Gradients

  • problem
    Favourite

    At Right Angles

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

    Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

  • Surprising Transformations
    problem
    Favourite

    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
    Favourite

    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?

  • Ladder and Cube
    problem
    Favourite

    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
    Favourite

    Parabella

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

    This is a beautiful result involving a parabola and parallels.

  • Lying and Cheating
    problem

    Lying and Cheating

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

    Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

  • Electric Kettle
    problem

    Electric Kettle

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

    Explore the relationship between resistance and temperature

  • Mediant madness
    problem

    Mediant Madness

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

    Kyle and his teacher disagree about his test score - who is right?

  • 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?

  • From all corners
    problem

    From All Corners

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

    Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.