# Linear Maths Edexcel Gcse Mock Paper Non Calculator

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```					GCSE Mathematics Linked Pair Pilot –
Beginning to teach

10NMB01
Presented by
Edexcel Principal Examiners

Slide 1
Course code 10NMB01
Session 1 Aims

The purpose of this event is to:
• Review the GCSE Linked Pair in more detail
• Review differences between GCSE Linked Pair and GCSE
Maths at unit 2 in particular
• Consider some teaching implications
• Discuss and share entry practice

Slide 2
Course code 10NMB01/02
Session 2
Examination Timetable Applications - Final dates

Monday 6 June
5AM1F Applications of Mathematics
Unit 1 F Tier: Paper 1
(Calculator) (1h 45m)

5AM1H Applications of Mathematics
Unit 1 H Tier: Paper 1
(Calculator) (1h 45m)
Slide 3
Course code 10NMB01/02
Session 2
Examination Timetable Applications - Final dates
Friday 10 June

5AM2F Applications of Mathematics
Unit 2 F Tier: Paper 1 (Calculator) (1h 45m)
5AM2H Applications of Mathematics
Unit 2 H Tier: Paper 1
(Calculator) (1h 45m)
Please note, first certification of this
qualification is in June 2011 (until June 2013)
Slide 4
Course code 10NMB01/02
Session 2
Examination Timetable Methods - Final dates
Monday 13 June
5MM1F Methods of Mathematics
Unit 1 F Tier: Paper 1
(Non-Calculator) (1h 45m)

5MM1H Methods of Mathematics
Unit 1 H Tier: Paper 1
(Non-Calculator) (1h 45m)

Slide 5
Course code 10NMB01/02
Session 2
Examination Timetable Methods - Final dates
Monday 21st June
5MM2F Methods of Mathematics
Unit 2 F Tier: Paper 1
(Calculator) (1h 45m)

5MM2H Methods of Mathematics
Unit 2 H Tier: Paper 1
(Calculator) (1h 45m)

Slide 6
Course code 10NMB01/02
Session 3
Feedback on Unit 1 issues

*Spreadsheets – modelling v testing v accessibility
*Flowcharts – what symbols are required?
Currency calculations at F Tier
Financial calculations at F tier
Similar triangles at F tier
*Intersecting chords – resource material
*Linear programming – resource material
*Sets –Venn Diagrams – prob - required notation

Slide 7
Course code 10NMB01/02
Session 3

Spreadsheets – initial examples were judged

Slide 8
Course code 10NMB01/02
Session 3
1. Ronnie wants to buy some carpets.
She can buy 3 types of carpets, wool, nylon and sisal.
Complete the spreadsheet so that she can compare the costs of carpeting
some of the rooms in her house.

A           B         C        D          E           F
Wool £20   Nylon £15   Sisal £10
1   Length (m)   Width (m)   Area
per m²     per m²      per m²
2       4           3
3       5           4

Slide 9
Training from Edexcel
Session 3
Flowcharts – what symbols are required?
Process

Decision

Start/Stop

Input/Output

Slide 10
Course code 10NMB01/02
Session 3

Currency calculations at F Tier

Financial Calculations at F tier
(Personal Finance)(Index Numbers)

Slide 11
Course code 10NMB01/02
Session 3
Currency calculations at F Tier
5. £1 = €1.20

A watch costs £50 in the UK. The same make of watch costs €63 in France. Work out the
difference between the cost in the UK and the cost in France. Give your answer in £.

9. £1 = \$1.50
Jim has £4000
He wants to buy \$ for a holiday.
The agent will charge Jim 2% commission
Work out how the largest number of \$ Jim can get.

Slide 12
Training from Edexcel
Session 3
Financial Calculations at F Tier
1. Jim earns £250. He gets a wage rise of 10%. Work out his new wage.

20. Rail operators are allowed to raise fares by the cost of living index
increase + 1%. In 2010, the cost of living increase was 4.5%.
The fare from Bristol to London in 2010 was £120.

What is the fare going to be in 2011?

Slide 13
Training from Edexcel
Session 3
• Sets –Venn Diagrams – Probability - required notation

F Tier – {1, 4, 7}, A′ ø,

H Tier - {1, 4, 7}, A′ ø,

No more than 3 sets for any Venn diagram at H tier
Generally 2 sets at F Tier

Slide 14
Course code 10NMB01/02
Session 3

• Similar Triangles at F tier

8 cm
4 cm

60o          40o          60o          xo

6 cm                      y cm

These two triangles are similar.

(a) Write down the value of x
(b) Find the value of y

Slide 15
Training from Edexcel
Session 3

• H Tier
• Intersecting chords – resource material

Linear Programming – resource material

Slide 16
Training from Edexcel
Session 3               Compound Interest at F Tier (and H Tier)

• Work out the amount an investment is worth
• given the number of years and interest rate

• Use multipliers to work out appreciation and
• depreciation

Slide 17
Training from Edexcel
Session 4
• New material at F Tier – Unit 2
Risk
Here is some information about injuries in some sports

Sport             Number of   Number of
games       injuries
Football          348         37
Rugby             247         21
Extreme Ironing   96          11

Which sport caries the greatest risk of injury?
Slide 18
Training from Edexcel
Session 4
New material at F Tier – Unit 2

Sport             Rel Freq   Rel Freq

Football              37     0.106
348
Rugby                  21    0.085
247
Extreme Ironing        11    0.115
96

Slide 19
Training from Edexcel
Session 4
New material at H Tier

• Risk

Key idea is that of a cost – usually monetary

The probability that my freezer will fail next year
is 0.15 . It would cost £120 to fix it.
Insurance costs £35. Should I take out insurance?

Slide 20
Training from Edexcel
Session 4
New material at H Tier
Risk

Estimate of cost of breakdown = 0.15 × £120
= £18

Slide 21
Training from Edexcel
Session 4                           Risk
A company generates electricity from an offshore site with wind turbines.
If a high wind becomes a gale the probability of
damage to the wind turbines increases.
The probability of damage in a gale is 0.04.
The probability of damage in a high wind is 0.005
The probability that a high wind becomes
a gale is 0.3

This site has 50 high wind days each year. Work out an estimate for the number of times
it will be damaged in a period of 10 years                                                          The probability tree
Damage    has been used to
0.005                  show the structure of
the problem so that
the probability of
High
damage on any high
Wind
0.70                              0.995         No        wind day can be
damage    found.
The red figures have
been calculated by
Damage
0.04                  subtraction from 1

0.30           Gale

No
0.96        damage
Slide 22
Training from Edexcel
Session 4

New material at H Tier

Midpoint theorem, its converse and the
intercept theorem

Slide 23
Training from Edexcel
Session 4

• 5.[A] ABCD is a rectangle. K, L, M and N are the
midpoints of AB, BC, CD and DA respectively. Use the
midpoint theorem to show that the quadrilateral KLMN is
a parallelogram.

Slide 24
Training from Edexcel
Session 4 Midpoint – a bit more challenging
P
Y                                  X

T
S

Q                        R

S and T are the midpoints of PQ and PR.
QTX is a straight line with QT = TX
RSY is a straight line with RS = SY

Prove (i) XPY is a straight line.
(ii) XY = 2QR
Slide 25
Training from Edexcel
Session 4
• New material at H Tier – Exponential growth and decay

Key idea – y =abx

Key idea - compound interest formula

Applied to population growth and decay,
radioactivity, decay of chemicals in the body and
compound interest.
Slide 26
Training from Edexcel
Session 4 Exponential Growth/decay

The mass, m grams, of a radioactive substance                 Mass
(grams)
decreases exponentially as shown in this graph.                         1
0

Equation of graph is                                   8
m = 9×0.8x

6

4

(a) Work out the original mass of the substance.
(b) Work out the mass of the substance after 6 hours.                 2
(c) (i) Work out the multiplier. (ii) Work out the percentage
rate of decrease.
0   2   4   6        8             1
Time (t hours)
0

Slide 27
Training from Edexcel
Session 4
New material at H Tier – gradients of curves

Key Idea – the gradient of a curve at a point is equal
to the gradient of the tangent to the curve at that
point

No Calculus!

Key ideas – gradients of the d/t graph and the v/t
graph as well as water tanks.
Slide 28
Training from Edexcel
8.[A] The graph shows the distance, y m, that a car has             y
travelled during t seconds                                         100

90

80

70

(a) Calculate an estimate of the speed of the car at t = 20.             60
(b) Calculate the average speed of the car between t = 10 and t = 50.
50

40

30

20

10

O    10   20   30    40        50   60   x

Slide 29
Training from Edexcel
Session 4
• New material – Area under a curve

Key idea – find an estimate for the area under a
curve (the area between the curve and the x- axis)
by using trapeziums to approximate the region

No negative areas - use 4 or 5 trapeziums

Key idea – area under a v/t graph

Slide 30
Training from Edexcel
Session 4 Area under a curve
Velocity m/s
18
4. [A]                                                            0
The graph gives information about the velocity of a              16
particle during the first 40 seconds of its motion.               0
14
0
(a) Calculate an estimate for the distance travelled             12
during the first 40 seconds.                                  0
10
(b) State, with a reason, whether your answer to (a) is an        0
overestimate or underestimate of the true distance                8
0
travelled                                                         6
0
4
0
2
0
0   1   2          3   4   t
0   0          0   0

Slide 31
Training from Edexcel
Session 5
• Scheme of Learning F Tier Methods

Slide 32
Training from Edexcel
Session 5
• Scheme of Learning H Tier - Methods

Slide 33
Training from Edexcel
Session 5 Planning and strategy

Which groups/classes are following the
course in your school – why this choice?

In what order are you teaching the course –
why this choice?

Slide 34
Training from Edexcel
Session 6
• Resource Review
Includes
Methods exemplification booklet
Applications exemplification booklet
Matching Doc to Spec A book from Edexcel
Matching Doc from St Peter’s school
Book chapters in the LP book
Further Practice Material.
New mock papers
Functional skills - common scenarios
Slide 35
Training from Edexcel
Session 6
• Exemplification booklets

Slide 36
Training from Edexcel
Session 6

Edexcel matchings to the Spec A books

St Peter’s matchings – skill doc showing which
skills are present where
M1   M2   A1   A2
by factorisation and completing the
square                              P

Slide 37
Training from Edexcel
Session 6
• Book Chapters in the LP book
1 Mid-point/intersecting chord   Methods          Unit 2                H
2 Linear programming                       Apps            Unit 1       H
3 Quadratic sequences            Methods          Unit 1                H
4 Venn diagrams                  Methods          Unit 1                F+H
5 Probability/Venn diagrams      Methods          Unit 1                F+H
6 Exponential growth/decay                 Apps            Unit 2       H
7 Area under curves                        Apps            Unit 2       H
8 Gradients                                Apps            Unit 2       H
9 Fin. and Bus. AER                        Apps            Unit 1       F+H
10 Flowcharts                              Apps            Unit 1       F+H
11 Spreadsheets                            Apps            Unit 1       F+H
12 Time series/Moving averages             Apps            Unit 1       F+H
13 Prob (Risk)                             Apps            Unit 2       F+H
Slide 38
Training from Edexcel
Session 6 Venn diagrams Methods Unit 1                                        F+H

R
F
1. Some boys were asked if they played football or rugby.                                3
19        6
The Venn diagram shows this information.
7

(a) How many boys were asked if they played football or rugby?
(b) How many boys played just rugby?
(c) How many boys do not play football?
(d) How many boys play both rugby and football?

Slide 39
Training from Edexcel
Session 6                Probability and Venn Diagrams

3.   (a) On a Venn diagram

show the whole numbers from 1 to 12
set E where E = {2, 4, 6, 8, 10, 12}
set F where F = {1, 2, 3, 4, 6, 12}

(b) A number is chosen at random from those in the Venn diagram.

Find
(i) P(E) (ii) P(F′) (iii) P(E ∩ F) (iv) P(E U F)

Slide 40
Training from Edexcel
Session 6 Further practice material

Functional skills scenarios.

Tiling problems – carpet and wall – area, costs,
percentages, conversion of units

Slide 41
Course code 10NMB01/02
Session 6 Functional Skills

Tiling
Here is a scale drawing of Jim’s floor. Each centimetre
square on the scale drawing represents 1m2

Jim wants to put carpet tiles on all his floor.
Each carpet tile is 1 m2 and costs £7.99
Work out how much it will cost Jim to put carpet tiles on all his floor.

Slide 42
Training from Edexcel
Session 6 Functional Skills
2m

2m                             2m

Jim wants to tile this part of a wall.            60cm        60 cm
He wants to use square tiles with an edge of 20 cm.
The tiles are sold in boxes of 10.
Work out the number of boxes he will need.

Slide 43
Training from Edexcel
Session 6 Mock papers
• New papers more like the standard of papers to be set

• F Tier Applications U1 and U2

• F Tier Methods U1 and U2

• H Tier Applications U1 and U2

• H Tier Methods U1 and U2

Slide 44
Course code 10NMB01/02
Other Goodies
Mixed up proofs
Autograph demos
Compound Int at F

Slide 45
Training from Edexcel
Mixed up proofs
Here are the first 5 terms an arithmetic sequence
2            5          8          11       14
Prove that the difference between the squares of consecutive terms is always a multiple of 3.

Step

1             Square of (n+1)th term = (3n+2)2

2             Difference of the terms = 18n + 3

3             Difference of the terms = (9n2+12n+4) - (9n2-6n+1)

4             (n + 1)th term = 3n-1 +3 = 3n+2

5             Difference of the terms = 3(6n+1)

6             Square of nth term = (3n -1)2

7             Since 6n + 1 is an integer, the difference is a multiple of 3

8             Difference of the terms = 9n2+12n+ 4 -9n2+6n-1

9             nth term = 3n -1

10            Difference of the terms = (3n+2)2 - (3n -1)2

Slide 46
Training from Edexcel

experts to help with subject specific queries

• Ask the Expert will put customers in direct email contact with over
300 senior subject examiners and verifiers

• Information on all our subject experts will be made available on the
Edexcel website so customers can see who they are dealing with

• Ask the Expert will be complemented by online subject support
information and teacher forums, enabling peer-to-peer support

Slide 47
Course code 10NMB01/02
Results Plus

• Free!
• Especially useful for a unitised examination

Slide 48
Training from Edexcel

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