OpenRevise

Flashcards · Maths

Graphs

80 cards from 5 lessons

  1. What is the formula for the gradient of a line?

    Gradient \(= \dfrac{\text{change in } y}{\text{change in } x}\).

  2. What does a positive gradient look like?

    The line goes up from left to right.

  3. What does a negative gradient look like?

    The line goes down from left to right.

  4. What does \(m\) mean in \(y = mx + c\)?

    The gradient of the line.

  5. What does \(c\) mean in \(y = mx + c\)?

    The \(y\)-intercept, where the line crosses the \(y\)-axis.

  6. What is the gradient of \(y = 5 - 3x\)?

    \(-3\).

  7. What is the equation of a vertical line through 4 on the x-axis?

    \(x = 4\).

  8. What is the equation of a horizontal line through 3 on the y-axis?

    \(y = 3\).

  9. What is the equation of the x-axis?

    \(y = 0\).

  10. What is the equation of the y-axis?

    \(x = 0\).

  11. How do you know two lines are parallel from their equations?

    They have the same gradient.

  12. How do you check whether a point is on a line?

    Put its coordinates into the equation and see if both sides match.

  13. How can you sketch \(y = 2x + 1\) without a table?

    Mark \((0, 1)\) and then go across 1 and up 2.

  14. Find the gradient of the line through \((1, 7)\) and \((4, 1)\).

    \(\dfrac{1 - 7}{4 - 1} = -2\).

  15. Where does a line cross the x-axis?

    Where \(y = 0\).

  16. How many points do you need to draw a straight line?

    Two, but plot three to check.

  17. How do you find the equation of a line through two points?

    Find the gradient, substitute a point to find \(c\), then write \(y = mx + c\).

  18. What is the formula for the midpoint of two points?

    \(\left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)\).

  19. What is the midpoint of \((2, 1)\) and \((6, 9)\)?

    \((4, 5)\).

  20. What is true about the gradients of parallel lines?

    They are equal.

  21. What is the equation of a line with gradient 3 through \((2, 9)\)?

    \(y = 3x + 3\).

  22. What is the gradient of \(2y - 4x = 6\)?

    2, because it rearranges to \(y = 2x + 3\).

  23. What do the gradients of perpendicular lines multiply to (Higher tier)?

    \(-1\).

  24. What is the gradient perpendicular to 2 (Higher tier)?

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

  25. What is the gradient perpendicular to \(-\dfrac{3}{4}\) (Higher tier)?

    \(\dfrac{4}{3}\).

  26. How do you find where a line crosses the y-axis?

    Put \(x = 0\).

  27. How do you find where a line crosses the x-axis?

    Put \(y = 0\).

  28. Where does \(3x + 2y = 12\) cross the axes?

    \((0, 6)\) and \((4, 0)\).

  29. How do you find the length of a line segment (Higher tier)?

    Use Pythagoras with the change in \(x\) and the change in \(y\).

  30. What is the gradient of the line through \((2, 1)\) and \((6, 9)\)?

    2.

  31. How can you check an equation you have found?

    Put the other point into it.

  32. If the midpoint and one end are known, how do you find the other end?

    Double the midpoint and subtract the end you know.

  33. What is the graph of a quadratic called?

    A parabola.

  34. What shape is a parabola with a positive \(x^2\) term?

    A U shape.

  35. What shape is a parabola with a negative \(x^2\) term?

    An upside-down U.

  36. What are the roots of a quadratic graph?

    Where the curve crosses the \(x\)-axis.

  37. What is the turning point?

    The lowest point of a U-shaped curve, or the highest of an upside-down U.

  38. Where is the line of symmetry of a parabola?

    Vertically through the turning point, halfway between the roots.

  39. What is the \(y\)-intercept of \(y = x^2 - 2x - 3\)?

    \(-3\).

  40. How do you solve \(x^2 - 2x - 3 = 0\) from its graph?

    Read the \(x\)-values where the curve crosses the \(x\)-axis.

  41. How do you solve \(x^2 - 2x - 3 = -3\) from the graph?

    Draw \(y = -3\) and read the \(x\)-values where it meets the curve.

  42. What is \((-2)^2\)?

    4, because a negative times a negative is positive.

  43. What is \(y\) when \(x = -2\) on \(y = x^2 - 2x - 3\)?

    \(4 + 4 - 3 = 5\).

  44. How should the curve be drawn?

    With a smooth freehand line through the points.

  45. If the roots are 1 and 5, what is the line of symmetry?

    \(x = 3\).

  46. What is the turning point of \(y = (x - 3)^2 - 4\) (Higher tier)?

    \((3, -4)\).

  47. What does a quadratic usually have, one solution or two?

    Two.

  48. Where is \(x^2 - 2x - 3\) negative?

    Between the roots, for \(-1 < x < 3\).

  49. What shape is a linear graph?

    A straight line.

  50. What shape is a quadratic graph?

    A U shape or an upside-down U.

  51. What shape is a cubic graph?

    An S shape.

  52. What shape is the graph of \(y = \dfrac{1}{x}\)?

    Two separate curved branches that never touch the axes.

  53. What is the value of \(x^3\) when \(x = -2\)?

    \(-8\).

  54. What are the values of \(y = x^3\) for \(x = -1, 0, 1\)?

    \(-1, 0, 1\).

  55. What is \(\dfrac{1}{x}\) when \(x = 4\)?

    \(\dfrac{1}{4}\).

  56. Why does \(y = \dfrac{1}{x}\) have a gap at \(x = 0\)?

    You cannot divide by zero.

  57. Where does \(y = 2^x\) cross the y-axis?

    At \((0, 1)\).

  58. What is \(2^3\)?

    8.

  59. What does \(2^{-1}\) equal?

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

  60. What is the highest power in a cubic equation?

    \(x^3\).

  61. What is the equation of a circle with centre the origin and radius 5 (Higher tier)?

    \(x^2 + y^2 = 25\).

  62. Is \((3, 4)\) on the circle \(x^2 + y^2 = 25\) (Higher tier)?

    Yes, because \(9 + 16 = 25\).

  63. How can you quickly test which equation matches a graph?

    Substitute an \(x\)-value and compare the \(y\)-value with the graph.

  64. What happens to an exponential graph for large \(x\)?

    It increases faster and faster.

  65. What does the gradient of a conversion graph show?

    The number of units on the vertical axis for each unit on the horizontal axis.

  66. How do you use a conversion graph?

    Go from the value you know to the line, then across or down to the other axis.

  67. Why does a conversion line start at the origin?

    Zero in one unit is zero in the other.

  68. What does the intercept of a cost graph mean?

    The fixed charge, the cost for none of the quantity.

  69. What does the gradient of a cost graph mean?

    The cost for each extra unit.

  70. A taxi costs £3 plus £2 per km. What is the equation for the cost \(C\) of \(d\) km?

    \(C = 2d + 3\).

  71. What does a steep part of a depth-time graph show?

    The depth is rising quickly.

  72. Which container's graph gets steeper as it fills?

    One that gets narrower towards the top.

  73. What does the gradient of a velocity-time graph show?

    Acceleration.

  74. What does the area under a velocity-time graph show?

    Distance travelled.

  75. What does a horizontal line on a velocity-time graph mean?

    Constant velocity, so no acceleration.

  76. What does a downward slope on a velocity-time graph mean?

    Deceleration, or negative acceleration.

  77. What are the units of acceleration?

    \(\text{m/s}^2\).

  78. Find the acceleration when velocity goes from 0 to 12 m/s in 4 seconds.

    \(\dfrac{12}{4} = 3\) m/s\(^2\).

  79. How do you estimate the gradient at a point on a curve (Higher tier)?

    Draw a tangent at the point and find its gradient.

  80. How do you estimate the area under a curve (Higher tier)?

    Split it into trapezia or rectangles and add their areas.