Maths Tallis - Homepage
[pic]
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 18 questions on this paper; the total mark is 78
• 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 18 questions are AO2/AO3 only.
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.
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 = [pic](a + b)h
[pic] [pic]
Volume of sphere [pic]πr3 Volume of cone [pic]πr2h
Surface area of sphere = 4πr2 Curved surface area of cone = πrl
[pic] [pic]
In any triangle ABC The Quadratic Equation
The solutions of ax2+ bx + c = 0
where a ≠ 0, are given by
x = [pic]
Sine Rule [pic]
Cosine Rule a2 = b2+ c2– 2bc cos A
Area of triangle = [pic]ab sin C
Answer ALL EIGHTEEN questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
You must NOT use a calculator.
1. Rita is going to make some cheeseburgers for a party.
She buys some packets of cheese slices and some boxes of burgers.
There are 20 cheese slices in each packet.
There are 12 burgers in each box.
Rita buys exactly the same number of cheese slices and burgers.
(i) How many packets of cheese slices and how many boxes of burgers does she buy?
.............................................. packets of cheese slices
.............................................. boxes of burgers
Rita wants to put one cheese slice and one burger into each bread roll.
She wants to use all the cheese slices and all the burgers.
(ii) How many bread rolls does Rita need?
.............................................. bread rolls
(Total for Question 1 is 4 marks)
___________________________________________________________________________
2. Paula wants to find out how much money people spend buying CDs.
She uses this question on a questionnaire.
|How much money do you spend buying CDs? |
| |
|( £10 – £30 ( £30 – £50 ( £50 – £70 ( more than £70 |
(a) Write down two things wrong with this question.
1 .................................................................................................................................................
.....................................................................................................................................................
2 ..................................................................................................................................................
.....................................................................................................................................................
(2)
Paula asks 100 people in a CD store to do her questionnaire.
(b) Her sample is biased.
Explain why.
.....................................................................................................................................................
.....................................................................................................................................................
(1)
(Total for Question 2 is 3 marks)
___________________________________________________________________________
*3. The diagram shows the floor of a small field.
[pic]
Kevin is going to keep some pigs in the field.
Each pig needs an area of 36 square metres.
Work out the greatest number of pigs Kevin can keep in the field.
(Total for Question 3 is 4 marks)
___________________________________________________________________________
4. Trams leave Piccadilly
to Eccles every 9 minutes
to Didsbury every 12 minutes
A tram to Eccles and a tram to Didsbury both leave Piccadilly at 9 a.m.
At what time will a tram to Eccles and a tram to Didsbury next leave Piccadilly at the same time?
.......................................................
(Total for Question 4 is 3 marks)
___________________________________________________________________________
5. Greg sells car insurance and home insurance.
The table shows the cost of these insurances.
|Insurance |car insurance |home insurance |
|Cost |£200 |£350 |
Each month Greg earns
£530 basic pay
5% of the cost of all the car insurance he sells
and 10% of the cost of all the home insurance he sells
In May Greg sold
6 car insurances
and 4 home insurances
Work out the total amount of money Greg earned in May.
£ ....................................
(Total for Question 5 is 5 marks)
___________________________________________________________________________
*6. The diagram shows the floor of a village hall.
[pic]
The caretaker needs to polish the floor.
One tin of polish normally costs £19.
One tin of polish covers 12 m2 of floor.
There is a discount of 30% off the cost of the polish.
The caretaker has £130.
Has the caretaker got enough money to buy the polish for the floor?
You must show all your working.
(Total for Question 6 is 5 marks)
___________________________________________________________________________
*7.
|Competition |
| |
|a prize every 2014 seconds |
In a competition, a prize is won every 2014 seconds.
Work out an estimate for the number of prizes won in 24 hours.
You must show your working.
(Total for Question 7 is 4 marks)
___________________________________________________________________________
*8. 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.
[pic]
(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 8 is 4 marks)
___________________________________________________________________________
9. ABC is a triangle.
[pic]
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.
.............................................. cm
(Total for Question 9 is 5 marks)
___________________________________________________________________________
*10.
[pic]
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 10 is 4 marks)
___________________________________________________________________________
*11.
[pic]
ABC is parallel to EFGH.
GB = GF
Angle ABF = 65°
Work out the size of the angle marked x.
Give reasons for your answer.
(Total for Question 11 is 4 marks)
___________________________________________________________________________
12. The diagram shows part of a pattern made from tiles.
[pic]
The pattern is made from two types of tiles, tile A and tile B.
Both tile A and tile B are regular polygons.
Work out the number of sides tile A has.
.................................................
(Total for Question 12 is 4 marks)
___________________________________________________________________________
*13.
[pic]
A, B, C and D are points on the circumference of a circle, centre O.
Angle AOC = y.
Find the size of angle ABC in terms of y.
Give a reason for each stage of your working.
(Total for Question 13 is 4 marks)
___________________________________________________________________________
14. Fiza has 10 coins in a bag.
There are three £1 coins and seven 50 pence coins.
Fiza takes at random, 3 coins from the bag.
Work out the probability that she takes exactly £2.50.
..............................................
(Total for Question 14 is 4 marks)
___________________________________________________________________________
15. OACB is a parallelogram.
[pic]
[pic] = a and [pic] = b.
D is the point such that [pic] = [pic].
The point N divides AB in the ratio 2 : 1.
(a) Write an expression for [pic] in terms of a and b.
..............................................
(3)
*(b) Prove that OND is a straight line.
(3)
(Total for Question 15 is 6 marks)
___________________________________________________________________________
16.
[pic]
ABCD is a square with a side length of 4x.
M is the midpoint of DC.
N is the point on AD where ND = x.
BMN is a right-angled triangle.
Find an expression, in terms of x, for the area of triangle BMN.
Give your expression in its simplest form.
..........................................
(Total for Question 16 is 4 marks)
___________________________________________________________________________
17. Sumeet has a pond in the shape of a prism.
[pic]
The pond is completely full of water.
Sumeet wants to empty the pond so he can clean it.
Sumeet uses a pump to empty the pond.
The volume of water in the pond decreases at a constant rate.
The level of the water in the pond goes down by 20 cm in the first 30 minutes.
Work out how much more time Sumeet has to wait for the pump to empty the pond completely.
..............................................
(Total for Question 17 is 6 marks)
___________________________________________________________________________
18. The diagram shows a solid shape.
[pic]
The solid shape is made from a cylinder and a hemisphere.
The radius of the cylinder is equal to the radius of the hemisphere.
The cylinder has a height of 10 cm.
The curved surface area of the hemisphere is 32π cm2.
Work out the total surface area of the solid shape.
Give your answer in terms of π.
.......................................... cm2
(Total for Question 18 is 5 marks)
___________________________________________________________________________
TOTAL FOR PAPER IS 78 MARKS
|1MA0/1H – AO2/AO3 Practice Paper |
|Question |Working |Answer |Mark |Notes | |
| |(ii) | |60 | |B1 for 60 or ft from their correct answer in (i) or ft ‘common multiple’ |
|2 |(a) | |2 reasons |2 |B2 for 2 different reasons from given examples |
| | | | | |(B1 for 1 reason from given examples) |
| | | | | |eg No time frame |
| | | | | |eg No box for less than £10 accept no box for zero or none or £0 |
| | | | | |eg Overlapping intervals or boxes or £30 and/ or £50 in two boxes |
| |(b) | |1 reason |1 |C1 for reason why the sample is biased eg |
| | | | | |they are only in the CD store, |
| | | | | |the people in the store are more likely to buy CDs |
| | | | | |she needs to ask people outside the store oe |
|*3 | | |3 |4 |M1 for a method to calculate at least one area eg 10 × 7 (=70) or 16 × 10 (=160) |
| | | | | |M1 for a method to find the total area (=124) |
| | | | | |M1 (dep on M1) for “124” ÷ 36 |
| | | | | |C1 (dep on M3) for 3 (pigs) clearly identified and supported by correct calculations |
| | | | | |OR |
| | | | | |M1 for an area of 36m² drawn with dimensions shown |
| | | | | |M1 for 3 areas of 36m² drawn with dimensions shown |
| | | | | |M1 (dep on M1) for method to find the area left (=16) |
| | | | | |C1 (dep on M3) for 3 (pigs) clearly identified and supported by correct calculations |
|Question |Working |Answer |Mark |Notes | |
|5 | | |730 |5 |M1 for [pic] ( = 10) oe |
| | | | | |M1 for [pic] ( = 35) oe |
| | | | | |M1 for 6 × ‘10’ or 4 × ‘35’ |
| | | | | |M1 (dep on M1 earned for a correct method for a percentage calculation) for “60” + “140”+ 530|
| | | | | | |
| | | | | |A1 cao |
| | | | | | |
| | | | | |OR |
| | | | | |M1 for 6 × 200 (= 1200) or 4 × 350 (= 1400) |
| | | | | |M1 for [pic] oe |
| | | | | |M1 for [pic]oe |
| | | | | |M1(dep on M1 earned for a correct method for a percentage calculation) for “60” + “140”+ 530 |
| | | | | |A1 cao |
|Question |Working |Answer |Mark |Notes | |
|*7 | | |Answer in range |4 |M1 for a method to either find the exact or approximate number of seconds in one day, e.g. |
| | | |35 – 50 | |24 × 60 × 60 (=86400) or the number of minutes in 2014 seconds, e.g. 2014 ÷ 60 or 2000 ÷ 60 |
| | | | | |(≈30) |
| | | | | |M1 for a correct method to find the number of prizes; eg. ‘24 × 60 × 60’ ÷ 2014 oe or 60 ÷ |
| | | | | |“30” × 24 oe |
| | | | | |B1 for rounding at least one appropriate value in the working to 1 sf, e.g. 24 rounded to 20 |
| | | | | |or 2014 rounded to 2000 or 86400 rounded to 90000 |
| | | | | |C1 (dep on M2) for answer in 35 – 50 clearly identified |
|Question|Working|Answer |Mark |Notes | |
| |(b) | |Ed is cheaper up to 20 miles, |3 |M1 for correct line for Ed intersecting at (20,30) ±1 sq tolerance or |
| | | |Bill is cheaper for more than 20 | |10 + x = 1.5x oe |
| | | |miles | |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 ≤ 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 |
| | |Miles | | |(C1 (dep on M1) for a correct conclusion |
| | |0 | | |eg. cheaper at 10 miles with Ed; eg. cheaper at 50 miles with Bill |
| | |10 | | |eg. same cost at 20 miles; eg for £5 go further with Bill OR |
| | |20 | | |A general statement covering short and long distances eg. Ed is cheaper for shorter |
| | |30 | | |distances and Bill is cheaper for long distances) |
| | |40 | | | |
| | |50 | | |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 |
| | |Ed | | | |
| | |0 | | |QWC: Decision and justification should be clear with working clearly presented and |
| | |15 | | |attributable |
| | |30 | | | |
| | |45 | | | |
| | |60 | | | |
| | |75 | | | |
| | | | | | |
| | |Bill | | | |
| | |10 | | | |
| | |20 | | | |
| | |30 | | | |
| | |40 | | | |
| | |50 | | | |
| | |60 | | | |
| | | | | | |
|9 | | |38 |5 |M1 3x ( 5 = 19 – x |
| | | | | |M1 for a correct operation to collect the x terms or the number terms on one side of an |
| | | | | |equation of the form ax + b = cx + d |
| | | | | |A1 for x = 6 |
| | | | | |M1 for substituting their value of x in the three expressions and adding or substituting |
| | | | | |their value of x after adding the three expressions |
| | | | | |A1 cao |
|Question |Working |Answer |Mark |Notes | |
|Question |Working |Answer |Mark |Notes | |
|12 | | |12 |4 |B1 for 60 seen |
| | | | | |M1 for (360 – 60) ÷ 2 (=150) |
| | | | | |M1 for 360 ÷ (180 – 150) or 150×n=180(n-2) oe |
| | | | | |A1 cao |
| | | | | | |
| | | | | |OR |
| | | | | |B1 for 60 seen |
| | | | | |M1 for 60 ÷ 2 (=30) |
| | | | | |M1 for 360 ÷ (60÷2) |
| | | | | |A1 cao |
| | | | | | |
| | | | | |OR |
| | | | | |M2 for 30 seen |
| | | | | |M1 for 360 ÷ 30 |
| | | | | |A1 cao |
| | | | | | |
|Question |Working |Answer |Mark |Notes | |
|14 | |50 1 1 |[pic] |4 |M1 for 3 fractions [pic]where a < 10, b < 9 |
| | |1 50 1 | | |and c < 8 |
| | |1 1 50 | | |M1 for [pic] or [pic] or [pic] (=[pic] |
| | | | | | |
| | | | | |M1 for [pic] + [pic] [pic] + [pic] [pic] |
| | | | | | |
| | | | | |or 3 × [pic] |
| | | | | | |
| | | | | |A1 for [pic] oe. eg. [pic] |
| | | | | | |
| | | | | |Alternative Scheme for With Replacement |
| | | | | |M1 for [pic] (=[pic] |
| | | | | | |
| | | | | |M1 for [pic] × 3 (=[pic] |
| | | | | |M0 A0 No further marks |
|Question |Working |Answer |Mark |Notes | |
| |(b) |[pic]=[pic]+[pic]+[pic] |Proof |3 |M1 for a correct vector statement for [pic]or[pic]in terms of a and b, e.g. [pic] = a + b|
| | |= a + b + b | | |+ b oe or [pic]= [pic]((b + a) + b + b oe |
| | |= a + 2b | | |A1 for correct and fully simplified vectors for [pic](may be seen in (a)) and for [pic](=|
| | |[pic]= 3([pic]a+[pic]b ) | | |a + 2b) or [pic](=[pic]a + [pic]b) |
| | |[pic] = 3[pic] | | |C1 (dep on A1) for statement that [pic] or [pic] is a multiple of [pic] (+ common point)|
|Question |Working |Answer |Mark |Notes | |
|17 | | |1 hour 45 mins |6 |M1 for method to find volume of pond, |
| | | | | |eg [pic](1.3 + 0.5) × 2 × 1 (= 1.8) |
| | | | | |M1 for method to find the volume of water emptied |
| | | | | |in 30 minutes, eg 1 × 2 × 0.2 (= 0.4), 100 × 200 × 20 (= 400000) |
| | | | | |A1 for correct rate, eg 0.8 m³/hr, 0.4 m³ in 30 minutes |
| | | | | |M1 for correct method to find total time taken to empty the pond, |
| | | | | |eg “1.8” ÷ “0.8” |
| | | | | |M1 for method to find extra time, |
| | | | | |eg 2 hrs 15 minutes − 30 minutes |
| | | | | |A1 for 1.75 hours, 1[pic] hours, 1 hour 45 mins or 105 mins |
| | | | | |OR |
| | | | | |M1 for method to find volume of water emptied |
| | | | | |in 30 minutes,.eg. 1 × 2 × 0.2 (= 0.4), |
| | | | | |100 × 200 × 20 (= 400000) |
| | | | | |M1 for method to work out rate of water loss eg. “0.4” × 2 |
| | | | | |A1 for correct rate, eg 0.8 m³/hr |
| | | | | |M1 for correct method to work out remaining volume of water |
| | | | | |eg. [pic] (1.1 + 0.3) × 2 × 1 (= 1.4) |
| | | | | |M1 for method to work out time, eg “1.4” ÷ “0.8” |
| | | | | |A1 for 1.75 hours, 1[pic] hours, 1 hour 45 mins or 105 mins |
| | | | | |NB working could be in 3D or in 2D and in metres or cm throughout |
|18 | | |128π |5 |M1 for [pic] = 32π oe |
| | | | | |A1 for (r =) 4 |
| | | | | |M1 for 2×π×"4"×10 (=80π) or π×"4"2 (=16π) or ft their r |
| | | | | |M1 for 32π + "80π" + "16π" oe or 402.1 −402.3 or ft their r |
| | | | | |A1 cao |
Results Plus data for AO2/AO3 Practice Paper 1H:
Qu. No. |Series |Question |Spec ref |Score |Marks |AO2 |AO3 |Percent | |1 |Nov-13 |7 |Nc |3.50 |4 |3 |1 |87.5 | |2 |Mar-13 |3 |SPc,SPb |2.48 |3 |2 |1 |82.7 | |3 |Jun-14 |7 |GMx, Na |3.13 |4 |2 |2 |78.3 | |4 |Mar-13 |8 |Nc,GMo |2.27 |3 |2 |1 |75.7 | |5 |Mar-13 |11 |Na,Nm,No |3.60 |5 |4 |1 |72.0 | |6 |Nov-13 |10 |GMx,Na |3.21 |5 |3 |2 |64.2 | |7 |Jun-14 |13 |Nu, GMp |1.75 |4 |2 |2 |43.8 | |8 |Jun-12 |3 |As |1.68 |4 |2 |2 |42.0 | |9 |Nov-13 |8 |Ad,Af |1.55 |5 |2 |3 |31.0 | |10 |Mar-13 |10 |GMa,GMb |1.08 |4 |3 |1 |27.0 | |11 |Nov-14 |8 |Gma, GMb |0.95 |4 |2 |2 |23.8 | |12 |Nov-12 |18 |GMa,GMb,GMc |0.92 |4 |2 |2 |23.0 | |13 |Nov-13 |22 |GMj,Ab |0.65 |4 |2 |2 |16.3 | |14 |Jun-13 |26 |SPq |0.63 |4 |3 |1 |15.8 | |15 |Nov-13 |24 |GMcc |0.74 |6 |3 |3 |12.3 | |16 |Jun-13 |20 |GMx |0.46 |4 |2 |2 |11.5 | |17 |Jun-13 |17 |GMaa |0.51 |6 |3 |3 |8.5 | |18 |Nov-14 |20 |GMz, GMbb |0.19 |5 |2 |3 |3.8 | | | | | |29.30 |78 |44 |34 |37.6 | |
-----------------------
AO2/AO3 Practice Papers
Higher Tier
1 hour 20 minutes
1MA0 / 1H
10
20
30
40
5
10
15
20
25
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