Creating and Manipulating Linear and Quadratic Expressions Short Problems: Age 11-14

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 11-14.

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

Printable worksheet: Age 11-14 ⭐   Printable worksheet: Age 11-14 ⭐⭐   Printable worksheet solutions


  • Small pepper seedlings in orange pots.
    problem

    Starting Fibonacci

    Age
    11 to 14
    Challenge level

    What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

  • Small pepper seedlings in orange pots.
    problem

    No Matter

    Age
    11 to 14
    Challenge level

    After performing some operations, what number is your answer always a multiple of?

  • Small pepper seedlings in orange pots.
    problem

    Nine in a Line

    Age
    11 to 14
    Challenge level

    The sum of 9 consecutive positive whole numbers is 2007. What is the largest of these numbers?

  • Small pepper seedlings in orange pots.
    problem

    Paul's Children

    Age
    11 to 14
    Challenge level

    Paul is 32 years old. In ten years time, Paul's age will be the sum of the ages of his three sons. What do his sons' ages add up to now?

  • Small pepper seedlings in orange pots.
    problem

    Cube Pile

    Age
    11 to 14
    Challenge level

    Rick has five cubes, each one 2cm taller than the previous one. The largest is the same height as a tower built of the two smallest. How high would a tower of all five cubes be?

  • Small pepper seedlings in orange pots.
    problem

    Grow Up Fast

    Age
    11 to 14
    Challenge level

    How old will Julie be when her age is equal to the sum of her daughters' ages?

  • Small pepper seedlings in orange pots.
    problem

    8 in a Row

    Age
    11 to 14
    Challenge level

    The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these integers?

  • Small pepper seedlings in orange pots.
    problem

    Adding and Multiplying

    Age
    11 to 14
    Challenge level

    Amy misread a question and got an incorrect answer. What should the answer have been?

  • Small pepper seedlings in orange pots.
    problem

    Sum and Differences

    Age
    11 to 14
    Challenge level

    Three numbers add up to 100. The difference between the larger two is 12 and the difference between the smaller two is 2. What are the numbers?

  • Small pepper seedlings in orange pots.
    problem

    Not a Polite Question

    Age
    11 to 14
    Challenge level

    When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

  • Small pepper seedlings in orange pots.
    problem

    Multiple Magic

    Age
    11 to 14
    Challenge level

    Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?

  • Small pepper seedlings in orange pots.
    problem

    Building Up

    Age
    11 to 14
    Challenge level

    In the diagram, the number in each box is obtained by adding the two immediately below. What is the number in the top box?

  • Small pepper seedlings in orange pots.
    problem

    Square Total

    Age
    11 to 14
    Challenge level

    What is the smallest number Anastasia could have thought of, if after performing some operations, the total is a square number?

  • Small pepper seedlings in orange pots.
    problem

    Standing on the Table

    Age
    11 to 14
    Challenge level

    Clement and Dmitri both measure how much taller they are than the other when standing on a table. Can you work out how tall the table is?

  • Small pepper seedlings in orange pots.
    problem

    Adding in Pairs

    Age
    11 to 14
    Challenge level

    These are the results when 3 numbers were added in pairs. What were the numbers?

  • Small pepper seedlings in orange pots.
    problem

    Forming Groups

    Age
    11 to 14
    Challenge level

    Seventy pupils are divided into two groups. Can you work out the difference between the number of boys in group 1 and the number of girls in group 2?

  • Small pepper seedlings in orange pots.
    problem

    Black and Gold Storeys

    Age
    11 to 14
    Challenge level

    25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

  • Small pepper seedlings in orange pots.
    problem

    There and Back

    Age
    14 to 16
    Challenge level

    Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

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