Functional Skills Qualifications Functional Skills Maths — Measures, Shape and Space Syllabus

What is the approximate metric equivalent of 1 inch and 1 foot?

$1\text{ inch} \approx 2.5\text{ cm}$ and $1\text{ foot} \approx 30\text{ cm}$ (a foot is 12 inches).

What is the approximate conversion between miles and kilometres?

$5\text{ miles} \approx 8\text{ km}$ (so $1\text{ mile} \approx 1.6\text{ km}$). To go miles to km multiply by 1.6.

What is the approximate conversion for 1 kilogram in pounds (lb), and 1 litre in pints?

$1\text{ kg} \approx 2.2\text{ lb}$ and $1\text{ litre} \approx 1.75\text{ pints}$ (a gallon $\approx 4.5$ litres).

Roughly how many centimetres are in a foot, and how would you convert 6 feet to cm?

About 30 cm per foot, so $6 \times 30 = 180\text{ cm}$ (approximately).

What is a compound measure, and name three common examples?

A compound measure combines two different units/quantities. Examples: speed (distance per time), density (mass per volume), and rate of pay (money per hour).

State the formula linking speed, distance and time, and rearrange it for distance and time.

$\text{speed} = \frac{\text{distance}}{\text{time}}$, so $\text{distance} = \text{speed} \times \text{time}$ and $\text{time} = \frac{\text{distance}}{\text{speed}}$.

A car travels 150 miles in 3 hours. What is its average speed?

$\text{speed} = \frac{\text{distance}}{\text{time}} = \frac{150}{3} = 50\text{ mph}$.

State the formula for density in terms of mass and volume.

$\text{density} = \frac{\text{mass}}{\text{volume}}$, commonly measured in $\text{g/cm}^{3}$ or $\text{kg/m}^{3}$.

Water freezes and boils at what temperatures on the Celsius scale?

Water freezes at $0^{\circ}\text{C}$ and boils at $100^{\circ}\text{C}$.

The temperature is $-3^{\circ}\text{C}$ and rises by $8^{\circ}\text{C}$. What is the new temperature?

Add the rise to the starting value: $-3 + 8 = 5^{\circ}\text{C}$.

The temperature falls from $4^{\circ}\text{C}$ to $-6^{\circ}\text{C}$. By how many degrees did it fall?

Find the difference: $4 - (-6) = 4 + 6 = 10^{\circ}\text{C}$.

What is normal human body temperature in degrees Celsius?

Approximately $37^{\circ}\text{C}$.

What is the perimeter of a shape, and how do you find it?

The perimeter is the total distance around the outside of a 2D shape. You find it by adding the lengths of all the sides together.

What is the formula for the perimeter of a rectangle with length $l$ and width $w$?

$P = 2l + 2w$ (or equivalently $P = 2(l + w)$).

How do you find the circumference (perimeter) of a circle with radius $r$ or diameter $d$?

$C = \pi d$ or $C = 2\pi r$, using $\pi \approx 3.14$.

What is the area of a shape and what units is it measured in?

Area is the amount of flat space inside a 2D shape, measured in square units such as $\text{cm}^{2}$ or $\text{m}^{2}$.

State the formula for the area of a rectangle and the area of a triangle.

Rectangle: $A = l \times w$. Triangle: $A = \frac{1}{2} \times b \times h$ (half base times perpendicular height).

What is the formula for the area of a circle with radius $r$?

$A = \pi r^{2}$, using $\pi \approx 3.14$ and the radius (not the diameter).

State the formula for the area of a parallelogram and a trapezium.

Parallelogram: $A = b \times h$. Trapezium: $A = \frac{1}{2}(a + b)h$ where $a$ and $b$ are the parallel sides.

What is volume, what units is it measured in, and what is the formula for the volume of a cuboid?

Volume is the space inside a 3D shape, measured in cubic units like $\text{cm}^{3}$. For a cuboid: $V = l \times w \times h$.

How do you find the volume of a prism (e.g. a cylinder)?

$V = \text{area of cross-section} \times \text{length}$. For a cylinder: $V = \pi r^{2} h$.

How many millilitres are in 1 cubic centimetre, and how does this help with capacity?

$1\text{ cm}^{3} = 1\text{ ml}$, so a container with volume $500\text{ cm}^{3}$ holds $500\text{ ml}$ ($0.5$ litres).

What is the difference between a 2D and a 3D shape?

A 2D (two-dimensional) shape is flat with only length and width (e.g. square, circle). A 3D shape is solid with length, width and height/depth (e.g. cube, sphere).

Define the faces, edges and vertices of a 3D shape, and state how many each a cube has.

A face is a flat surface, an edge is where two faces meet, a vertex is a corner. A cube has 6 faces, 12 edges and 8 vertices.

Name the special types of triangle based on their sides, and one key fact about each.

Equilateral: all 3 sides and angles equal ($60^{\circ}$ each). Isosceles: 2 equal sides and 2 equal base angles. Scalene: all sides and angles different. (A right-angled triangle has one $90^{\circ}$ angle.)

What are the four types of angle classified by size?

Acute: less than $90^{\circ}$. Right angle: exactly $90^{\circ}$. Obtuse: between $90^{\circ}$ and $180^{\circ}$. Reflex: greater than $180^{\circ}$ (a straight line is $180^{\circ}$).

What do the angles on a straight line add up to, and what do angles around a point add up to?

Angles on a straight line add up to $180^{\circ}$, and angles around a point add up to $360^{\circ}$.

How are coordinates written, and in which order do the axes go?

Coordinates are written as $(x, y)$ where $x$ is the horizontal position (across) and $y$ is the vertical position (up). Remember 'along the corridor, then up the stairs.'

On a map grid reference system, how do you read a four-figure grid reference?

Read the eastings (the numbers going across/right) first, then the northings (the numbers going up). 'Along the corridor and up the stairs' — give the easting before the northing.

What are the plan view and the elevations of a 3D object, and what is a net?

The plan is the view looking down from directly above; the front and side elevations are the views looking horizontally from the front and side. A net is a 2D flat pattern that folds up to form the 3D shape (e.g. 6 squares fold into a cube).