Edexcel Jan 2022 IGCSE 4MA1/1HR

Edexcel Jan 2022 IGCSE, 4MA1/1HR questions (pdf)

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1. n is an integer.
   (a) Write down all the values of n such that –2 ≤ n < 3
   (b) On the number line, represent the inequality y ≤ 1
2. Each time John plays a game, the probability that he wins the game is 0.65
   John is going to play the game 300 times.
   Work out an estimate for the number of games that John wins.
3. The shaded shape is made using three identical right-angled triangles and a square.
   Work out the perimeter of the shaded shape.
4. (a) Complete the table of values for y = x² – 4x + 3
   (b) On the grid, draw the graph of y = x² – 4x + 3 for values of x from –2 to 4
5. Yusuf sat 8 examinations.
   Here are his marks for 5 of the examinations.
   68 72 75 77 80
   For his results in all 8 examinations
   the mode of his marks is 80
   the median of his marks is 74
   the range of his marks is 16
   Find Yusuf’s marks for each of the other 3 examinations.

6. (a) Work out the lowest common multiple (LCM) of 36 and 120
7. Milly went on a car journey.
   She travelled from Anesey to Breigh to Clando and then to Duckbridge.
   For Anesey to Breigh, Milly drove the 245km in 2.5 hours.
   For Breigh to Clando, Milly drove the 220km at an average speed of 80 km/h
   For Clando to Duckbridge, Milly drove at an average speed of 72km/h in 50 minutes.
   Work out Milly’s average speed, in km/h, for the journey from Anesey to Duckbridge.
   Give your answer correct to one decimal place.
8. (a) Write 5 × 10⁴ as an ordinary number.
   (b) Write 0.00006 in standard form.
9. (a) Simplify x⁴ × x⁵
10. Jonty has a storage container in the shape of a cuboid, as shown in the diagram.
    Jonty is going to paint the outside of his storage container, apart from the base which is shown shaded in the diagram.
    He needs enough paint to cover the four sides and the top.
    Each tin of paint covers an area of 15m²
    The cost of each tin of paint recently increased by 10%
    After the increase, the cost of each tin of paint is £26.95
    Jonty says
    “Before the increase, I could have bought enough paint for less than £200”
    Show that Jonty is correct.
    Show your working clearly
11. The diagram shows sector OPQ of a circle, centre O
    OP = OQ = 7.1 cm
    Angle POQ = 110°
    Calculate the area of sector OPQ
    Give your answer correct to one decimal place.
12. (a) Expand and simplify n(n – 4)(3n + 5)
13. Hector has a bag that contains 12 counters.
    There are 7 green counters and 5 red counters in the bag.
    Hector takes at random a counter from the bag.
    He looks at the counter and puts the counter back into the bag.
    Hector then takes at random a second counter from the bag.
    He looks at the counter and puts the counter back into the bag.
    (a) Complete the probability tree diagram.
    14.A, B, C and D are points on a circle, centre O
    AOC is a diameter of the circle.
    Angle BAC = 55°
    Work out the size of angle ADB
    Give a reason for each stage of your working.
14. Using algebra, prove that, given any 3 consecutive whole numbers, the sum of the square of the smallest number and the square of the largest number is always 2 more than twice the square of the middle number
15. An arithmetic series has first term 1 and common difference 4
    Find the sum of all terms of the series from the 41st term to the 100th term inclusive.
16. The Venn diagram shows a universal set E and three sets A, B and C
17. The three solids A, B and C are similar such that
    the surface area of A : the surface area of B = 4 : 9
    and
    the volume of B : the volume of C = 125 : 343
    Work out the ratio
    the height of A : the height of C
    Give your ratio in its simplest form
18. Given that
19. The curve with equation y = f(x) has one turning point.
    The coordinates of this turning point are (– 6, – 4)
    (a) Write down the coordinates of the turning point on the curve with equation
    (i) y = f(x) + 5
20. The histogram gives information about the weights, in kg, of all the watermelons in a field.
    There are 16 watermelons with a weight between 8kg and 8.5 kg
    Work out the total number of watermelons in the field
21. The diagram shows triangle ABC
22. Two particles, P and Q, move along a straight line.
    The fixed point O lies on this line.
23. OXYZ is a trapezium.

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