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.

Cube Pile

Age 11 to 14 Short
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?

Nine in a Line

Age 11 to 14 Short
Challenge Level

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

Grow up Fast

Age 11 to 14 Short
Challenge Level

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

Adding and Multiplying

Age 11 to 14 Short
Challenge Level

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

Paul's Children

Age 11 to 14 Short
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?

Starting Fibonacci

Age 11 to 14 Short
Challenge Level

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

8 in a Row

Age 11 to 14 Short
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?

No Matter

Age 11 to 14 Short
Challenge Level

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

Sum and Differences

Age 11 to 14 Short
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?

Adding in Pairs

Age 11 to 14 Short
Challenge Level

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

Standing on the Table

Age 11 to 14 Short
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?

Multiple Magic

Age 11 to 14 Short
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?

Building Up

Age 11 to 14 Short
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?

Not a Polite Question

Age 11 to 14 Short
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...

Square Total

Age 11 to 14 Short
Challenge Level

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

Forming Groups

Age 11 to 14 Short
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?

Black and Gold Storeys

Age 11 to 14 Short
Challenge Level

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

Length, Width and Area

Age 14 to 16 Short
Challenge Level

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

Square and Cube

Age 14 to 16 Short
Challenge Level

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

Cuboid Perimeters

Age 14 to 16 Short
Challenge Level

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

Little Difference

Age 14 to 16 Short
Challenge Level

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

Order the Products

Age 14 to 16 Short
Challenge Level

Can you put these products in order of size?

Granny's Age

Age 14 to 16 Short
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?

Divisible Expression

Age 14 to 16 Short
Challenge Level

Can you show this algebraic expression is divisible by 4?

Brian's Number

Age 14 to 16 Short
Challenge Level

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

Adding to 400

Age 14 to 16 Short
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.

Clever Calculation

Age 14 to 16 Short
Challenge Level

Find the shortcut to do this calculation quickly!

Big Fibonacci

Age 14 to 16 Short
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?

Third Side

Age 14 to 16 Short
Challenge Level

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

Find the Factor

Age 14 to 16 Short
Challenge Level

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

Stolen Pension

Age 14 to 16 Short
Challenge Level

How much money did the pensioner have before being robbed?

Months and Years

Age 14 to 16 Short
Challenge Level

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

Choir Boys

Age 14 to 16 Short
Challenge Level

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