Practice Papers Set G Higher Tier QWC · 04/04/2014 · Answer all questions. ... Mr Weaver’s garden is in the shape of a rectangle. In the garden there is a patio in the shape

Instructions

Use black ink or ball-point pen.

Fill in the boxes at the top of this page with your name,

centre number and candidate number.

Answer all questions.

Answer the questions in the spaces provided – there may be more space than you need.

Calculators must not be used.

Information

There are 27 questions on this paper; the total mark is 100

The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

All questions labelled with an asterisk (*) and are ones where the quality of your written communication will be assessed.

Advice

Read each question carefully before you start to answer it.

Keep an eye on the time.

Try to answer every question.

Check your answers if you have time at the end.

Practice Papers Set G Higher Tier – QWC

1MA0 / 2MB01 1 hour 45 minutes

2

GCSE Mathematics (Linear) 1MA0

Formulae: Higher Tier

You must not write on this formulae page.

Anything you write on this formulae page will gain NO credit.

Volume of prism = area of cross section × length Area of trapezium = 21 (a + b)h

Volume of sphere 34 πr3 Volume of cone

31 πr2h

Surface area of sphere = 4πr2 Curved surface area of cone = πrl

In any triangle ABC The Quadratic Equation

The solutions of ax2+ bx + c = 0

where a ≠ 0, are given by

x = a

acbb

2

)4( 2

Sine Rule C

c

B

b

A

a

sinsinsin

Cosine Rule a2 = b2+ c2– 2bc cos A

Area of triangle = 21 ab sin C

3

Answer ALL TWENTY SEVEN questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

*1. 225 grams of flour are needed to make 9 cakes.

Marian wants to make 20 of these cakes.

She has 475 grams of flour.

Does Marian have enough flour to make 20 cakes?

You must show all your working.

(Total for Question 1 is 3 marks)

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4

*2. Here is a list of ingredients for making 18 mince pies.

Ingredients for 18 mince pies

225 g of butter

350 g of flour

100 g of sugar

280 g of mincemeat

1 egg

Elaine wants to make 45 mince pies.

Elaine has

1 kg of butter

1 kg of flour

500 g of sugar

600 g of mincemeat

6 eggs

Does Elaine have enough of each ingredient to make 45 mince pies?

You must show clearly how you got your answer.


___________________________________________________________________________

5

*3. A company sells boxes to factories.

Fred buys boxes.

The boxes are sold in packs of 1000

Each pack costs £193.86

Fred orders 3 packs of boxes.

He gets a discount on his total order.

The table shows the discount he will get.

Total Order Discount

£100 – £300 5%

£301 – £400 10%

£401 and above 15%

Work out the total cost of the order after the discount.

You must show your working.


___________________________________________________________________________

6

*4. Mr Weaver’s garden is in the shape of a rectangle.

In the garden

there is a patio in the shape of a rectangle

and two ponds in the shape of circles with diameter 3.8 m.

The rest of the garden is grass.

Mr Weaver is going to spread fertiliser over all the grass.

One box of fertiliser will cover 25 m2 of grass.

How many boxes of fertiliser does Mr Weaver need?



___________________________________________________________________________

7

*5. Potatoes cost £9 for a 12.5 kg bag at a farm shop.

The same type of potatoes cost £1.83 for a 2.5 kg bag at a supermarket.

Where are the potatoes the better value, at the farm shop or at the supermarket?



___________________________________________________________________________

8

*6.

ABCD is a parallelogram.

Angle ADB = 38.

Angle BEC = 41.

Angle DAB = 120.

Calculate the size of angle x.

You must give reasons for your answer.


___________________________________________________________________________

9

*7. Peter goes for a walk.

He walks 15 miles in 6 hours.

5 miles = 8 km.

Sunita says that Peter walked more than 20 km.

Is Sunita right?



_______________________________________________________________________

10

*8. Plants are sold in three different sizes of tray.

A small tray of 30 plants costs £6.50.

A medium tray of 40 plants costs £8.95.

A large tray of 50 plants costs £10.99.

Kaz wants to buy the tray of plants that is the best value for money.

Which size tray of plants should she buy?



___________________________________________________________________________

11

*9.

PRS and TWY are parallel straight lines.

QRWZ is a straight line.

Work out the value of x.

Give reasons for your answer.


___________________________________________________________________________

12

*10. The table gives some information about student attendance at a school on Friday.

Number of students

Year Present Absent Total

Year 7 192 16 208

Year 8 219 22 241

Year 9 234 28 262

Year 10 233 28 261

Year 11 214 24 238

The school has a target of 94% of students being present each day.

Did the school meet its target on Friday?


___________________________________________________________________________

13

*11. In the UK, petrol costs £1.24 per litre.

In the USA, petrol costs 3.15 dollars per US gallon.

1 US gallon = 3.79 litres

£1 = 1.47 dollars

Is petrol cheaper in the UK or in the USA?


___________________________________________________________________________

14

*12. Saphia is organising a conference.

People at the conference will sit at circular tables.

Each table has a diameter of 140 cm.

Each person needs around 60 cm around the circumference of the table.

There are 12 of these tables in the conference room.

A total of 90 people will be at the conference.

Are there enough tables in the conference room?


___________________________________________________________________________

15

*13. Axel and Lethna are driving along a motorway.

They see a road sign.

The road sign shows the distance to Junction 8

It also shows the average time drivers will take to get to Junction 8

To Junction 8

30 miles

26 minutes

The speed limit on the motorway is 70 mph.

Lethna says,

‘We will have to drive faster than the speed limit to go 30 miles in 26 minutes.’

Is Lethna right?

You must show how you got your answer.


___________________________________________________________________________

16

*14. (i) Factorise 2t2 + 5t + 2

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

(ii) t is a positive whole number.

The expression 2t2 + 5t + 2 can never have a value that is a prime number.

Explain why.

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

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

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


___________________________________________________________________________

17

*15. Viv wants to invest £2000 for 2 years in the same bank.

The International Bank

Compound Interest

4% for the first year

1% for each extra year

The Friendly Bank

Compound Interest

5% for the first year

0.5% for each extra year

At the end of 2 years, Viv wants to have as much money as possible.

Which bank should she invest her £2000 in?


___________________________________________________________________________

18

*16. Peter has £20 000 to invest in a savings account for 2 years.

He finds information about two savings accounts.

Peter wants to have as much money as possible in his savings account at the end of 2 years.

Which of these savings accounts should he choose?


___________________________________________________________________________

19

*17. Henry is thinking about having a water meter.

These are the two ways he can pay for the water he uses.

Henry uses an average of 180 litres of water each day.

Henry wants to pay as little as possible for the water he uses.

Should Henry have a water meter?


___________________________________________________________________________

20

*18.

S and T are points on the circumference of a circle, centre O.

PT is a tangent to the circle.

SOP is a straight line.

Angle OPT = 32°.

Work out the size of the angle marked x.

Give reasons for your answer.

..............................................°


___________________________________________________________________________

21

*19. Katie travels to work by train.

The cost of her weekly train ticket increases by 12.5% to £225.

Katie’s weekly pay increases by 5% to £535.50.

Compare the increase in the amount of money Katie has to pay for her weekly train ticket

with the increase in her weekly pay.


___________________________________________________________________________

22

*20. The diagram shows a ladder leaning against a vertical wall.

The ladder stands on horizontal ground.

The length of the ladder is 6 m.

The bottom of the ladder is 2.25 m from the bottom of the wall.

A ladder is safe to use when the angle marked y is about 75°.

Is the ladder safe to use?



___________________________________________________________________________

23

*21. Prove algebraically that

(2n + 1)2 – (2n + 1) is an even number

for all positive integer values of n.


___________________________________________________________________________

24

*22. Shabeen has a biased coin.

The probability that the coin will land on heads is 0.6.

Shabeen is going to throw the coin 3 times.

She says the probability that the coin will land on tails 3 times is less than 0.1.

Is Shabeen correct?



___________________________________________________________________________

25

*23. A road is 4530 m long, correct to the nearest 10 metres.

Kirsty drove along the road in 205 seconds, correct to the nearest 5 seconds.

The average speed limit for the road is 80 km/h.

Could Kirsty’s average speed have been greater than 80 km/h?



___________________________________________________________________________

26

*24. s

mt

s = 3.47 correct to 2 decimal places.

t = 8.132 correct to 3 decimal places.

By considering bounds, work out the value of m to a suitable degree of accuracy.

You must show all your working and give a reason for your final answer.


_______________________________________________________________________

27

*25. The diagram shows the triangle PQR.

PQ = x cm

PR = 2x cm

Angle QPR = 30°

The area of triangle PQR = A cm2

Show that x = A2


___________________________________________________________________________

28

*26. A and B are straight lines.

Line A has equation 2y = 3x + 8.

Line B goes through the points (–1, 2) and (2, 8).

Do lines A and B intersect?



___________________________________________________________________________

29

*27.

AOC and BOD are diameters of a circle, centre O.

Prove that triangle ABD and triangle DCA are congruent.


TOTAL FOR PAPER IS 103 MARKS

1MA0 2H– Practice Paper (Set G) QWC

Question Working Answer Mark Notes *1 No +

comparison

3 M1 for a correct start to the process

eg. or or or

M1 for completion of a fully correct method that will lead to an appropriate

comparison

C1 (dep on M2) for a correct statement with conclusion with 500 g

or 25g more needed

or 19 cakes

or 25g and 23.75g

SC :If no working then B1 for a correct statement with correct figures and units

*2 Not enough

mincemeat

since

600<700

OR

Only able to

make 38

mince pies

since

insufficient

mincemeat

4

M1 for 45 ÷ 18 (= 2.5)

M1 for 2.5 used as factor or divisor

A1 for ingredients as 562.5 and 875 and 250 and 700 and 2.5 (accept 2 or 3)

OR for availables as 400, 400, 200 240, 2.4 (accept 2 or 3)

C1 ft (dep on at least M1) for identifying and stating which ingredient is

insufficient for the recipe (with some supportive evidence)

OR

M1 for a correct method to determine the number of pies one ingredient could

produce

M1 for a correct method to determine the number of pies all ingredient could

produce

A1 for 80 and 51 and 90 and 38 and 108

C1 ft (dep on at least M1) for identifying and stating which ingredient is

insufficient for the recipe. (with some supportive evidence)

31


Question Working Answer Mark Notes *3 3 £193.86 £581.58

£581.58 ×0.85=£494.343

£494.34 5 M1 3 × 193.86 (= 581.58)

B1 ft correct discount % identified or used in working

(may be identified in table)

M1 ‘581.58’× '0.15' (=87.23(7))

M1 (dep on the previous M1) ‘581.58’ − '87.23(7)'

(= 494.34(3) or 494.35)

C1 (dep on all method marks) for £494.34 or £494.35 identified as final

answer with correct money notation

OR

M1 3 × 193.86 (= 581.58)

B1 ft correct discount % identified or used in working

(may be identified in table)

M2 ‘581.58’× '0.85' (= 494.34(3))

(M1 '581.58' × '1.15' (=668.81(7))

C1 (dep on all method marks) for £494.34 or £494.35 identified as final

answer with correct money notation

NB. Throughout, values may be rounded or truncated to 2 decimal places

*4 (17 – 2.8) × 9.5 = 134.9

π × (3.8 ÷ 2)2 = 11.34...

134.9 – 2 × 11.34... = 112.21

112.21 ÷ 25 = 4.488

5 5 M1 for (17 – 2.8) × 9.5 (=134.9)

or 17×9.5 – 2.8×9.5 ( = 161.5 – 26.6 = 134.9)

M1 for π × (3.8 ÷ 2)2 (= 11.33 – 11.35)

M1 (dep on M1) for ‘134.9’ – 2 × ‘11.34’

A1 for 112 - 113

C1(dep on at least M1) for 'He needs 5 boxes' ft from candidate's calculation

rounded up to the next integer

32


Question Working Answer Mark Notes *5 Farm shop 4 M1 for 12.5 ÷ 2.5 (=5)

M1 for ‘5’×1.83 or ‘5’ × 183

A1 for (£)9.15 or 915(p)

C1 (dep on at least M1) for decision ft working shown

OR

M1 for 12.5 ÷ 2.5 (=5)

M1 for 9 ÷ ‘5’ or 900 ÷ ‘5’

A1 for (£)1.8(0) or 180(p)


OR M1 for 9 ÷ 12.5 (=0.72) or 1.83 ÷ 2.5 (=0.732)

M1 for 9 ÷ 12.5 (=0.72) and 1.83 ÷ 2.5 (=0.732)

A1 for 72(p) and 73.(2)(p) or (£)0.72 and (£)0.73(2)


OR M1 for 12.5 ÷ 9 (= 1.388...)

M1 for 2.5 ÷ 1.83 (= 1.366...)

A1 for 1.38.... and 1.36... truncated or rounded


33


Question Working Answer Mark Notes *6 Angle DEC = 180 – 41 =139

Angles on a straight line sum to 180o

Angle EDC = 60 – 38 or

Angle ABD = 180 – 120 – 38 (=22)

Co-interior/allied angles of parallel lines sum to

180o or

Angles in a triangle sum to 180o and Alternate

angles

x = )180 – '139' – '22' (=19)

Angles in a triangle sum to 180o

OR

Angle ADC = 180o – 120o = 60o

Co-interior/allied angles of parallel lines sum to

180o Angle EDC = 22o

Angle ECD = 41o – 22o = 19o

Exterior angle of triangle equals sum of the two

opposite interior angles

OR

Angle DBC = 38o Alternate angles

Angle BCE = 101o Angle sum of a

triangle is 180o

Angle BCD = 120o Opposite angles of a

parallelogram are equal

Angle ECD = 120o – 101o = 19o

x = 19o and

reasons

4

M1 for DBC = 38o or

ADC = 60o(can be implied by BDC = 22o) or ABC = 60o or

DCB = 120o or

(ABD =) 180 – 120 –38 (=22)

M1 for (BDC =) 60 − 38 (=22) or

BDC = '22' or

(DEC =) 180 − 41 (=139) or

(BCE =) 180 −41 − 38 (=101)

M1 (dep on both previous M1) for complete correct method to find x or

(x = ) 19

C1 for x = 19o AND

Co-interior/allied angles of parallel lines sum to 180o

or

Opposite angles of a parallelogram are equal

or Alternate angles

AND Angles on a straight line sum to 180o

or Angles in a triangle sum to 180o

or Exterior angle of triangle equals sum of the two opposite interior angles

or Angles in a quadrilateral sum to 360o

34


Question Working Answer Mark Notes *7

Yes +

evidence

2

M1 for a correct method to change 15 miles into kilometres

C1(dep M1) for 24 km and statement with correct conclusion

[SC: B1 for “Yes” oe and 24 km shown if M0 scored]

or

M1 for a correct method to change 20 kilometres into miles

C1(dep M1) for 12.5 miles and statement with correct conclusion

[SC: B1 for “Yes” oe and 12.5 miles shown if M0 scored]

35


Question Working Answer Mark Notes *8 Small with

correct

figures for

comparison

4 M1 for one calculation eg 6.5 ÷ 30 (=0.216...) or 8.95 ÷ 40 (=0.22375) or 10.99

÷ 50 (=0.2198)

M1 for all three calculations eg 6.5 ÷ 30 (=0.216...) and 8.95 ÷ 40 (=0.22375)

and 10.99 ÷ 50 (=0.2198)

A1 for 0.216(6...) and 0.223(75) and 0.219(8...); can be rounded or truncated

as long as they remain different

C1 (dep on M1) for conclusion ft from three comparable figures

[could use different figures relating to 30, 40, 50]

OR M1 for one calculation eg 6.5 × 20 (=130) or 8.95 × 15 (=134.25) or 10.99 ×

12 (=131.88)

M1 for three calculations eg 6.5 × 20 (=130) and 8.95 × 15 (=134.25) and

10.99 × 12 (=131.88)

A1 for 130 and 134(.25) and 131(.88); can be rounded or truncated as long as

they remain different

C1 (dep on M1) for conclusion ft from three comparable figures eg cost of 600

plants or comparing small and medium and small and large e.g. 120 plants and

150 plants separately]

OR

M1 for one calculation e.g 30 ÷ 6.5 (= 4.615…) or 40 ÷ 8.95 (= 4.469…) or

50 ÷ 10.99 (= 4.549…)

M1 for three calculations e.g. 30 ÷ 6.5 (= 4.615…) and 40 ÷ 8.95 (= 4.469…)

and

50 ÷ 10.99 (= 4.549…)

A1 for 4.6(15…) and 4.4(69…) and 4.5(49…) can be rounded or truncated as

long as they remain different

C1 (dep on M1) for conclusion ft from three comparable figures

[or any other calculations leading to comparable figures]

36


Question Working Answer Mark Notes *9 54 with

reasons

3 M1 for angle RWY or angle TWZ = 180 − 126 (= 54) or angle TWR or angle

WRS = 126 (may be marked on diagram)

A1 for 54

C1 for appropriate reasons for method shown eg.

Angles on a straight line add up to 180 and Alternate angles are equal

OR

Corresponding angles are equal and

Angles on a straight line add up to 180

OR

Vertically opposite angles are equal and

Allied angles / Co-interior angles add up to 180

OR

Angles at a point add up to 360 with other reasons as above.

*10 Decision (No

the

attendance

target was

not met)

3 M1 for attempting to find total number of students or 1210 seen

M1 for '1210'

'1092'× 100 oe or

'1210'

'118'× 100 oe

C1 for correct decision with 90.(2479...) or correct decision

with 6 and 9.(752...)

OR

M1 for attempting to find total number of students or 1210 seen

M1 for 100

94× ‘1210’ oe

C1 for correct decision with 1137 (.4) and 1092 or correct decision with 72(.6)

and 118

OR

M1 for a correct % method for one year,

e.g. 192

208× 100 or

94

100× 208

M1 for a correct % method for each year

C1 for correct decision with 92.(30...), 90.(87...), 89.(31...), 89.(27...), 89.(91...)

or 195(.5..), 226.(9…), 246.(2..), 245.(3…), 223.(7…)

37


Question Working Answer Mark Notes *11 22 5 2t t = (2 1)( 2)t t

(2 1)( 2)t t

3 M1 (2t + 2)(t + 1) oe or 2t(t + 2) + 1(t + 2) or

t(2t + 1) + 2(2t + 1)

A1 (2 1)( 2)t t

This is always a product of two whole numbers

each of which is greater than 1

Correct

explanation

B1 ft from (i) for a convincing explanation referring to factors found in (i)

*12 No + reason 4 M1 for intention to find the circumference

eg 140 × π (= 439.82...)

A1 for circumference = 439 - 440

M1 (dep on M1) for a complete method shown that could arrive at two figures

that are comparable eg “C”÷60×12 (=87.96..) , 90÷12×60 (=450) , 90×60÷“C”

(=12.27), “C”÷90×12 (=58.64..)

C1 (dep on both M marks) for No and explanation that shows a correct

comparison eg only 84 people could sit around the tables or that 13 tables are

needed or that 480 cm is needed.

*13 Distance ÷ speed: 30 ÷ 70 (= 0.42-0.43);

Distance ÷ time: 30 ÷ 26 (=1.15…);

Speed × time: = 70 × 26 (=1820 mins);

mph to miles/min =70÷ 60 (=1.16-1.17);

Minutes to hours is 26 ÷ 60 (=0.43…)

No with

correct figure

3 M1 for a calculation which uses the Time × Speed = Distance relationship OR

a conversion of units eg between hours & minutes or between mph & miles per

min

M1 for a calculation involving both of the above

C1 for “no” with a correct calculation, with units, from working: 25.2-25.8

minutes, 30.1-30.8 miles, 69-69.3 mph

NB: 70 ÷ 26 × 30 as a single stage calculation gets 0 marks

38


Question Working Answer Mark Notes *14 For example

UK USA

$ per US gal ($)6.90(8412) [$3.15]

£ per litre [£1.24] (£)0.56(53...)

£ per US gal (£)4.69(96) (£)2.14(28...)

$ per litre ($)1.82(28) ($)0.83(11...)

Cost in £ per US gal of UK fuel= £1.24 × 3.79

= £4.6996

Cost in $ per US gal of UK fuel = $1.47 ×

4.6996 = $6.908412

OR Cost in £ of 1 US gal of US fuel = $3.15 ÷ 1.47

= £2.14

Cost in £ per litre of US fuel = £2.14 ÷ 3.79

=£0. 56(5..

OR

Cost in UK in £ per US gal = £1.24 × 3.79

(=£4.6996)

Cost in USA in £ per US gal = £3.15 ÷ 1.47

(=2.1428)

OR Cost in UK is $ per litre = £1.24 × 1.47

(=1.8228)

Cost in USA in $ per litre = 3.15 ÷ 3.79

(=0.8311...)

Cheaper in

US

4

M1 for 1.24 × 3.79 (= 4.6996) or

1.24 × 1.47 (=1.8228)

M1 for 1.47 × ‘4.6996’ or 3.79 × '1.8228'

A1 for 6.90(8412)

C1 (dep on M2) for $’6.90(8412)’ or $'6.91' and reaching a conclusion

consistent with their calculation

OR

M1 for 3.15 ÷ 1.47 (=2.1428..) or

3.15 ÷ 3.79 (=0.8311)

M1 for ‘2.14’ ÷ 3.79 or '0.8311' ÷ 1.47

A1 for 0. 56(53…)

C1 (dep on M2) for £’0. 56(53...)’ or '£0.57' and reaching a conclusion


OR

M1 1.24 × 3.79 (= 4.6996)

M1 3.15 ÷ 1.47 (=2.1428..)

A1 4.69(96) and 2.14(28...)

C1 (dep on M2) for £'4.69(96)' or £'4.70’ AND £‘2.14(28...)’ and reaching a

conclusion consistent with their calculation

OR M1 for 1.24 × 1.47 (=1.8228)

M1 for 3.15 ÷ 3.79 (=0.8311...)

A1 for 1.82(28) and 0.83(11...)

C1 (dep on M2) for $'1.82(28)' and $'0.83(11...)' and reaching a conclusion


NB: Throughout values can be rounded or truncated to 1 or more decimal

places. In order to award the communication mark, correct currency must be

shown with the calculated value(s) but these can still be rounded or truncated to

one or more decimal places as they are being used for comparison.

39


Question Working Answer Mark Notes *15 The Friendly

Bank

4 M1 for a correct method to find interest for the first year for either bank OR

correct method to find the value of investment after one year for either bank

OR use of the multiplier 1.04 or 1.05

M1 for a correct full method to find the value of the investment (or the value of

the total interest) at the end of 2 years in either bank

A1 for 2100.8(0) and 2110.5(0) (accept 100.8(0) and 110.5(0))

C1 (dep on M1) ft for a correct comparison of their total amounts, identifying

the bank from their calculations

OR

M1 for either 1.04 × 1.01 or 1.05 × 1.005

M1 for 1.04 × 1.01 and 1.05 × 1.005

A1 for 1.0504 and 1.05525

C1 (dep on M1) ft for a correct comparison of their total multiplying factors

identifying the bank from their calculations

*16 1.0252 = 1.050625

1.04×1.015

= 1.0556

Bonus Saver

with correct

comparable

values

4 M1 for a method to calculate 4% or 2.5% of 20000 (= 800 or 20800 or 500 or

20500)

M1 for a method to calculate using a compound interest method, eg 1.0252 oe

or 1.04 followed by 1.015 oe

A1 for 1.050625 or 1.0556 or 10556 or 556 or 21112 or 21012.5 or 1112 or

1012.5

C1 for a correct decision in a statement with two correct comparable values.

NB all final money values can be rounded or truncated to nearest integer or left

unrounded.

40


Question Working Answer Mark Notes *17 180 × 365 =65700

65700 ÷1000 =65.7

65.7 × 91.22 =5993.154

5993.154÷100 + 28.20 =88.13...

D U C T

366 65880 6010 88.30

365 65700 5993 88.13

65000 5929 87.49

66000 6020 88.40

364 65520 5976 87.96

360 64800 5911 87.31

336 60480 5517 83.37

Decision

(Should have

a water meter

installed)

5 Per year

M1 for 180 × ‘365’ (= 65700)

M1 for ‘65700’ ÷ 1000 (= 65.7 or 65 or 66)

M1 for ‘65.7’ × 91.22 (= 5993...)

A1 for answer in range (£)87 to (£)89

C1 (dep on at least M1) for conclusion following from working seen

OR (per day)

M1 for 107 ÷ ‘365’ (= 0.293…)

M1 for 180 ÷ 1000 × 91.22 (= 16.4196)

M1 for 28.2 ÷ ‘365’ + ‘0.164196’ (units must be consistent)

A1 for 29 – 30(p) and 24 – 24.3(p) oe


OR M1 for (107 – 28.20) ÷ 0.9122 (= 86.384..)

M1 for ‘86.384..’× 1000 (= 86384.5…)

M1 for ‘365’ × 180 (= 65700)

A1 for 65700 and 86384.5...


NB : Allow 365 or 366 or 52×7 (=364) or 12 × 30 (=360) or 365¼ for number

of days

41


Question Working Answer Mark Notes *18 Angle POT = 180 – 90 – 32 = 58

(angle between radius and tangent = 90o and

sum of angles in a triangle = 180o)

Angle OST =angle OTS = 58÷2

(ext angle of a triangle equal to sum of int opp

angles and base angles of an isos triangle are

equal) or (angle at centre = 2x angle at

circumference)

OR

Angle SOT = 90 + 32 = 122

(ext angle of a triangle equal to sum of int opp

angles)

(180 – 122) ÷ 2 (base angles of an isos triangle

are equal)

29 5 B1 for angle OTP = 90o, quoted or shown on the diagram

M1 for a method that leads to 180 – ( 90 + 32) or 58 shown at TOP

M1 for completing the method leading to “58”÷2 or 29 shown at TSP

A1 cao

C1 for “angle between radius and tangent = 90o” and one other correct reason

given from theory used

NB: C0 if inappropriate rules listed

OR

B1 for angle OTP = 90o, quoted or shown on the diagram

M1 for a method that leads to 122 shown at SOT

M1 for (180 – “122”) ÷ 2 or 29 shown at TSP

A1 cao

C1 for “angle between radius and tangent = 90o” and one other correct reason

given from theory used

NB: C0 if inappropriate rules listed

*19 Train Pay Diff

Old 200 510 310

New 225 535.50 310.50

Diff 25 25.50 50p

Comparison 3 M1 for method to find cost of tickets before increase eg

125.1

225 (=200) oe or

22512.5

112.5 oe or pay before increase,

05.1

50.535 (=510) oe

A1 for 25 (train) and 25.5(0) (pay) or 310 and 310.5(0)

C1 (dep on M1) ft for statement comparing rises leading to conclusion based on

two comparable amounts eg pay increase greater than train increase

42


Question Working Answer Mark Notes *20 cos y = 2.25 ÷ 6

y = cos-1 (2.25 ÷ 6)

OR

6cos 75 = 1.55…

The ladder is

not safe

because y is

not near to 75

3 M1 for cos y = 2.25 ÷ 6 oe

M1 for cos-1 (2.25 ÷ 6)

C1 for sight of 67-68 and a statement eg this angle is NOT (near to) 75o and so

the ladder is not steep enough and so not safe.

OR

M1 for cos 75 = x ÷ 6

M1 for 6cos 75

C1 for sight of 1.55(29…) and a statement eg that 2.25 NOT (near to) 1.55 and

so the ladder is not steep enough and so not safe.

*21 (4n² + 2n + 2n + 1)

− (2n + 1)

= 4n² + 4n + 1 − 2n − 1

= 4n² + 2n

= 2n(2n + 1)

Proof 3 M1 for 3 out of 4 terms correct in the expansion of (2n + 1)²

or (2n + 1) 1)12( n

A1 for 4n² + 2n or equivalent expression in factorised form

C1 for convincing statement using 2n(2n + 1) or 2(2n² + n) or 4n² + 2n to prove

the result

*22 Yes 3 M1 for 1 − 0.6 (=0.4)

M1 for (“0.4”)³ oe

C1 (dep on M1) for 0.064 oe leading to a correct deduction

OR

M1 for 1−Pr(3H, 0T) − Pr(2H, 1T) − Pr(1H, 2T) oe

M1 for 1−(0.6)³−3(0.6)²(0.4)−3(0.6)(0.4)²

C1 (dep on M1) for 0.064 oe leading to a correct deduction

*23 Yes, average

speed could

have been as

high as

80.622...

5 B1 for 4535 or 4534.999... or 202.5

M1 for 4535 (oe) ÷ 202.5

M1 for ×3600 and ÷1000

A1 for 80.622...

C1 (dep on first M1) for correct conclusion from their calculations

43


Question Working Answer Mark Notes *24

0.229

because the

LB and UB

agree to that

number of

figures

5 B1 for 3.465 or 3.475 or 3.474999…

B1 for 8.1315 or 8.1325 or 8.132499…

M1 for as UB OR as LB

C1 (dep on all previous marks) for 0.2292… and 0.2288… both values must

clearly come from working with correct values

C1 for 0.229 from 0.2292… and 0.2288… and ‘both LB and UB round to

0.229’

*25 o1

2 sin 302

A x x

212 0.5

2A x

OR

Height = o2 sin 30x = x

2

2 2

x x xA

OR

Height = x sin 30 = 2

x

212

2 2 2

x xA x

2x A shown

3 M1

o1( ) 2 sin 30

2A x x

A1 2 0.5A x or

2

2

xA

C1 for completion with all steps shown

OR M1 height = 2xsin 30 (= x)

A1 2 0.5A x or

2

2

xA


OR

M1 for height = x sin 30 (= 2

x )

A1 2 0.5A x or

2

2

xA


44


Question Working Answer Mark Notes *26 Yes with

explanation

3 M1 For Line A: writes equation as y = 1.5x + 4 or gives the gradient as 1.5 or

constant term of 4

OR for Line B: shows a method which could lead to finding the gradient or

gives the gradient as 2 or constant term of 4 or calculates a sequence of points

including (0,4) or writes equation of line as y = 2x + 4

M1 Shows correct aspects relating to an aspect of Line A and an aspect of Line

B that enables some comparison to be made eg gradients, equations or points.

C1 for gradients 1.5 and 2 and Yes with explanation that the gradients are

different or states the lines intersect at (0,4) or explanation that interprets

common constant term (4) from equations

OR

M1 for a diagram that shows both lines drawn and intersecting at (0,4)

M1 for a diagram that shows both lines and their intersection point identified as

(0,4)

C1 for Yes and states the intersection point as (0,4)

45


Question Working Answer Mark Notes *27 Proof 3 M1 for one pair of equal angles or sides with reason

M1 for second pair of equal angles or sides with reason

C1 for proof completed correctly with full reasons and reason for congruence

Acceptable reasons:

AD common (oe eg both same)

Angle BAD = angle CDA (angles in a semicircle are 90o)

Angle ABO = angle DCA (angles in the same segment are equal)

Triangle ABD and triangle DCA are congruent - ASA

OR BD = CA (diameters of the circle)

Angle BAD = angle CDA (angles in a semicircle are 90o.)

AD common

Triangle ABD and triangle DCA are congruent - RHS

OR BD = CA (diameters of the circle)

AD is common

Angle ADB = angle CAD

(base angles of an isosceles triangle are equal.)

Triangle ABD and triangle DCA are congruent - SAS

Results Plus data for these questions:

New Question

Original Question

Original Paper

Skill tested Mean score

Maximum score

Mean Percent

1 2 2H 1303 Solve a ratio problem in a context 2.38 3 79

2 2 2H 1306 Solve a ratio problem in a context 2.81 4 70

3 3 2H 1211 Use percentages to find prices after a percentage increase or decrease 3.56 5 71

4 5 2H 1206 Recall and use the formulae for the circumference of a circle and the area enclosed by a circle

3.13 5 63

5 6 2H 1206 Add, subtract, multiply and divide whole numbers, integers, fractions, decimals and numbers in index form

3.41 4 85

6 6 2H 1211 Understand and use the angle properties of parallel lines, triangles and quadrilaterals

1.60 4 40

7 7b 2H 1303 Convert between imperial and metric measures 1.52 2 76


2.70 4 68

9 7 2H 1406 Understand and use the angle properties of parallel lines 2.17 3 72

10 9 2H 1411 Use percentages to solve problems 1.60 3 53

11 10 2H 1211 Calculate an unknown quantity from quantities that vary in direct or inverse proportion

1.01 4 25

12 11 2H 1411 Find circumferences of circles and areas enclosed by circles 1.40 4 35

13 13 2H 1311 Understand and use compound measures, including speed and density 1.06 3 35

14 14c 2H 1211 Factorise quadratic expressions 0.30 3 10

15 14 2H 1306 Use percentages to calculate Compound Interest 2.22 4 56

16 14 2H 1411 Calculate repeated proportional change 1.45 4 36


3.03 5 61

18 16 2H 1306 Give reasons for angle calculations involving the use of tangent theorems 2.18 5 44

19 18b 2H 1406 Understand the multiplicative nature of percentages as operators 0.61 3 20

20 20 2H 1306 Understand, recall and use trigonometric relationships in right-angled triangles, and use these to solve problems in 2-D and in 3-D configurations

1.16 3 39

21 21b 2H 1406 Simplify rational expressions by cancelling, adding, subtracting, and multiplying

0.38 3 13

22 22 2H 1406 Understand conditional probabilities 1.31 3 44

23 23 2H 1411 Calculate the upper and lower bounds of calculations, particularly when working with measurements

0.19 5 4

24 24 2H 1303 Find the upper and lower bounds in real life situations using measurements given to appropriate degrees of accuracy

0.46 5 9

25 25 2H 1211 Calculate the area of a triangle given the length of two sides and the included angle

0.14 3 5

47

New Question

Original Question

Original Paper

Skill tested Mean score

Maximum score

Mean Percent

26 25 2H 1311 Interpret and analyse a straight line graph 0.29 3 10

27 28 2H 1311 Understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles using formal arguments, and to verify standard ruler and a pair of compasses constructions

0.23 3 8

TOTAL 42.30 100 42

Documents

Practice Papers Set G Higher Tier QWC · 04/04/2014 · Answer all questions. ... Mr Weaver’s garden is in the shape of a rectangle. In the garden there is a patio in the shape