Practice Papers Set G
Higher Tier – QWC
40 minutes
1MA0 / 2MB01
Instructions
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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
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There are 9 questions on this paper; the total mark is 38
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 are labelled with an asterisk (*) and are ones where the quality of
your written communication will be assessed.
Advice
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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.
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 =
1
2
(a + b)h
Volume of sphere 43 πr3
Surface area of sphere = 4πr2
Volume of cone 13 πr2h
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
 b  (b 2  4ac)
x=
2a
Sine Rule
a
b
c


sin A sin B sin C
Cosine Rule a2 = b2+ c2– 2bc cos A
Area of triangle =
1
2
ab sin C
2
Answer ALL NINE questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
You must NOT use a calculator.
1*.
Here is part of Gary’s electricity bill.
Electricity bill
New reading
Old reading
7155 units
7095 units
Price per unit 15p
Work out how much Gary has to pay for the units of electricity he used.
(Total for Question 1 is 4 marks)
_______________________________________________________________________
3
2*.
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?
£ ..............................................
(1)
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.
(3)
(Total for Question 2 is 4 marks)
___________________________________________________________________________
4
3*.
Railtickets and Cheaptrains are two websites selling train tickets.
Each of the websites adds a credit card charge and a booking fee to the ticket price.
Railtickets
Cheaptrains
Credit card charge: 2.25% of ticket price
Credit card charge: 1.5% of ticket price
Booking fee: 80 pence
Booking fee: £1.90
Nadia wants to buy a train ticket.
The ticket price is £60 on each website.
Nadia will pay by credit card.
Will it be cheaper for Nadia to buy the train ticket from Railtickets or from Cheaptrains?
(Total for Question 3 is 4 marks)
___________________________________________________________________________
5
4*.
CDEF is a straight line.
AB is parallel to CF.
DE = AE.
Work out the size of the angle marked x.
You must give reasons for your answer.
(Total for Question 4 is 4 marks)
___________________________________________________________________________
6
5*.
Talil is going to make some concrete mix.
He needs to mix cement, sand and gravel in the ratio 1 : 3 : 5 by weight.
Talil wants to make 180 kg of concrete mix.
Talil has
15 kg of cement
85 kg of sand
100 kg of gravel
Does Talil have enough cement, sand and gravel to make the concrete mix?
(Total for Question 5 is 4 marks)
___________________________________________________________________________
7
6*.
B, C and D are points on the circumference of a circle, centre O.
AB and AD are tangents to the circle.
Angle DAB = 50°
Work out the size of angle BCD.
Give a reason for each stage in your working.
(Total for Question 6 is 4 marks)
___________________________________________________________________________
8
7*.
Prove algebraically that the difference between the squares of any two consecutive integers is
equal to the sum of these two integers.
(Total for Question 7 is 4 marks)
___________________________________________________________________________
9
8.
OAYB is a quadrilateral.
OA = 3a
OB = 6b
(a) Express AB in terms of a and b.
....................................................................
(1)
X is the point on AB such that AX : XB = 1 : 2
and BY = 5a – b
*(b) Prove that
OX =
2
OY
5
(4)
(Total for Question 8 is 5 marks)
___________________________________________________________________________
10
9.
APB is a triangle.
N is a point on AP.
AB = a
AN = 2b
NP = b
(a) Find the vector PB , in terms of a and b.
.....................................................
(1)
B is the midpoint of AC.
M is the midpoint of PB.
*(b) Show that NMC is a straight line.
(4)
(Total for Question 9 is 5 marks)
TOTAL FOR PAPER IS 38 MARKS
11
BLANK PAGE
12
1MA0 1H – Practice Paper (Set G) QWC
Question
Working
Answer
Mark
9
4
M1 for 7155 – 7095 or 60 seen or 7155×15 (or .15) or 7095×15 (or
.15) or 107325 or 106425 or 1073.25 or 1064.25
M1 for ‘60’ ×15 or 7155 ×15 – 7095 × 15 [or .15 instead of 15]
A1 for 9 or 9.00 or 900
C1 (ft ) for answer with correct units (money notation) identified as
the answer.
(a)
10
1
B1 cao
(b)
Ed is cheaper up to 20
miles, Bill is cheaper
for more than 20 miles
3
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)
1*
2*
y
40
30
20
10
0
10
5
Miles
Ed
Bill
0
0
10
15
10
15
20
20
20
30
30
30
45
40
25
40
60
50
30
50
75
60
x
Notes
OR
M1 for correct method to work out Ed's delivery cost for at least 2
values of n miles where 0 < n ≤ 50 OR
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
1MA0 1H – Practice Paper (Set G) QWC
Question
Working
3
2.25 × 60 ÷ 100 = 1.35
1.35 + 0.80 = 2.15
1.5 × 60 ÷ 100 = 0.90
0.90 + 1.90 = 2.80
Answer
Mark
Railtickets with correct
calculations
4
Notes
NB. All work may be done in pence throughout
M1 for correct method to find credit card charge for one company
eg. 0.0225 × 60(=1.35) oe or 0.015 × 60 (=0.9) oe
M1 (dep) for correct method to find total additional charge or total
price for one company
eg. 0.0225×60 + 0.80 or 0.015×60 + 1.90 or
2.15 or 2.8(0) or 62.15 or 62.8(0)
A1 for 2.15 and 2.8(0) or 62.15 and 62.8(0)
C1 (dep on M1) for a statement deducing the cheapest company, but
figures used for the comparison must also be stated somewhere, and a
clear association with the name of each company
OR
M1 for correct method to find percentage of (60+booking fee)
eg. 0.0225 × 60.8(=1.368) oe or 0.015 × 61.9(=0.9285)
M1 (dep) for correct method to find total cost or total additional cost
eg. '1.368' + 60.8(=62.168) or '1.368' + 0.8 (=2.168) or
'0.9285' + 61.9 (=62.8285) or '0.9285' +1.9 (=2.8285)
A1 for 62.168 or 62.17 AND 62.8285 or 62.83 OR
2.168 or 2.17 AND 2.8285 or 2.83
C1 (dep on M1) for a statement deducing the cheapest company, but
figures used for the comparison must also be stated somewhere, and a
clear association with the name of each company
OR
M1 for correct method to find difference in cost of credit card charge
eg. (2.25 – 1.5) × 60 ÷ 100 oe or 0.45 seen
M1 (dep) for using difference with booking fee or finding difference
between booking fees
eg. 0.80 + “0.45”(=1.25) or
1.90 – “0.45” (=1.45) or 1.90 – 0.8 (=1.1(0))
A1 1.25 and 1.9(0) or 0.45 and 1.1(0)
C1 (dep on M1) for a statement deducing the cheapest company, but
figures used for the comparison must also be stated somewhere, and a
clear association with the name of each company
OR
2.25 – 1.5 = 0.75
0.075 × 60 ÷ 100 = 0.45
0.80 + 0.45 = 1.25
1.25 < 1.90
QWC: Decision and justification should be clear with working clearly
presented and attributable
14
1MA0 1H – Practice Paper (Set G) QWC
Question
Working
4*
–2
(1)
x
y
–1
3
0
(5)
1
7
2
9
Answer
Mark
3, 7, 9
2
B2 for all three values correct in the table
(B1 for 2 values correct)
graph of
y = 2x + 5
2
(From their table of values)
M1 ft for plotting at least 2 of their points (any points from their table
must be correctly plotted)
A1 for correct line from x = –2 to x = +2
y
1
0
Notes
(Use of y = mx + c)
M1 for line drawn with gradient of 2 or line drawn with a y intercept
of 5 and a positive gradient)
A1 for correct line from x = –2 to x = +2
8
6
4
2
2
5*
O
180÷9×1:180÷9×3:180÷9
×5
=20:60:100
Not enough cement
(but enough sand and
enough gravel)
2 x
2
No + reason
4
OR
1×15:3×15:5×15
=15:45:75
15+45+75=135 (<180)
Not enough cement (to
make 180kg of concrete)
15
M1 for 180 ÷ (1+3+5) ( = 20) or 3 multiples of 1: 3: 5
M1 for 1×”20” or 3×”20” or 5×”20” or 20 seen or 60 seen or 100
seen
A1 for (Cement =) 20, (Sand =) 60, (Gravel) = 100
C1 ft (provided both Ms awarded) for not enough cement oe
OR
M1 for (1×15 and) 3×15 and 5×15 or 9×15 or sight of the numbers
15, 45, 75 together.
M1 for ‘15’ + ‘45’ + ‘75’
A1 for 135 (<180)
C1 ft (provided both Ms awarded) for not enough cement oe
1MA0 1H – Practice Paper (Set G) QWC
Question
Working
6*
ABO = ADO = 90°
(Angle between tangent
and radius is 90°)
DOB = 360 – 90 – 90 – 50
(Angles in a quadrilateral
add up to 360°)
BCD = 130 ÷ 2
(Angle at centre is twice
angle at circumference)
Answer
Mark
65o
4
Notes
B1 for ABO = 90 or ADO = 90 (may be on diagram)
B1 for BCD = 65 (may be on diagram)
C2 for BCD = 65o stated or DCB = 65o stated or angle C = 65o stated
with all reasons:
angle between tangent and radius is 90o;
angles in a quadrilateral sum to 360o;
angle at centre is twice angle at circumference
(accept angle at circumference is half (or
OR
ABD = (180 – 50) ÷ 2
(Base angles of an
isosceles triangle)
BCD = 65
(Alternate segment
theorem)
1
) the angle at the centre)
2
(C1 for one correct and appropriate circle theorem reason)
QWC: Working clearly laid out and reasons given using correct
language
OR
B1 for ABD = 65 or ADB = 65 (may be on diagram)
B1 for BCD = 65 (may be on diagram)
C2 for BCD = 65o stated or DCB = 65o stated or angle C = 65o stated
with all reasons:
base angles of an isosceles triangle are equal;
angles in a triangle sum to 180o;
tangents from an external point are equal;
alternate segment theorem
(C1 for one correct and appropriate circle theorem reason)
QWC: Working clearly laid out and reasons given using correct
language
16
1MA0 1H – Practice Paper (Set G) QWC
Question
Working
7*
(n + 1)2 – n2
= n2 + 2n + 1 – n2 = 2n
+1
(n + 1) + n = 2n + 1
Answer
Mark
proof
4
Notes
M1 for any two consecutive integers expressed algebraically
eg n and n +1
M1(dep on M1) for the difference between the squares of ‘two
consecutive integers’ expressed algebraically eg (n + 1)2 – n2
OR
A1 for correct expansion and simplification of difference of
squares, eg 2n + 1
(n + 1) – n
= (n + 1 + n)(n + 1 – n)
= (2n + 1)(1) = 2n + 1
(n + 1) + n = 2n + 1
2
2
C1 (dep on M2A1) for showing statement is correct,
eg n + n + 1 = 2n + 1 and (n + 1)2 – n2 = 2n + 1 from correct
supporting algebra
OR
n2 – (n + 1)2 = n2 – (n2 +
2n + 1) =
–2n – 1 = – (2n + 1)
Difference is 2n + 1
(n + 1) + n = 2n + 1
8*
6b – 3a
1
4
B1 for 6b – 3a oe
M1 for AX =
1
1
AB or ’(6b – 3a)’ or ft to 2b – a
3
3
M1 for OY = OB + BY = 6b + 5a – b (= 5b + 5a ) oe
M1 for OX = 3a + ‘2b – a’ = 2a + 2b oe
Or
OX = 6b –
‘(6b – 3a)’ (= 2a + 2b) oe
C1 for 2 OY = 2 ×5(a + b) = 2(a + b) = OX
5
17
5
1MA0 1H – Practice Paper (Set G) QWC
Question
Working
9*
(a)
*(b)
Answer
Mark
a – 3b
1
B1
Notes
4
M1 for (NC =) 2a  2b oe
for a – 3b oe
M1 for (NM =) b 
A1 for
C1
1
"  a  3b  "
2
1
 a  b  oe and 2a  2b oe
2
for NC is a multiple of NM (+ common point)
OR
M1 for (NC =) 2a  2b oe
M1 for (MC =)
A1 for
C1
1
"  a  3b  " a
2
3
 a  b  oe and 2a  2b oe
2
for NC is a multiple of MC (+ common point)
OR
M1 for (NM =) b 
1
"  a  3b  "
2
1
"  a  3b  " a
2
1
3
A1 for
 a  b  oe and  a  b  oe
2
2
M1 for (MC =)
C1
18
for NM is a multiple to MC (+ common point)
Results Plus data for these questions:
New
Question
1
2a
2b
3
4
5
6
7
8a
8b
9a
9b
Original
Question
3
3a
3b
10
10
13
21
21
26a
26b
28a
28b
Original
Paper
1H 1211
1H 1206
1H 1206
1H 1206
1H 1303
1H 1211
1H 1206
1H 1303
1H 1303
1H 1303
1H 1211
1H 1211
Skill tested
Add, subtract, multiply and divide any number
Discuss, plot and interpret graphs modelling real situations
Discuss, plot and interpret graphs modelling real situations
Use percentages in real life situations
Understand and use the angle properties of parallel lines
Divide a quantity in a given ratio
Find missing angles on diagrams
Algebraic proof
Understand and use vector notation
Apply vector methods for simple geometrical proofs
Understand and use vector notation
Solve geometrical problems in 2-D using vector methods
TOTAL
19
Mean
score
1.85
0.71
0.97
2.19
1.08
1.76
0.89
0.11
0.32
0.29
0.19
0.14
10.5
Maximum
score
4
1
3
4
4
4
4
4
1
4
1
4
38
Mean
Percent
46
71
32
55
27
44
22
3
32
7
19
4
28