Royal Navy Recruiting Test (RT) Numeracy Test Syllabus

How do you round $5\,279$ to the nearest hundred?

The tens digit is 7 (5 or more), so round up: $5\,279 \approx 5\,300$.

How do you simplify a ratio such as $12 : 18$?

Divide both parts by their HCF (6): $12 : 18 = 2 : 3$.

How do you divide $\pounds60$ in the ratio $2 : 3$?

Add the parts: $2 + 3 = 5$. One part is $60 \div 5 = 12$. So the shares are $2 \times 12 = \pounds24$ and $3 \times 12 = \pounds36$.

What is direct proportion, and how do you use it to scale a quantity?

Two quantities are in direct proportion when one increases the other increases at the same rate (their ratio stays constant). Find the value of one unit, then multiply. E.g. if 4 pens cost $\pounds2$, one pen costs $\pounds0.50$, so 10 pens cost $\pounds5$.

If a recipe for 4 people needs 200 g of flour, how much flour is needed for 6 people?

Per person: $200 \div 4 = 50$ g. For 6 people: $50 \times 6 = 300$ g.

How do you calculate the mean of a set of numbers?

Add all the values together and divide by how many values there are: $\text{mean} = \dfrac{\text{sum of values}}{\text{number of values}}$.

How do you find the median of a data set?

Arrange the values in ascending order and take the middle value. If there are two middle values (even count), the median is their mean.

What is the mode of a data set?

The value that occurs most frequently. A data set can have no mode, one mode, or more than one mode.

Find the mean, median and mode of $4, 7, 7, 9, 13$.

Mean: $\frac{4+7+7+9+13}{5} = \frac{40}{5} = 8$. Median (middle value): $7$. Mode (most frequent): $7$.

How do you calculate the range of a data set?

Subtract the smallest value from the largest value: $\text{range} = \text{maximum} - \text{minimum}$.

What is the range of the data set $12, 5, 18, 9, 3$?

$\text{range} = 18 - 3 = 15$.

List the common metric conversions for length: mm, cm, m and km.

$10\ \text{mm} = 1\ \text{cm}$, $100\ \text{cm} = 1\ \text{m}$, $1000\ \text{m} = 1\ \text{km}$ (so $1\ \text{m} = 1000\ \text{mm}$).

State the metric conversions for mass and capacity (g, kg, ml, litre).

$1000\ \text{g} = 1\ \text{kg}$ and $1000\ \text{ml} = 1\ \text{litre}$.

Convert $2.5\ \text{km}$ into metres.

$2.5 \times 1000 = 2500\ \text{m}$.

How many minutes are in $2$ hours $45$ minutes, and how do you convert between hours and minutes?

Multiply hours by 60 and add the minutes: $2 \times 60 + 45 = 165$ minutes.

If a train leaves at 14:50 and arrives at 16:35, how long is the journey?

From 14:50 to 16:35 is 1 hour 45 minutes (10 minutes to 15:00, then 1 hour 35 minutes).

A jumper costs $\pounds14.65$ and you pay with a $\pounds20$ note. How much change do you get?

$\pounds20.00 - \pounds14.65 = \pounds5.35$.

If 3 identical books cost $\pounds26.85$ in total, what is the price of one book?

$\pounds26.85 \div 3 = \pounds8.95$.

State the formula linking speed, distance and time.

$\text{speed} = \dfrac{\text{distance}}{\text{time}}$, which rearranges to $\text{distance} = \text{speed} \times \text{time}$ and $\text{time} = \dfrac{\text{distance}}{\text{speed}}$.

A car travels $150\ \text{km}$ in $2$ hours. What is its average speed?

$\text{speed} = \dfrac{150}{2} = 75\ \text{km/h}$.

How far does a cyclist travel in $3$ hours at $16\ \text{km/h}$?

$\text{distance} = \text{speed} \times \text{time} = 16 \times 3 = 48\ \text{km}$.

When reading a timetable, how do you work out how long a journey between two listed times takes?

Find the departure time in the correct column/row and the arrival time, then subtract the departure from the arrival (counting up through the hour if needed).

On a bar chart, how do you read off the value represented by a bar?

Read straight across (or down) from the top of the bar to the value axis and read the scale; note the size of each gridline interval before reading.

On a pie chart, what fraction and angle represent a category that is $25\%$ of the total?

$25\% = \frac{1}{4}$ of the data, and as an angle it is $\frac{1}{4} \times 360^{\circ} = 90^{\circ}$.

What does an upward sloping line on a line graph indicate, and how do you describe a trend?

An upward (rising) line shows an increasing trend; a downward line shows a decreasing trend; a flat line shows no change. The steeper the line, the faster the rate of change.

What is a sensible step-by-step approach to solving a worded data problem?

Read the question carefully, identify the relevant numbers/units, choose the correct operation or statistic, carry out the calculation, and check the answer is reasonable and in the right units.

How do you solve the linear equation $3x + 5 = 20$?

Subtract 5 from both sides: $3x = 15$; divide both sides by 3: $x = 5$.

Substitute $x = 4$ into the formula $y = 2x^{2} - 3$. What is $y$?

$y = 2(4)^{2} - 3 = 2 \times 16 - 3 = 32 - 3 = 29$.

For the sequence $5, 8, 11, 14, \dots$, what is the nth-term rule and the 10th term?

The common difference is 3, so the rule is $3n + 2$. The 10th term is $3 \times 10 + 2 = 32$.

What is the value of $7^{2}$, $\sqrt{81}$ and $\sqrt{144}$?

$7^{2} = 49$, $\sqrt{81} = 9$, and $\sqrt{144} = 12$.