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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# SEAMC Published Shorts

### Powerful Expressions

### Growing Triangle

### XOXOXO

### Diagonal Area

### Three Right Angles

### Square in a Circle in a Square

### Strike a Chord

### Dolly Dolphin

### Black and White Socks

### Doubly Isosceles

### Maximum Mean

### Snapped Palm Tree

### Hexagon Perimeter

### Photocopied Map

### 3-4-5 Circle

### Square to a Rectangle

### Inches and Barleycorns

### Elephants and Geese

### Pay Attention

### Late for Work

### Nested Square Roots

### Triangular Intersection

### Changing Averages

### The Roller and the Triangle

### Graph Triangles

### Two Trains

### Folded Rectangle

### Overlapping Ribbons

### Boys and Girls

### Inside a Parabola

### Power of 3

### Third Side

### How Many Gorillas?

### Square Overlap

### Laps

### Four Circles

### Stolen Pension

### Triangular Slope

### Petrol Stop

### A Third of the Area

### Dropouts

### Smartphone Screen

### Adding a Square to a Cube

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The problems in this collection have been adapted from problems that have been set in South East Asian Mathematics Competitions.

Age 14 to 16

ShortChallenge Level

Put these expressions in order, from smallest to largest.

Age 14 to 16

ShortChallenge Level

If the base and height of a triangle are increased by different percentages, what happens to its area?

Age 14 to 16

ShortChallenge Level

6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?

Age 14 to 16

ShortChallenge Level

A square has area 72 cm$^2$. Find the length of its diagonal.

Age 14 to 16

ShortChallenge Level

Work your way through these right-angled triangles to find $x$.

Age 14 to 16

ShortChallenge Level

What is the ratio of the areas of the squares in the diagram?

Age 14 to 16

ShortChallenge Level

Can you work out the radius of a circle from some information about a chord?

Age 14 to 16

ShortChallenge Level

Can you find Dolly Dolphin's average speed as she swims with and against the current?

Age 14 to 16

ShortChallenge Level

There are 20 black socks and some white socks in a drawer. Can you work out how many of the socks are white?

Age 14 to 16

ShortChallenge Level

Find the missing distance in this diagram with two isosceles triangles

Age 14 to 16

ShortChallenge Level

What is the largest that the mean of these numbers could be?

Age 14 to 16

ShortChallenge Level

A palm tree has snapped in a storm. What is the height of the piece that is still standing?

Age 14 to 16

ShortChallenge Level

A circle of radius 1 is inscribed in a regular hexagon. What is the perimeter of the hexagon?

Age 14 to 16

ShortChallenge Level

What will the scale on this map be after it has been photocopied?

Age 14 to 16

ShortChallenge Level

Can you find the radius of the circle inscribed inside a '3-4-5 triangle'?

Age 14 to 16

ShortChallenge Level

Kevin has moved some tiles to change the shape of his patio from a square to a rectangle. What are the lengths of the sides of the rectangle?

Age 14 to 16

ShortChallenge Level

How many barleycorns are there in one inch?

Age 14 to 16

ShortChallenge Level

Yesterday, at Ulaanbaatar market, a white elephant cost the same amount as 99 wild geese. How many wild geese cost the same amount as a white elephant today?

Age 14 to 16

ShortChallenge Level

If some of the audience fell asleep for some of this talk, what was the average proportion of the talk that people heard?

Age 14 to 16

ShortChallenge Level

What average speed should Ms Fanthorpe drive at to arrive at work on time?

Age 14 to 16

ShortChallenge Level

Can you find the value of this expression, which contains infinitely nested square roots?

Age 14 to 16

ShortChallenge Level

What is the largest number of intersection points that a triangle and a quadrilateral can have?

Age 14 to 16

ShortChallenge Level

Find the value of $m$ from these statements about a group of numbers

Age 14 to 16

ShortChallenge Level

How much of the inside of this triangular prism can Clare paint using a cylindrical roller?

Age 14 to 16

ShortChallenge Level

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

Age 14 to 16

ShortChallenge Level

Two trains started simultaneously, each travelling towards the other. How long did each train need to complete the journey?

Age 14 to 16

ShortChallenge Level

Can you find the perimeter of the pentagon formed when this rectangle of paper is folded?

Age 14 to 16

ShortChallenge Level

Two ribbons are laid over each other so that they cross. Can you find the area of the overlap?

Age 14 to 16

ShortChallenge Level

Can you find the total number of students in the school, given some information about ratios?

Age 14 to 16

ShortChallenge Level

A triangle of area 64 square units is drawn inside the parabola $y=k^2-x^2$. Find the value of $k$.

Age 14 to 16

ShortChallenge Level

What power of 27 is needed to get the correct power of 3?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

If the numbers in this news article have been estimated, then what is the largest number of gorillas that there could have been 10 years ago?

Age 14 to 16

ShortChallenge Level

The top square has been rotated so that the squares meet at a 60$^\text{o}$ angle. What is the area of the overlap?

Age 14 to 16

ShortChallenge Level

On which of the hare's laps will she first pass the tortoise?

Age 14 to 16

ShortChallenge Level

Can you find the radius of the larger circle in the diagram?

Age 14 to 16

ShortChallenge Level

How much money did the pensioner have before being robbed?

Age 14 to 16

ShortChallenge Level

Can you find the gradients of the lines that form a triangle?

Age 14 to 16

ShortChallenge Level

From the information given, can you work out how long Roberto drove for after putting petrol in his car?

Age 14 to 16

ShortChallenge Level

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?

Age 14 to 16

ShortChallenge Level

What percentage of students who graduate have never been to France?

Age 14 to 16

ShortChallenge Level

Can you find the length and width of the screen of this smartphone in inches?

Age 14 to 16

ShortChallenge Level

If you take a number and add its square to its cube, how often will you get a perfect square?