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MathematicsYear 11English

Cambridge IGCSE Mathematics 0580 Paper 4 Extended Sample 2023

This paper is designed to mirror the challenge and breadth of the real Paper 4 Extended exams—testing whether you can move fluently from pure geometry to applied calculations under time pressure. You'll face a mix of coordinate geometry, mensuration, trigonometry, and algebraic problem-solving across 15 questions, mostly multiple choice with a few fill-in-the-blank items to keep you sharp. It's built for Year 11 students preparing for the IGCSE extended tier, where marks often hinge on spotting the right formula and avoiding calculation slips. Work through this paper and you'll gain the muscle memory to spot whether a problem wants Pythagoras, trigonometry, or coordinate methods—and finish with at least 5 extra marks you weren't expecting.

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  1. Question 1

    The line passing through points A(2,5)A(2, 5) and B(6,13)B(6, 13) has gradient mm. What is the value of mm?

  2. Question 2

    Find the distance between the points P(−1,3)P(-1, 3) and Q(2,7)Q(2, 7).

  3. Question 3

    The equation of a line is 2y−4x=62y - 4x = 6. What is the gradient of this line?

  4. Question 4

    A right-angled triangle has an angle of 35°35° and the side opposite to this angle is 77 cm. Using the sine rule, what is the length of the hypotenuse?

  5. Question 5

    A cylinder has radius 33 cm and height 1010 cm. What is its volume in cubic centimetres?

  6. Question 6

    A bearing of N40°EN 40° E from point AA to point BB means:

  7. Question 7

    Solve the simultaneous equations: x+2y=5x + 2y = 5 and 2x−y=52x - y = 5.

  8. Question 8

    A circle has equation (x−3)2+(y+1)2=16(x - 3)^2 + (y + 1)^2 = 16. What is the radius?

  9. Question 9

    The area of a rectangle is 120120 cm² and its width is 88 cm. What is its perimeter?

  10. Question 10

    Solve the quadratic inequality x2−5x+6>0x^2 - 5x + 6 > 0.

  11. Question 11

    A cone has base radius 55 cm and slant height 1313 cm. What is its curved surface area?

  12. Question 12

    Two sides of a triangle are 77 cm and 99 cm, and the included angle is 60°60°. Using the cosine rule, find the third side.

  13. Question 13

    The midpoint of the line segment joining (−4,2)(−4, 2) and (6,8)(6, 8) is:

  14. Question 14

    A sphere has radius 66 cm. What is its surface area?