GCSE MathsGRADE BOOSTER HigherRevision Workshop

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7

%£

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18 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

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:

Write the amount of percentage change on the arrows between the amounts in the boxes shown opposite:

Percentages-13.2Worked Examples

Applying Percentage Change

Calculating Percentage Change

A

B

C

Percentage Change Original Price New PriceItem

Marmite

Ben & Jerry’s

Pot Noodle

Beef Mince

Chicken Thighs

Shower Gel

12.5%

10%

4%

23%

31%

8%

£2.35

£4.00

£1.00

£3.86

£3.25

£1.24

Calculating Percentage ChangeApplying Percentage Change

Increase 146 by 32%There are two methods that can be used:

Method 1:Find 32% of 146

Reverse Percentages:A jumper is reduced in price by 30% and now costs £70. What was the original cost?

Method 2:Using a multiplier – increasing by 32% meansyou are finding 132% overall of 146

A jumper costing £45 is put into the sale andnow costs £28. Find the percentage change.

The jumper has been decreased by 37.78% (2 dp)

32100

x 146 = 46.72

45 − 28 = 17

1745

100 = 37.78% (2 dp) x

700.7

= £100146 x 1.32 = 192.72

30 40

55 50

46.72 + 146 = 192.72

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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.

Finding Profit and Loss Question D

1

2

Shops 4 U have labelled a tea cup they are selling with a “45% off” label. It now costs £6.88.What price was the tea cup selling for originally?

(Total for Question 1 is 2 marks)

(Total for Question 1 is 3 marks)

Clayton bought some comic books in 2012. 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?

Reverse Percentages Exam Questions

Polaroid Mobile Printer Disney mugUSB Powered Desk Fan

Bought £7.40 Bought £125 Bought £27

Sold £10.99 Sold £150.50 Sold £19.25

20 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

Compound Interest QuestionAnn 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?

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 UpYou 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 usedin the calculation.

Percentages-23.3Compound Interest A

Increase by 6%

Decrease by 6%

Increase by 94%

Decrease by 94%

1.94

1.06

0.94

0.06

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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 C0 = 250, calculate: i. C1 ii. C4

(b) Nina is predicting that after k minutes the number of cells will have decreased to less than 70.

Calculate the value of k.

Growth & DecayB

1 Here are the interest rates for two accounts which Clare is considering to invest in.

(Total for Question 1 is 4 marks)

Clare has £1800 to invest for 3 years. Which account gives the best return on her investment?

Exam Question

Account A• 3% per annum compound interest

Account B• 2% per annum compound

interest up to £1500• 5% per annum compound interest

on amounts above £1500

22 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

3.4A

C

You need to know these formulae, which you will not be given in the exam:

Speed, Density and PressureFormulae

Mass

2.5 kg

Volume

Mass

250 g

Volume

0.84 m3

Density

Volume

Mass

g

Volume

375 mm3

Density

46 g/cm3

Mass

Mass

kg

Mass

Density

2 Kg/m3

Density

Density Volume

1.3 m3

Density

4.72 g/cm3

Volume

Volume

4 m3

Density

8 g/m3

1 Luke is traveling to Alton Towers from London which is 150 miles to the nearest 5 miles. Hetravels 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)

Exam Question

distancetime

speed = massvolume

forcearea

density = pressure =

How fast are the planets?

Planet

Neptune

Distance from sun (million km)

Time for 1 orbit of Sun (days)

60,200

Speed(km/h)

Mercury 58 88

Mars 228 86,885

Saturn 1,427 10,760

19,557

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.

Speed, Distance and Time: The Planets B

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!

Density, Mass and Volume

Start

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2

3

The two wooden boxes shown are being examined.

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/m2.

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.

When the cuboid is put onto it’s front face (shaded grey), pressure is put onto it. Find the pressure exertedonto the cuboid.

(Total for Question 2 is 5 marks)

(Total for Question 3 is 5 marks)

Exam Question

Exam Question

The density of the cuboid is 1.2 g/cm3 The mass of the cylinder is 1.89 g

10cm 10cm

6cm8cm

6cm $

$

Practice Questions (a) The pressure of a concrete block which covers 220 cm2 is 150 N/m2. Calculate the force applied

(b) Arlo applies a force of 90 N to a cuboid with 80 cm lengths. Calculate the pressure.

Growth & DecayD

10cm

8cm

6cm

$$ $

$

40cm

$$

24 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

Complete the table below for the statements of proportionality and formule.

Match each graph to the correct relationship, a), b) or c).

Relationship a) 𝑦 y ∞ x b) 𝑦 y ∞ 𝑦 𝑦 c) 𝑦 y ∞

A B C

Direct and Inverse Proportion3.5

Proportionality Statements

Graph Matching

Identify and circle whether the following equations describe a direct proportion relationship, or inverse proportion relationship.

Direct or InverseA

B

C

6x2

y =

y = 5x

y =

a)

b)

c)

5x

Direct Inverse

Direct Inverse

Direct Inverse 2x3

y

y = 12x3

y =

d)

e)

f)

Direct Inverse

Direct Inverse

Direct Inverse

x = 8√

Proportionality in words Statement of proportionality Formula

r is directly proportional to thesquare of y

r is directly proportional to theroot of y

r is inversely proportional tothe cube of y

r is inversely proportional tothe square of y

x√ 1x

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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.

Sally is now asked to answer the following questions, using these worked examples to guide her.

Ordering ActivityD

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 P = kQ 𝑦 𝑦

𝑦 x = 4.5 𝑦 𝑦

y =𝑦 𝑦 9x

y =𝑦 𝑦 kx

2 =𝑦 𝑦 9x

y ∞ 1x

6 =𝑦 𝑦 k1.5

k = 9

y is inversely proportional to x.y = 6 when x = 1.5, find x when y = 2

Practice Questions 1) r𝑟is directly proportional to s. If r = 21 when s = 3

Find a) r when s = 9, b) s when r = 70

26 GCSE MATHS GRADE BOOSTER HIGHER Revision Workshop

Key PointsE

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

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)

Exam Question

Inverse ProportionDirect Proportion

As one variable increases or decreases, the othervariable 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 othervariable increases or decreases in the opposite directionby a constant amount.

If x is inversely proportional to t;

you can write x ∞ 𝑦

to write this as an equation, x =

1t

kt

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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 2017. 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

Session One: Ready Set Go • Calculations with fractions • Sets, Venn diagrams and conditional probability • Frequency tables

Session Four: Shape Up! • Pythagoras’ and trigonometry • Congruence and similarity • Vectors

Session Two: Power Up! • Powers, roots and indices • Standard form • Linear graphs and simulataneous equations

Session Five: No problem – get onand revise! • Problem solving • Revision advice • Exam techniques

Session Three: Factors and Formulae • Substitution into formulae • Quadratics • Rearranging formulae

Programme

grade booster higher workshops

GCSE maths 2017

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GCSE Maths Grade Booster Higher – exam workshopIntensive One-Day Exam Support for Year 11 GCSE Students

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