Gradients

  • Surprising Transformations
    problem

    Surprising transformations

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

  • Which is bigger?
    problem

    Which is bigger?

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

  • Building Up
    problem

    Triangular slope

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    Can you find the gradients of the lines that form a triangle?

  • Ladder and Cube
    problem

    Ladder and cube

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

  • Parabella
    problem

    Parabella

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    This is a beautiful result involving a parabola and parallels.

  • Spot the difference
    problem

    Spot the difference

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    If you plot these graphs they may look the same, but are they?
  • Towards Maclaurin
    problem

    Towards Maclaurin

    Age
    16 to 18
    Challenge level
    filled star filled star filled star

    Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.