =y y 9 x 6 =y y k 1.5 k = 9 y is inversely proportional to x. y = 6 when x = 1.5, find x when y = 2 y =y y k x 2 =y y 9 x y 1 x Sally is now asked to answer the following questions, using these worked examples to guide her. Practice Questions 1) rris directly proportional to s. If r = 21 when s = 3 Find a) r when s = 9, b) s when r =

10 2) yris inversely proportional to the square of x. if y = 4 when x = 2 Find a) y when x = 10, b) x when y = 20 Exam Question 1 The time, t, taken in minutes for passengers to board a train is inversely proportional to the square of the number of train carriages, c, available. It takes 12 minutes for passengers to board the train when there are 10 carriages available. Work out how long (to the nearest minute) it will take for all passengers to board when there are 14 carriages available. (Total for Question 1 is 3 marks) E Key Points Direct Proportion Inverse Proportion As one variable increases or decreases, the other variable increases or decreases in the same direction by a constant amount. If x is directly proportional to t; you can write x t y to write this as an equation, x = kt y y As one variable increases or decreases, the other variable increases or decreases in the opposite directionby a constant amount. If x is inversely proportional to t; 1 you can write x y t k to write this as an equation, x = t 26 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

GCSE maths 2017 grade booster higher workshops Designed to build confidence in the essential assessment skills and provide a clear focus for students on how to make the most effective use of their

11 GCSE maths 2017 grade booster higher workshops Designed to build confidence in the essential assessment skills and provide a clear focus for students on how to make the most effective use of their remaining revision time for the first GCSE Maths (9-1) exams in May and June The Workshops are for students aiming for a grade 7 or 8 and for those predicted a grade 6 who might reach a 7, who need an extra push to step-up to the next grade, with the added benefit of helping schools achieve the new progress measures. The GCSE Maths Grade Booster Workshop (Higher) combines: Three and a half hours intensive large-group tuition by our experienced GCSE Maths presenter team A workshop booklet containing all the session content, extension activities and other essential revision materials designed for students in the final weeks before their GCSE Maths exams Guidance on how to refine and sharpen exam technique to deliver marginal gains in exam performance, including how to respond to questions involving reasoning and problem solving Programme Session One: Ready Set Go Calculations with fractions Sets, Venn diagrams and conditional probability Frequency tables Session Two: Power Up! Powers, roots and indices Standard form Linear graphs and simulataneous equations Session Three: Factors and Formulae Substitution into formulae Quadratics Rearranging formulae Session Four: Shape Up! Pythagoras and trigonometry Congruence and similarity Vectors Session Five: No problem get on and revise! Problem solving Revision advice Exam techniques 2s7 17

12 GCSE Maths Grade Booster Higher exam workshop Intensive One-Day Exam Support for Year 11 GCSE Students BOOKING FORM Important notice: Only confirmed bookings are accepted. Screen capacity at each workshop is fixed and we allocate places on a first-confirmed basis only. Teacher places are FREE if accompanying groups of 5 or more students. Each student place is 25 + VAT. Teachers may not attend on their own. Places required: Course Location / Date London / Vue Cinema - Westfield Stratford London / Vue Cinema - Westfield Stratford Manchester / Vue Cinema - Lowry (Salford) Birmingham / Vue Cinema - Star City Date Students Staff 20th April st April nd May th May 2017 Invoice / Order Details Purchase Order Ref Booking Contact Name / Position School or College Name Address Town / City Contact: Address / Phone Postcode: Phone: To order your places on this course Phone: tutor2u on (choose Option 1) Fax: this form to events@tutor2u.net Post to: tutor2u, Coach House, 214 High Street, Boston Spa, LS23 6AD Order online at:

Applications of Mathematics

Write your name here Surname Other names Edexcel GCSE Centre Number Candidate Number Applications of Mathematics Unit 1: Applications 1 For Approved Pilot Centres ONLY Higher Tier Tuesday 11 June 2013