Edexcel GCSE Mathematics November 2015 - Paper 1

Questions and Worked Solutions for Edexcel GCSE Mathematics November 2015 Paper 1 (No Calculator).

Edexcel GCSE Mathematics November 2015 Past Paper 1 (Pdf)

Edexcel GCSE November 2015 Paper 1 (No Calculator) Solutions for Questions 1 - 22

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1. Sean wants to go on holiday.
   He is going to get a loan of £ 720 to help pay for the holiday.
   Sean will have to pay back the £ 720 plus interest of 15 %.
   He will pay this back in 12 equal monthly installments.
   How much money will Sean pay back each month?
2. Use the fact that
   5.4 × 36 = 194.4
   to find the value of
   (i) 5.4 × 3.6
   (ii) 54 × 360
3. Here are the first four terms of an arithmetic sequence.
   11, 17, 23, 29 (a) Find, in terms of n, an expression for the nth term of this arithmetic sequence.
   (b) Is 121 a term of this arithmetic sequence?
   You must explain your answer.
4. There are some black pens, some blue pens, some red pens and some green pens in a box.
   The table shows the probabilities that a pen taken at random from the box will be black or will be blue or will be red.
   There are 200 pens in the box.
   (a) Work out the number of black pens in the box.
   A pen is taken at random from the box.
   (b) Work out the probability that the pen will be green.
5. Here are the ingredients needed to make 8 shortbread biscuits.
   Tariq is going to make some shortbread biscuits.
   He has the following ingredients
   330 g butter, 200 g caster sugar, 450 g flour
   Work out the greatest number of shortbread biscuits that Tariq can make with his ingredients.
   You must show all your working.
6. ABCD and EFG are parallel lines.
   BC = CF
   Angle BFE = 70°
   Work out the size of the angle marked x.
   Give reasons for each stage of your working.
7. Martin wants to find out how often students use the local tram service.
   He uses this question on a questionnaire.
   How often do you use the local tram service?
   (a) Write down two things wrong with this question.
   (b) Design a better question for a questionnaire for Martin to find out how often students use the local tram service.
8. Milk is sold in 1/2 pint bottles, in 1 pint bottles and in 2 pint bottles.
   One weekend a shop sold 100 bottles of milk.
   46 of the bottles were sold on Sunday.
   15 of the bottles sold on Sunday were 2 pint bottles.
   31 of the bottles sold on Saturday were 1/2 pint bottles.
   22 of the bottles sold were 2 pint bottles.
   30 of the bottles sold were 1 pint bottles.
   How many 1 pint bottles were sold on Sunday?
9. The diagram shows a container for oil.
   The container is in the shape of a cuboid.
   The container is empty.
   Sally has to fill the container with oil.
   A bottle of oil costs £ 3.50
   There are 3000 cm³ of oil in each bottle.
   Sally must not spend more than £ 60 buying the oil.
   Can Sally buy enough oil to fill the container?
   You must show all your working
10. (a) Expand x(x + 2)
    (b) Expand and simplify 3(y + 2) + 4(x – 1)
    (c) Expand and simplify (2t - t)(t + 5)
    (d) Factorise fully 8a² + 12a
    (e) Factorise y² – y – 2

11. Manchester airport is on a bearing of 330° from a London airport.
    (a) Find the bearing of the London airport from Manchester airport.
    The London airport is 200 miles from Manchester airport.
    A plane leaves Manchester airport at 10 am to fly to the London airport.
    The plane flies at an average speed of 120 mph.
    (b) What time does the plane arrive at the London airport?
    
12. (a) Complete the table of values for y = x² – 3x + 2
    (b) On the grid, draw the graph of y = x² – 3x + 2 for values of x from –1 to 5
    (c) Find estimates for the solutions of the equation x² – 3x + 2 = 4
    
13. There are 18 packets of sweets and 12 boxes of sweets in a carton.
    The mean number of sweets in all the 30 packets and boxes is 14
    The mean number of sweets in the 18 packets is 10
    Work out the mean number of sweets in the boxes.
    
14. ABCDEFGH is a regular octagon.
    KLQFP and MNREQ are two identical regular pentagons.
    Work out the size of the angle marked x.
    You must show all your working
    15 Sue works for a company that delivers parcels.
    One day the company delivered 80 parcels.
    The table shows information about the weights, in kg, of these parcels.
    (a) Complete the cumulative frequency table.
    (b) On the grid opposite, draw a cumulative frequency graph for your table.
    Sue says,
    “75 % of the parcels weigh less than 3.4 kg.”
    (c) Is Sue correct?
    You must show how you get your answer
    
15. ABCD is a trapezium.
    STUV is a rectangle.
    All measurements are in centimetres.
    The two shapes have the same perimeter.
    Work out the length of ST.
    
16. Solve
    2x + 3y = 2/3
    3x – 4y = 18
    
17. Rationalise the denominator of 10/√5
    Give your answer in its simplest form.
    
18. The diagram shows a solid shape.
    The solid shape is made from a hemisphere and a cone.
    The radius of the hemisphere is equal to the radius of the base of the cone.
    The cone has a height of 10 cm.
    The volume of the cone is 270πcm³.
    Work out the total volume of the solid shape.
    Give your answer in terms of π.
    
19. ACEF is a parallelogram.
    B is the midpoint of AC.
    M is the midpoint of BE.
    CB = a
    ED = b
    DC = 2b
    Show that AMD is a straight line.
    
20. (a) Write as a single fraction in its simplest form 5/(2 - x) - 4/x
    (b) Make y the subject of the formula
    
21. A, B, D and E are points on a circle.
    ABC and EDC are straight lines.
    Prove that triangle BCD is similar to triangle ECA.
    You must give reasons for your working.

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