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Flashcards · Maths

Geometry and Measures

80 cards from 5 lessons

  1. What do angles on a straight line add up to?

    \(180^\circ\).

  2. What do angles around a point add up to?

    \(360^\circ\).

  3. What are vertically opposite angles?

    The equal angles opposite each other where two straight lines cross.

  4. What do the angles in a triangle add up to?

    \(180^\circ\).

  5. What do the angles in a quadrilateral add up to?

    \(360^\circ\).

  6. What is the rule for the exterior angle of a triangle?

    It equals the sum of the two opposite interior angles.

  7. Which angles are equal and form a Z shape between parallel lines?

    Alternate angles.

  8. Which angles are equal and form an F shape between parallel lines?

    Corresponding angles.

  9. Which angles add up to \(180^\circ\) and form a C shape between parallel lines?

    Co-interior angles.

  10. What is the sum of the interior angles of an \(n\)-sided polygon?

    \((n - 2) \times 180^\circ\).

  11. What do the exterior angles of any polygon add up to?

    \(360^\circ\).

  12. What is each exterior angle of a regular polygon with \(n\) sides?

    \(360 \div n\).

  13. How do you find an interior angle of a regular polygon from the exterior angle?

    Subtract the exterior angle from \(180^\circ\).

  14. What is the interior angle of a regular hexagon?

    \(120^\circ\).

  15. A regular polygon has exterior angle \(24^\circ\). How many sides?

    \(360 \div 24 = 15\).

  16. Why must you state the angle fact in an exam?

    Mark schemes award marks for the reason as well as the answer.

  17. What is the formula for the area of a rectangle?

    \(A = l \times w\).

  18. What is the formula for the area of a triangle?

    \(A = \dfrac{1}{2} \times b \times h\).

  19. What is the formula for the area of a parallelogram?

    \(A = b \times h\), using the perpendicular height.

  20. What is the formula for the area of a trapezium?

    \(A = \dfrac{1}{2}(a + b)h\).

  21. How do you find the area of a compound shape?

    Split it into simple shapes and add, or subtract a missing piece from a larger shape.

  22. What is the circumference formula?

    \(C = \pi d = 2\pi r\).

  23. What is the formula for the area of a circle?

    \(A = \pi r^2\).

  24. What is the relationship between diameter and radius?

    The diameter is twice the radius.

  25. What is the area of a circle with radius 5 cm, in terms of \(\pi\)?

    \(25\pi\) cm\(^2\).

  26. What is the circumference of a circle with diameter 14 cm?

    \(14\pi\) cm.

  27. What is an arc?

    A part of the circumference of a circle.

  28. What is a chord?

    A straight line joining two points on a circle.

  29. What is a tangent?

    A line that touches a circle at exactly one point.

  30. What is the area of a semicircle?

    \(\dfrac{1}{2}\pi r^2\).

  31. How do you find the area of a sector (Higher tier)?

    \(\dfrac{\theta}{360} \times \pi r^2\).

  32. What is the perimeter of a sector (Higher tier)?

    The arc length plus two radii.

  33. What is the volume of a cuboid?

    \(l \times w \times h\).

  34. What is the surface area of a cuboid?

    \(2lw + 2lh + 2wh\).

  35. What is the volume of a prism?

    The area of the cross-section multiplied by the length.

  36. What shape is the curved surface of a cylinder when it is opened out?

    A rectangle.

  37. What is the volume of a cylinder?

    \(\pi r^2 h\).

  38. What is the curved surface area of a cylinder?

    \(2\pi r h\).

  39. What is the total surface area of a closed cylinder?

    \(2\pi r h + 2\pi r^2\).

  40. What is the volume of a cylinder with radius 3 cm and height 10 cm?

    \(90\pi\) cm\(^3\).

  41. How many millilitres are in 1 cm\(^3\)?

    1 ml.

  42. What is the volume of a cone (Higher tier)?

    \(\dfrac{1}{3}\pi r^2 h\).

  43. What is the curved surface area of a cone (Higher tier)?

    \(\pi r l\), where \(l\) is the slant height.

  44. What is the volume of a sphere (Higher tier)?

    \(\dfrac{4}{3}\pi r^3\).

  45. What is the surface area of a sphere (Higher tier)?

    \(4\pi r^2\).

  46. What is the volume of a pyramid (Higher tier)?

    \(\dfrac{1}{3} \times\) base area \(\times\) vertical height.

  47. What is a net?

    A flat shape that folds up to make a 3D shape.

  48. How do you find the mass from the density and volume?

    Mass \(=\) density \(\times\) volume.

  49. What is Pythagoras' theorem?

    \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse.

  50. What is the hypotenuse?

    The longest side of a right-angled triangle, opposite the right angle.

  51. How do you find the hypotenuse?

    Square the two shorter sides, add them, then take the square root.

  52. How do you find a shorter side?

    Square the hypotenuse, subtract the square of the other side, then take the square root.

  53. What is a Pythagorean triple?

    Three whole numbers that satisfy \(a^2 + b^2 = c^2\).

  54. Name four Pythagorean triples.

    \(3, 4, 5\), \(5, 12, 13\), \(8, 15, 17\) and \(7, 24, 25\).

  55. What is the hypotenuse for shorter sides 6 cm and 8 cm?

    10 cm.

  56. What is the hypotenuse for shorter sides 9 cm and 12 cm?

    15 cm.

  57. How can you test if a triangle is right-angled?

    Check whether \(a^2 + b^2 = c^2\) for the longest side \(c\).

  58. How do you find the height of an isosceles triangle?

    Split it down the middle and use Pythagoras with half the base.

  59. What is the height of an isosceles triangle with base 10 cm and sides 13 cm?

    12 cm.

  60. Which triangle do you use to find the diagonal of a rectangle?

    The right-angled triangle made by the length, the width and the diagonal.

  61. What is the size of a shorter side if the hypotenuse is 13 and the other side is 5?

    12.

  62. What is \(\sqrt{20}\) in simplest surd form (Higher tier)?

    \(2\sqrt{5}\).

  63. How do you find the distance between two points on a grid (Higher tier)?

    Use the horizontal and vertical differences as the two shorter sides of a right-angled triangle.

  64. How do you find the diagonal of a cuboid (Higher tier)?

    Use Pythagoras twice.

  65. What is the hypotenuse?

    The longest side of a right-angled triangle, opposite the right angle.

  66. What is the opposite side?

    The side across from the angle you are using.

  67. What is the adjacent side?

    The side next to the angle you are using, apart from the hypotenuse.

  68. What is the formula for sine?

    \(\sin\theta = \dfrac{O}{H}\).

  69. What is the formula for cosine?

    \(\cos\theta = \dfrac{A}{H}\).

  70. What is the formula for tangent?

    \(\tan\theta = \dfrac{O}{A}\).

  71. What does SOH CAH TOA stand for?

    Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent.

  72. What is \(\sin 30^\circ\)?

    \(\dfrac{1}{2}\).

  73. What is \(\cos 60^\circ\)?

    \(\dfrac{1}{2}\).

  74. What is \(\tan 45^\circ\)?

    1.

  75. What is \(\sin 45^\circ\) and \(\cos 45^\circ\)?

    Both \(\dfrac{\sqrt{2}}{2}\).

  76. What are \(\sin 60^\circ\) and \(\cos 30^\circ\)?

    Both \(\dfrac{\sqrt{3}}{2}\).

  77. What is \(\tan 60^\circ\)?

    \(\sqrt{3}\).

  78. What is \(\sin 0^\circ\), \(\sin 90^\circ\) and \(\cos 90^\circ\)?

    0, 1 and 0.

  79. How do you find an angle when you know two sides?

    Use the inverse function, such as \(\tan^{-1}\left(\dfrac{O}{A}\right)\).

  80. What is the side opposite a \(30^\circ\) angle in terms of the hypotenuse?

    Half of the hypotenuse.