Creating and Manipulating Linear and Quadratic Expressions - Short Problems

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 and Age 14-16

Printable worksheets containing selections of these problems are available here.

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?

problem

No Matter

Age

11 to 14

Challenge level

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

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?

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?

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?

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?

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?

problem

Adding and multiplying

Age

11 to 14

Challenge level

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

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?

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...

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?

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?

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?

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?

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?

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?

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...

problem

length, width and area

Age

14 to 16

Challenge level

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

problem

Clever calculation

Age

14 to 16

Challenge level

Find the shortcut to do this calculation quickly!

problem

Order the Products

Age

14 to 16

Challenge level

Can you put these products in order of size?

problem

Divisible Expression

Age

14 to 16

Challenge level

Can you show this algebraic expression is divisible by 4?

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?

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?

problem

Little Difference

Age

14 to 16

Challenge level

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

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?

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.