# 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 22 questions on this paper; the total mark is 76

• 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 22 questions are 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 TWENTY TWO questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

You must NOT use a calculator.

1. Mr Brown and his 2 children are going to London by train.

An adult ticket costs £24.

A child ticket costs £12.

Mr Brown has a Family Railcard.

|Family Railcard gives |

|[pic]off adult tickets |

|60% off child tickets |

Work out the total cost of the tickets when Mr Brown uses his Family Railcard.

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

(Total for Question 1 is 4 marks)

___________________________________________________________________________

2. Each day a company posts some small letters and some large letters.

The company posts all the letters by first class post.

The tables show information about the cost of sending a small letter by first class post

and the cost of sending a large letter by first class post.

Small Letter Large Letter

|Weight |First Class Post | |Weight |First Class Post |

| | | |101–250 g |£1.50 |

| | | |251–500 g |£1.70 |

| | | |501–750 g |£2.50 |

One day the company wants to post 200 letters.

The ratio of the number of small letters to the number of large letters is 3 : 2.

70% of the large letters weigh 0–100 g.

The rest of the large letters weigh 101–250 g.

Work out the total cost of posting the 200 letters by first class post.

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

(Total for Question 2 is 5 marks)

___________________________________________________________________________

3.

[pic]

Describe fully the single transformation that maps triangle A onto triangle B.

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

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

(Total for Question 3 is 3 marks)

___________________________________________________________________________

4. Ria is going to buy a caravan.

The total cost of the caravan is £7000 plus VAT at 20%.

Ria pays a deposit of £3000.

She pays the rest of the total cost in 6 equal monthly payments.

Work out the amount of each monthly payment.

£..............................

(Total for Question 4 is 4 marks)

___________________________________________________________________________

*5. One sheet of paper is 9 × 10–3 cm thick.

Mark wants to put 500 sheets of paper into the paper tray of his printer.

The paper tray is 4 cm deep.

Is the paper tray deep enough for 500 sheets of paper?

You must explain your answer.

(Total for Question 5 is 3 marks)

___________________________________________________________________________

6. The diagram shows a garden in the shape of a rectangle.

[pic]

All measurements are in metres.

The perimeter of the garden is 32 metres.

Work out the value of x.

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

(Total for Question 6 is 4 marks)

___________________________________________________________________________

*7. Here is a map.

The position of a ship, S, is marked on the map.

[pic]

Scale 1 cm represents 100 m

Point C is on the coast.

Ships must not sail closer than 500 m to point C.

The ship sails on a bearing of 037°

Will the ship sail closer than 500 m to point C?

You must explain your answer.

(Total for Question 7 is 3 marks)

___________________________________________________________________________

*8. Here is part of Gary’s electricity bill.

| |

|Electricity bill |

| |

|New reading 7155 units |

|Old reading 7095 units |

| |

|Price per unit 15p |

Work out how much Gary has to pay for the units of electricity he used.

(Total for Question 8 is 4 marks)

___________________________________________________________________________

9.

[pic]

Describe fully the single transformation that maps shape P onto shape Q.

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

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

(Total for Question 9 is 3 marks)

___________________________________________________________________________

10. Margaret has some goats.

The goats produce an average total of 21.7 litres of milk per day for 280 days.

Margaret sells the milk in [pic] litre bottles.

Work out an estimate for the total number of bottles that Margaret will be able to fill with

the milk.

You must show clearly how you got your estimate.

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

(Total for Question 10 is 3 marks)

___________________________________________________________________________

11. AB is a line segment.

A is the point with coordinates (3, 6, 7).

The midpoint of AB has coordinates (–2, 2, 5).

Find the coordinates of B.

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

(Total for Question 11 is 2 marks)

___________________________________________________________________________

12. Here is a map.

The map shows two towns, Burford and Hightown.

[pic]

Scale: 1 cm represents 10 km

A company is going to build a warehouse.

The warehouse will be less than 30 km from Burford and less than 50 km from Hightown.

Shade the region on the map where the company can build the warehouse.

(Total for Question 12 is 3 marks)

___________________________________________________________________________

13. Jane has a carton of orange juice.

The carton is in the shape of a cuboid.

[pic]

The depth of the orange juice in the carton is 8 cm.

Jane closes the carton.

Then she turns the carton over so that it stands on the shaded face.

Work out the depth, in cm, of the orange juice now.

.............................................. cm

(Total for Question 13 is 3 marks)

___________________________________________________________________________

14. The diagram shows the plan of a floor.

[pic]

The area of the floor is 138 m2.

Work out the value of x.

(Total for Question 14 is 4 marks)

___________________________________________________________________________

15. Steve has a photo and a rectangular piece of card.

[pic]

The photo is 16 cm by 10 cm.

The card is 30 cm by 15 cm.

Steve cuts the card along the dotted line shown in the diagram below.

[pic]

Steve throws away the piece of card that is 15 cm by x cm.

The piece of card he has left is mathematically similar to the photo.

Work out the value of x.

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

(Total for Question 15 is 3 marks)

___________________________________________________________________________

16. Here is a scale drawing of a rectangular garden ABCD.

[pic]

Scale: 1 cm represents 1 metre.

Jane wants to plant a tree in the garden

at least 5m from point C,

nearer to AB than to AD

and less than 3m from DC.

On the diagram, shade the region where Jane can plant the tree.

(Total for Question 16 is 4 marks)

___________________________________________________________________________

*17.

[pic]

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 17 is 4 marks)

___________________________________________________________________________

*18.

[pic]

OAB is a triangle.

M is the midpoint of OA.

N is the midpoint of OB.

[pic] = m

[pic] = n

Show that AB is parallel to MN.

(Total for Question 18 is 3 marks)

___________________________________________________________________________

19.

[pic]

Shape P is reflected in the line x = –1 to give shape Q.

Shape Q is reflected in the line y = 0 to give shape R.

Describe fully the single transformation that maps shape P onto shape R.

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

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

(Total for Question 19 is 3 marks)

___________________________________________________________________________

20. The diagram shows a solid metal cylinder.

[pic]

The cylinder has base radius 2x and height 9x.

The cylinder is melted down and made into a sphere of radius r.

Find an expression for r in terms of x.

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

(Total for Question 20 is 3 marks)

___________________________________________________________________________

*21. 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 21 is 4 marks)

___________________________________________________________________________

*22. A is the point with coordinates (1, 3).

B is the point with coordinates (4, –1).

The straight line L goes through both A and B.

Is the line with equation 2y = 3x − 4 perpendicular to line L?

You must show how you got your answer.

(Total for Question 22 is 4 marks)

___________________________________________________________________________

TOTAL FOR PAPER IS 76 MARKS

|1MA0/1H – AO3 Practice Paper |

|Question |Working |Answer |Mark |Notes | |

|2 | | |164 |5 |M1 200 ÷ (3+2) (= 40) or an equivalent ratio seen |

| | | | | |M1 (dep) 3 ×‘40’ (= 120) or 2 ×‘40’ (= 80) or 120: 80 or 80:120 |

| | | | | |M1 a complete method to find 70% of their total number of large letters e.g. 0.7 × ‘80’ |

| | | | | |(=56) |

| | | | | |M1 multiplies their three totals by the correct unit price and adds, e.g. 60(p) × ‘120’ + |

| | | | | |(£)1 × ‘56’ + (£)1.50 × ‘24’ |

| | | | | |A1 164 |

|3 | | |Rotation |3 |B1 for rotation |

| | | |180° | |B1 for 180° |

| | | |Centre (3, 3) | |B1 for (3, 3) |

| | | | | | |

| | | |or | |OR |

| | | | | |B1 for enlargement |

| | | |Enlargement | |B1 for scale factor -1 |

| | | |Scale factor -1 | |B1 for (3, 3) |

| | | |Centre (3, 3) | | |

| | | | | |B0 for a combination of transformations |

|4 | | |900 |4 |M1 for 0.2 × 7000 (=1400) or 1.2 × 7000 (=8400) oe |

| | | | | |M1 for 7000 + "1400" − 3000 (=5400) oe |

| | | | | |M1 for "5400" ÷ 6 |

| | | | | |A1 cao |

|Question |Working |Answer |Mark |Notes | |

|6 | | |1.5 |4 |M1 for correct expression for perimeter |

| | | | | |eg. 4 + 3x + x + 6 + 4 + 3x + x + 6 oe |

| | | | | |M1 for forming a 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 a correct equation |

| | | | | |eg. 4 + 3x + x + 6 = 16 oe |

| | | | | |M1 for 4x = 6 or 6 ÷ 4 |

| | | | | |A1 for 1.5 oe |

|*7 | | |Yes with explanation |3 |M1 for bearing ± 2 ( within overlay |

| | | | | |M1 for use of scale to show arc within overlay or line drawn from C to ship’s course with |

| | | | | |measurement |

| | | | | |C1(dep M1) for comparison leading to a suitable conclusion from a correct method |

|*8 | | |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. |

|9 | | |Enlargement, |3 |B1 for enlargement |

| | | |scale factor 2.5, | |B1 for scale factor 2.5 oe |

| | | |centre (0,0) | |B1 for (0,0); accept origin or O |

| | | | | |NB: if two different transformations are stated then 0 marks. |

|10 | |[pic] |12000 |3 |B1 for 20 or 300 used |

| | | | | |M1 for “20” × “300” or [pic] or [pic] , values do not need to be rounded |

| | | | | |A1 for answer in the range 11200 –13200 |

| | | | | | |

| | | | | |SC B3 for 12000 with or without working |

|11 | |(3,6,7) to ((2,2,5) |((7, (2, 3) |2 |M1 for midpoint plus change or complete method for 2 out of 3 coordinates, can be implied |

| | |((5, (4, (2) | | |by 2 correct values |

| | |((2( 5, 2 ( 4, 5 ( 2) | | |A1 cao |

|12 | | |Region shaded |3 |B1 for circle arc of radius 3cm (± 2mm) centre Burford |

| | | | | |B1 for circle arc of radius 5 cm (± 2mm) centre Hightown |

| | | | | |B1 for overlapping regions of circle arcs shaded |

|Question |Working |Answer |Mark |Notes | |

|14 | | |9 |4 |M1 for method to find area of one rectangle, |

| | | | | |eg 15 × 8 (=120) or 15 × 11 (=165) |

| | | | | |M1 (dep) for subtracting from/by given area, |

| | | | | |eg (138 – “120”) (=18) or “165” – 138 (=27) |

| | | | | |M1 for final step from complete method shown, |

| | | | | |eg 15 − "18"÷ 3 or “27” ÷ 3 |

| | | | | |A1 cao |

| | | | | | |

| | | | | |OR |

| | | | | |M1 for a correct expression for the area of one rectangle, |

| | | | | |eg (8 + 3) × (15 − x) or 8 × x |

| | | | | |M1 (dep) for a correct equation |

| | | | | |eg (8 + 3) × (15 − x) + 8 × x = 138 |

| | | | | |M1 for correct method to isolate x, eg 3x = 27 |

| | | | | |A1 cao |

|Question |Working |Answer |Mark |Notes | |

|16 | | |Required region |4 |M1 arc radius 5 cm centre C |

| | | | | |M1 bisector of angle BAD |

| | | | | |M1 line 3 cm from DC |

| | | | | |A1 for correct region identified (see overlay) |

|*17 | |ABO = ADO = 90° |65o |4 |B1 for ABO = 90 or ADO = 90 (may be on diagram) |

| | |(Angle between tangent and radius is | | |B1 for BCD = 65 (may be on diagram) |

| | |90°) | | | |

| | |DOB = 360 – 90 – 90 – 50 | | |C2 for BCD = 65o stated or DCB = 65o stated or angle C = 65o stated with all reasons: |

| | |(Angles in a quadrilateral add up to | | |angle between tangent and radius is 90o; |

| | |360°) | | |angles in a quadrilateral sum to 360o; |

| | |BCD = 130 ÷ 2 | | |angle at centre is twice angle at circumference |

| | |(Angle at centre is twice angle at | | |(accept angle at circumference is half (or [pic] ) the angle at the centre) |

| | |circumference) | | |(C1 for one correct and appropriate circle theorem reason) |

| | | | | |QWC: Working clearly laid out and reasons given using correct language |

| | |OR | | | |

| | |ABD = (180 – 50) ÷ 2 | | |OR |

| | |(Base angles of an isosceles | | | |

| | |triangle) | | |PTO |

| | |BCD = 65 | | | |

| | |(Alternate segment theorem) | | | |

| | | | | |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 |

|*18 | | |Proof |3 |M1 for [pic] (= n – m) |

| | | | | |or [pic] (= m – n) |

| | | | | |or [pic] (= 2n – 2m) or [pic] (= 2m – 2n) |

| | | | | |M1 for [pic]= n – m and [pic]= 2n – 2m oe |

| | | | | |C1 (dep on M1, M1) for fully correct proof, with [pic]= 2[pic] or [pic]is a multiple of |

| | | | | |[pic] |

| | | | | |[SC M1 for [pic]= 0.5n – 0.5m |

| | | | | |and [pic]= n – m |

| | | | | |C1 (dep on M1) for fully correct proof, with [pic]= 2[pic] or [pic]is a multiple of of |

| | | | | |[pic]] |

|19 | |Q at (– 3, 1), (– 6, 1) |Rotation 180° |3 |M1 for showing R correctly on the grid without showing Q or for showing Q and R correctly on|

| | |(–5, 3) (– 3, 3) |about (–1, 0) | |the grid |

| | | | | |A1 for rotation of 180° |

| | |R at (–3, – 1), (–6, – 1), | | |A1 for (centre) (–1, 0) |

| | |(–5, – 3) (–3, –3) | | | |

| | | | | |OR |

| | | | | |M1 for showing R correctly on the grid without showing Q or for showing Q and R correctly on |

| | | | | |the grid |

| | | | | |A1 for Enlargement Scale Factor –1 |

| | | | | |A1 for centre (–1, 0) |

| | | | | |NB Award no marks for any correct answer from an incorrect diagram or any Accuracy marks if |

| | | | | |more than one transformation is given |

|20 | | Vol cylinder = π × (2x)2 × 9x |3x |3 |M1 for sub. into πr2h eg. π × (2x)2 × 9x oe |

| | |= 36πx3 | | |M1 for [pic] oe |

| | | | | |A1 oe eg. [pic] |

| | |[pic] | | | |

| | |r3 = 27x3 | | |NB : For both method marks condone missing brackets around the 2x |

|*21 | |(n + 1)2 – n2 |proof |4 |M1 for any two consecutive integers expressed algebraically |

| | |= n2 + 2n + 1 – n2 = 2n + 1 | | |eg n and n +1 |

| | |(n + 1) + n = 2n + 1 | | | |

| | | | | |M1(dep on M1) for the difference between the squares of ‘two consecutive integers’ expressed|

| | |OR | | |algebraically eg (n + 1)2 – n2 |

| | | | | | |

| | |(n + 1)2 – n2 | | |A1 for correct expansion and simplification of difference of squares, eg 2n + 1 |

| | |= (n + 1 + n)(n + 1 – n) | | | |

| | |= (2n + 1)(1) = 2n + 1 | | |C1 (dep on M2A1) for showing statement is correct, |

| | |(n + 1) + n = 2n + 1 | | |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 | | | |

|22 | |2y = 3x − 4 |No with reason |4 |M1 for [pic]oe or [pic] oe |

| | |y = [pic]x − 2; m = [pic] | | |M1 for method to find gradient of AB, eg [pic] or [pic]or [pic] oe |

| | | | | |A1 for identifying gradients as [pic]oe and [pic] oe |

| | |[pic]=[pic] | | |C1 (dep on M1) for a conclusion with a correct reason, eg No as product of [pic] and [pic] is|

| | |[pic]×[pic]= −2 | | |not −1, ft from their two gradients |

Results Plus data for AO3 Practice Paper 1H:

|Qu. No. |Series |Question |Spec ref |Score |Marks |Percent |

|2 |Nov-13 |11 |Na,No,Nt,SPe |3.03 |5 |60.6 |

|3 |Jun-12 |9 |GMl |1.76 |3 |59.0 |

|4 |Nov-14 |11 |Na, Nm, Nl |2.20 |4 |55.0 |

|5 |Jun-13 |15 |Ng |1.49 |3 |49.7 |

|6 |Jun-13 |10 |Ad |1.93 |4 |48.3 |

|7 |Jun-13 |13 |GMr |1.40 |3 |46.7 |

|8 |Nov-12 |3 |Na |1.85 |4 |46.0 |

|9 |Nov-12 |6 |GMl |1.38 |3 |46.0 |

|10 |Jun-13 |8 |Nu |1.22 |3 |40.7 |

|11 |Nov-13 |17 |Ak |0.80 |2 |40.0 |

|12 |Nov-12 |10 |GMw |1.18 |3 |39.0 |

|13 |Jun-12 |12 |GMaa |1.11 |3 |37.0 |

|14 |Nov-14 |7 |GMx, Ad |1.38 |4 |34.5 |

|15 |Jun-14 |20 |GMf |0.90 |3 |30.0 |

|16 |Mar-13 |15 |GMw,GMm |0.95 |4 |23.8 |

|17 |Jun-12 |21 |GMj |0.89 |4 |22.0 |

|18 |Jun-14 |24 |GMcc |0.59 |3 |19.7 |

|19 |Mar-13 |18 |GMl |0.55 |3 |18.3 |

|20 |Jun-12 |25 |GMbb |0.26 |3 |9.0 |

|21 |Mar-13 |21 |Ab,Ac,Ad |0.11 |4 |2.8 |

|22 |Nov-14 |24 |An |0.10 |4 |2.5 |

| | | | |27.56 |76 |36.26 |

-----------------------

AO3 Practice Papers

1MA0 / 1H

Higher Tier

1 hour 20 minutes

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

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