Creating and Manipulating Linear and Quadratic Expressions Short Problems: Age 14-16

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Creating and Manipulating Linear and Quadratic Expressions: Age 14-16.

We have put together a selection of these short problems as printable worksheets:

Printable worksheets: Age 14-16 ⭐⭐   Printable worksheet: Age 14-16 ⭐⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in orange pots.
    problem

    Length, Width and Area

    Age
    14 to 16
    Challenge level

    The area of a rectangle is 225 square units. Find its width.

  • Small pepper seedlings in orange pots.
    problem

    Divisible Expression

    Age
    14 to 16
    Challenge level

    Can you show this algebraic expression is divisible by 4?

  • Small pepper seedlings in orange pots.
    problem

    Big Fibonacci

    Age
    14 to 16
    Challenge level

    The fifth term of a Fibonacci sequence is 2004. If all the terms are positive integers, what is the largest possible first term?

  • Small pepper seedlings in orange pots.
    problem

    Square and Cube

    Age
    14 to 16
    Challenge level

    The square of a positive number is twice as big as the cube of that number. What is the number?

  • Small pepper seedlings in orange pots.
    problem

    Little Difference

    Age
    14 to 16
    Challenge level

    What is the value of $2015 \times 2017$ - $2016 \times 2016$?

  • Small pepper seedlings in orange pots.
    problem

    Granny's Age

    Age
    14 to 16
    Challenge level

    Weekly Problem 10 - 2015
    Granny is four times as old as I am. Five years ago she was five times as old as I was. What is the sum of our ages?

  • Small pepper seedlings in orange pots.
    problem

    Adding to 400

    Age
    14 to 16
    Challenge level

    Find four integers whose sum is 400 and such that the first integer is equal to twice the second integer, three times the third integer and four times the fourth integer.

  • Small pepper seedlings in orange pots.
    problem

    Brian's Number

    Age
    14 to 16
    Challenge level

    Brian chooses an integer and operates on it. Work out the largest integer that he could have chosen.

  • Small pepper seedlings in orange pots.
    problem

    Cuboid Perimeters

    Age
    14 to 16
    Challenge level

    Can you find the volume of a cuboid, given its perimeters?

  • Small pepper seedlings in orange pots.
    problem

    Clever Calculation

    Age
    14 to 16
    Challenge level

    Find the shortcut to do this calculation quickly!

  • Small pepper seedlings in orange pots.
    problem

    Order the Products

    Age
    14 to 16
    Challenge level

    Can you put these products in order of size?

  • Small pepper seedlings in orange pots.
    problem

    Months and Years

    Age
    14 to 16
    Challenge level

    The product of Mary's age at her last birthday and her age in complete months is 1800. How old is Mary?

  • Small pepper seedlings in orange pots.
    problem

    Choir Boys

    Age
    14 to 16
    Challenge level

    Can you work out how many members this choir has from these percentages?

  • Small pepper seedlings in orange pots.
    problem

    Third Side

    Age
    14 to 16
    Challenge level

    What are the possible lengths for the third side of this right-angled triangle?

  • Small pepper seedlings in orange pots.
    problem

    Stolen Pension

    Age
    14 to 16
    Challenge level

    How much money did the pensioner have before being robbed?

  • Small pepper seedlings in orange pots.
    problem

    Find the Factor

    Age
    14 to 16
    Challenge level

    Find a factor of $2^{48}-1$.

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