Exploring and noticing

  • Curve match
    problem

    Curve Match

    Age
    16 to 18
    Challenge level
    1 out of 3

    Which curve is which, and how would you plan a route to pass between them?

  • Gradient match
    problem

    Gradient Match

    Age
    16 to 18
    Challenge level
    1 out of 3

    What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

  • Turning to calculus
    problem

    Turning to Calculus

    Age
    16 to 18
    Challenge level
    1 out of 3

    Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

  • Cubic roots
    problem

    Cubic Roots

    Age
    16 to 18
    Challenge level
    1 out of 3

    Find the location of the point of inflection of this cubic.

  • Simply Graphs
    problem

    Simply Graphs

    Age
    16 to 18
    Challenge level
    1 out of 3

    Look for the common features in these graphs. Which graphs belong together?

  • Proving the Laws of Logarithms
    problem

    Proving the Laws of Logarithms

    Age
    16 to 18
    Challenge level
    1 out of 3

    Here you have an opportunity to explore the proofs of the laws of logarithms.

  • Inequalities
    problem

    Inequalities

    Age
    16 to 18
    Challenge level
    1 out of 3

    Which of the statements must be true?

  • The Koch Snowflake
    problem

    The Koch Snowflake

    Age
    16 to 18
    Challenge level
    1 out of 3

    Explore the strange geometrical properties of the Koch Snowflake.

  • Polite Numbers
    problem

    Polite Numbers

    Age
    16 to 18
    Challenge level
    2 out of 3

    A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?

  • What do functions do for tiny x?
    problem

    What Do Functions Do for Tiny X?

    Age
    16 to 18
    Challenge level
    2 out of 3

    Looking at small values of functions. Motivating the existence of the Maclaurin expansion.