Edexcel Jan 2019 IGCSE 4MA1/1H

Edexcel Jan 2019 IGCSE, 4MA1/1H (pdf)

• Show Step-by-Step Solutions

1. (a) Factorise fully 4p + 6pq
   (b) Expand and simplify (e + 3)(e – 5)
   (c) Solve y = (2y + 1)/5
   Show clear algebraic working
   
2. (a) Describe fully the single transformation that maps triangle A onto triangle B
   (b) On the grid, translate triangle A by the vector
   Label the new triangle C.
   (c) On the grid, enlarge triangle D with scale factor 1/2 and centre (-4,2)
   
3. Here is a biased 5-sided spinner.
   When the spinner is spun, it can land on red, blue, green, brown or yellow.
   The table gives the probabilities that the spinner lands on red or on blue or on green.
   When the spinner is spun once, the probability that the spinner lands on brown is 0.06 more than the probability that the spinner lands on yellow.
   Jenine spins the spinner 150 times.
   Work out an estimate for the number of times the spinner lands on yellow.
   
4. The table gives information about the price of gold
   (a) Work out the percentage increase in the price of gold between 1st February 2016 and 1st March 2016
   Give your answer correct to 3 significant figures.
   The price of one ounce of gold on 1st February 2016 was 1126.50 dollars.
   The price of gold increased by 19% from 1st February 2016 to 1st July 2016
   (b) Work out the price of one ounce of gold on 1st July 2016
   Give your answer correct to the nearest dollar.

5. BCD and AFE are straight lines.
   Show that BCD is parallel to AFE.
   Give reasons for your working.
   
6. (a) Complete the table of values for y = x² – 5x + 6
   (b) On the grid, draw the graph of y = x² – 5x + 6 for 0 ≤ x ≤ 5
   (c) By drawing a suitable straight line on the grid, find estimates for the solutions of the equation
   x² – 5x = x – 7
   
7. The table shows the volumes, in km³, of four oceans.
   (a) Write 7.18 x 10⁷ as an ordinary number
   (b) Calculate the total volume of these four oceans.
   The volume of the South China Sea is 9880 000 km³
   (c) Write 9880 000 in standard form
   
8. The diagram shows an isosceles triangle.
   The area of the triangle is 12 cm²
   Work out the perimeter of the triangle.
   Give your answer correct to 3 significant figures
   
9. The table shows information about the speeds of 60 cycles.
   (a) Complete the cumulative frequency table
   (b) On the grid, draw a cumulative frequency graph for your table.
   (c) Use your graph to find an estimate for the interquartile range of the speeds
   
10. Here is triangle ABD.
    The point C lies on BD.
    AD = 13 cm
    BC = 8cm
    angle ADB = 90°
    angle CAD = 20°
    Calculate the size of angle BAC.
    Give your answer correct to 1 decimal place.
    
11. Express 5/3 - (x+2)/2x as a single fraction in its simplest terms
    
12. The curve C has equation y = 1/3 x³ - 9x + 1
    (a) Find dy/dx
    (b) Find the range of values of x for which C has a negative gradient.
    
13. All the students in Year 11 at a school must study at least one of Geography (G), History (H) and Religious Studies (R).
    In Year 11 there are 65 students.
    Of these students
    15 study Geography, History and Religious Studies
    21 study Geography and History
    16 study Geography and Religious Studies
    30 study Geography
    18 study only Religious Studies
    37 study Religious Studies
    (a) Using this information, complete the Venn diagram to show the number of students in each region of the Venn diagram.
    A student in Year 11 who studies both History and Religious Studies is chosen at random.
    (b) Work out the probability that this student does not study Geography
    
14. T is directly proportional to the cube of r
    T = 21.76 when r = 4
    (a) Find a formula for T in terms of r
    (b) Work out the value of T when r = 6
    
15. The total surface area of a solid hemisphere is equal to the curved surface area of a cylinder.
    The radius of the hemisphere is r cm.
    The radius of the cylinder is twice the radius of the hemisphere.
    Given that
    volume of hemisphere : volume of cylinder = 1 :m
    find the value of m.
    
16. (a) Rationalise the denominator of
    where a is an integer and b is a prime number.
    Simplify your answer.
    (b) Given that where x ≠ y
    find the value of m.
    
17. Here is triangle ABC.
    Calculate the value of x.
    Give your answer correct to 3 significant figures
    
18. The graph of y = f(x) is shown on the grid
    (a) On the grid above, sketch the graph of y = f(1/2 x)
    The graph of y = f(x + k) is shown on the grid below
    (b) Write down the value of k
    
19. g is the function with domain x ≥ –3 such that g(x) = x² + 6x
    (a) Write down the range of g^-1
    (b) Express the inverse function g^-1 in the form g^-1 : x
    
20. A bowl contains n pieces of fruit.
    Of these, 4 are oranges and the rest are apples.
    Two pieces of fruit are going to be taken at random from the bowl.
    The probability that the bowl will then contain (n – 6) apples is 1/3
    Work out the value of n
    Show your working clearly.
    
21. (2x + 23), (8x + 2) and (20x – 52) are three consecutive terms of an arithmetic sequence.
    Prove that the common difference of the sequence is 12

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