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What is the question asking me?

What information do I already have?

What Maths will I be using?

What calculations / working out do I need to do?

How can I check that my answer is correct?

Two companies, Barry's Bricks and Bricks ArUs, deliver bricks. The graph shows the delivery costs of bricks from both companies. Prakash wants Bricks ArUs to deliver some bricks. He lives 2 miles away from Bricks ArUs. (a) Write down the delivery cost.

................................................................................

..............................................................

John needs to have some bricks delivered. He lives 4 miles from Barry's Bricks. He lives 5 miles from Bricks ArUs.(b) Work out the difference between the two delivery costs...............................................................................................................................................

(Total for Question is 4 marks)

A03 Question

What is the difference between the two delivery costs?

Reading information from a graph.

Subtraction.

Barry’s Bricks £50

Bricks R Us £65

£65 - £50 = £15

£50 + £15 = £65

SolutionQuestion Working Answer Mark Notes

(a)

(b) Barry's Bricks £50

Bricks ArUs £6565 − 50

56

15

1

3

B1 for 56 (accept answer in the range 55 to 57)

M1 for 50 or 65 (accept 64 – 66) M1 for 65 – 50 (accept 64-66 for 65) A1 for 15 (accept answer in range 14 to 16)

* Barbara goes on holiday to Prague. The currency in Prague is the Koruna (KC).This graph can be used to convert between £ (pounds) and KC (Koruna).The exchange rate is £1 = 30 KC. Barbara bought some things in London.She saw the same things on sale in Prague.The table shows the cost in £ (pounds) and the cost in KC (Koruna). Barbara thinks the total cost of these things was more in London than in Prague.Is she correct?Give a reason for your answer.You must show all your working.


A03 Question

Is the total cost more in London or in Prague

Converting between currencies,

Addition, Multiplication, Division

London £15 + £34 + £ 26 = £75£1 = 30KC£75 x 30 = 2250KC

Prague450KC + 750KC +810KC = 2010KC

She is wrong, 2050KC is more than 2010KC so cheaper in Prague.

2010KC ÷ 30 = £67

£67 is less than £75

SolutionQuestion Working Answer Mark Notes

London: £15, £34, £26 (£75) → 450, 1020, 780 (2250) KC

Prague: 450, 750, 810 KC (2010KC) → £15, £25, £27 (£67)

£ to KC is ×30;

KC to £ is ÷30.

Yes. Cheaper in Prague (More in London)

5 M1 conversion method (× or ÷ as appropriate) or evidence of use of graph (seen, or implied, by at least lines or evidence of conversion by marks on axes) for at least one figure. M1 (dep) conversion applied to 3 figures or totals (converted figures must be stated, marks on graph insufficient) A1 converted figures shown (all three individual items or totals converted correctly; NB: no tolerance on graph) M1 totalling converted amounts C1 (dep on at least M1) comparison of "totals" and correct conclusion Eg "2250KC">"2010KC", "£75">"£67" so cheaper to buy in Prague.

A03 QuestionThe diagram shows a garden in the shape of a rectangle. All measurements are in metres.The perimeter of the garden is 32 metres.Work out the value of x

. . . . . . . . . . . . . . . . . . . . . . (Total for Question is 4 marks)

Solve an Equation

To calculate perimeter add the lengths of all the sides.

Perimeter = 32cm

Write an expression

Simplify

Use inverse operations

4 + 3x + x + 6 + 4 + 3x + x + 6

Perimeter = 8x + 20

8x + 20 = 32

8x = 12

x = 1.5

Length 4 + (3 x 1.5) = 8.5Width 1.5 + 6 = 7.5

8.5 + 7.5 = 16

16 x 2 = 32

Solution

Question Working Answer Mark Notes 1.5 4 M1 for correct expression for

perimeter eg. 4 + 3x + x + 6 + 4 + 3x + x + 6 oe M1 for forming correct equation eg. 4 + 3x + x + 6 + 4 + 3x + x + 6= 32 oe M1 for 8x = 12 or 12 ÷ 8 A1 for 1.5 oe OR M1 for correct expression for semi-perimeter eg. 4 + 3x + x + 6 oe M1 for forming correct equation eg. 4 + 3x + x + 6 = 16 M1 for 4x = 6 or 6 ÷ 4 A1 for 1.5 oe

A03 QuestionABC is a triangle.

Angle ABC = angle BCA.

The length of side AB is (3x − 5) cm.The length of side AC is (19 − x) cm.The length of side BC is 2x cm.

Work out the perimeter of the triangle.Give your answer as a number of centimetres.


Solve an Equation

Work out the Perimeter

To calculate perimeter add the lengths of all the sides.

Isosceles triangles have two equal sides.

Write an equation

Solve an equation

Substitute the value of x into the equation

3x – 5 = 19 – x4x – 5 = 194x = 24x = 6

If x = 6

3x – 5 = 1319 – x = 13

So x = 619 – 6 = 136 x 2 = 1213 + 13 + 12 = 38cm

Solution

A03 Question* Bill uses his van to deliver parcels.For each parcel Bill delivers there is a fixed charge plus £1.00 for each mile.You can use the graph to find the total cost of having a parcel delivered by Bill. (a) How much is the fixed charge?

£ . . . . . . . . . . . . . . . . . . . . . .

(a) Ed uses a van to deliver parcels.For each parcel Ed delivers it costs £1.50 for each mile.There is no fixed charge.

(b) Compare the cost of having a parcel delivered by Bill with the cost of having a parcel delivered by Ed. (Total for Question is 4 marks)

Compare two delivery costs.

Plot information onto a graph.

Miles 5 10 15 20 25 30 35 40 45 50

Cost £7.50 £15 £22.50 £30 £37.50 £45.00 £52.50 £60 £67.50 £75.00

Ed is cheaper up to 20 miles.Ed and Bill cost the same for 20 miles.Bill is cheaper after 20 miles.

Plot the information from the table onto the graph.The graphs cross at 20 miles.Before 20 miles the graph for Bill is steeper.After 20 miles the graph for Ed is steeper.

SolutionQuestio

nAnswer Notes

(a) (b) 10 Ed is cheaper up to 20 miles, Bill is

cheaper for more than 20 miles

B1 cao M1 for correct line for Ed intersecting at (20,30) ±1 sq tolerance or 10 + x = 1.5x oe C2 (dep on M1) for a correct full statement ft from graph eg. Ed cheaper up to 20 miles and Bill cheaper for more than 20 miles (C1 (dep on M1) for a correct conclusion ft from graph eg. cheaper at 10 miles with Ed ; eg. cheaper at 50 miles with Bill eg. same cost at 20 miles; eg for £5 go further with Bill or A general statement covering short and long distances eg. Ed is cheaper for shorter distances and Bill is cheaper for long distances)OR M1 for correct method to work out Ed's delivery cost for at least 2 values of n miles where 0 < n ≤ 50or for correct method to work out Ed and Bill's delivery cost for n miles where 0 < n ≤ 50 C2 (dep on M1) for 20 miles linked with £30 for Ed and Bill with correct full statement eg. Ed cheaper up to 20 miles and Bill cheaper for more than 20 miles (C1 (dep on M1) for a correct conclusion eg. cheaper at 10 miles with Ed; eg. cheaper at 50 miles with Bill eg. same cost at 20 miles; eg for £5 go further with Bill or a general statement covering short and long distances eg. Ed is cheaper for shorter distances and Bill is cheaper for long distances) SC: B1 for correct full statement seen with no working eg. Ed cheaper up to 20 miles and Bill cheaper for more than 20 miles

QWC Decision and justification should be clear with working clearly presented and attributable

A03 Question There are 300 ml of medicine in a bottle.Mary has to take two 5 ml spoons full of medicine twice a day. Mary has to take the medicine until the bottle is empty.

(a) How many days does Mary have to take the medicine for? . . . . . . . . . . . . . . . . . . . . . . Days

You can work out the amount of medicine, c ml, to give to a child by using the formulac = ma⁄150m is the age of the child, in months.a is an adult dose, in ml.A child is 30 months old.An adult's dose is 40 ml.

(b) Work out the amount of medicine you can give to the child . . . . . . . . . . . . . . . . . . . . . . ml


How many days does Mary take the medicine for?

How much medicine can you give a child?

Substitution into a formula.

MultiplicationDivision

a) 5ml x 2 = 10ml10ml x 2 = 20ml a day300ml ÷ 20 = 15 days

b) (Age of child x adult dose) ÷ 150

(30 x 40) ÷ 1501200 ÷ 150 = 8 ml

a) 20ml a day x 15 days = 300ml

b) 8 x 150 = 1200

Solution

Question Working Answer Mark Notes

(a)

(b)

2 × 5 × 2 = 20 300 ÷ 20 =

c =

15

8

3

2

M2 for 300 ÷ ( 2 × 5 × 2 ) oe

(M1 for 2 × 5 × 2 or 20 seen or 300 ÷ (2 × 5) or 30 seen A1 cao

M1 for

or 1200 seen A1 cao

A03 QuestionThe diagram shows shape A.All the measurements are in centimetres.

(a) Find an expression, in terms of x, for the perimeter of shape A. . . . . . . . . . . . . . . . . . . . . .

A square has the same perimeter as shape A.(b) Find an expression, in terms of x, for the length of one side of this square. . . . . . . . . . . . . . . . . . . . . .


Write an expression for the perimeter.

To calculate perimeter add all the sides together.

Write an expression for the missing sides.

Write an expression for perimeter

Simplify

The missing sides are 2x + 1 and 3x + 3

Perimeter of shape = 16x + 8

Side of square = (16x + 8) ÷ 4Side of square = 4x + 2

4x + 2

4x + 2

4x +

2

4x + 2

4(4x + 2) = 16x + 8

Solution

Question Working Answer Mark Notes (a)

(b)

Missing sides are 2x + 1 and 3x + 3 Perimeter = 5x + 1 + x + 3x + 2x + 3 +2x + 1 + 3x + 3 OR 2(5x + 1) + 2(2x + 3 + x)

16x + 8

4x + 2

3

1

M1 for 5x + 1 –3x or 2x + 3 + x or identifying a missing side as 2x + 1 or 3x + 3(maybe on the diagram) M1 for adding 5 or 6 sides from x, 5x + 1, 3x, 2x + 3, '2x + 1', '3x + 3' where the missing sides are in the form ax ± b (a andb ≠ 0) or 2(5x + 1) + 2(2x + 3 + x) oe

A1 for 16x + 8 oe for unsimplified expression B1 ft for ['2(5x + 1) + 2(2x + 3 + x)'] ÷ 4 or ("16x + 8") ÷ 4 oe where the answer is an algebraic expression in x

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