RAF Airman/Airwoman Selection Test (AST) Numerical Reasoning Syllabus

In direct proportion, if 4 items cost $\pounds6$, what do 10 items cost?

$\pounds15$. Unit cost $= 6 \div 4 = \pounds1.50$; $10 \times 1.50 = \pounds15$.

State the formula linking speed, distance and time, and its two rearrangements.

$\text{speed} = \dfrac{\text{distance}}{\text{time}}$. Rearranged: $\text{distance} = \text{speed} \times \text{time}$ and $\text{time} = \dfrac{\text{distance}}{\text{speed}}$.

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

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

How long does a $240$ km journey take at $60$ km/h?

$4$ hours. $\text{time} = \dfrac{240}{60} = 4$ h.

How do you find the total cost of buying multiple items, and the change from a payment? 3 items at $\pounds2.50$ paid with a $\pounds10$ note.

Total $= 3 \times 2.50 = \pounds7.50$; change $= 10 - 7.50 = \pounds2.50$.

To convert $\pounds$ to another currency, do you multiply or divide by the exchange rate? Convert $\pounds50$ at $1\ \pounds = 1.20\ \$ $.

Multiply by the rate: $50 \times 1.20 = \$60$.

How many minutes are there between $14{:}45$ and $16{:}20$?

$95$ minutes (1 hour 35 minutes). From $14{:}45$ to $16{:}45$ is $2$ h, minus $25$ min = $1$ h $35$ min.

A train leaves at $09{:}50$ and the journey takes $2$ hours $40$ minutes. What is the arrival time?

$12{:}30$. $09{:}50 + 2$ h $= 11{:}50$; $+40$ min $= 12{:}30$.

Define the mean of a data set and give its formula.

The mean is the average: $\text{mean} = \dfrac{\text{sum of values}}{\text{number of values}}$.

Define the median and the mode of a data set.

The median is the middle value when data are placed in order (the mean of the two middle values if there is an even count). The mode is the value that occurs most often.

Find the mean, median and mode of: $4, 7, 7, 2, 5$.

Mean $= \dfrac{4+7+7+2+5}{5} = \dfrac{25}{5} = 5$. Ordered: $2,4,5,7,7$, so median $= 5$. Mode $= 7$.

What is the range of a data set, and what is the range of $3, 8, 5, 12, 6$?

Range $= \text{largest} - \text{smallest}$. Here $12 - 3 = 9$.

When reading a table of figures to answer a question, what is the key first step?

Identify the correct row and column headings that the question refers to, then read the value at their intersection (checking units and totals).

On a bar chart, what does the height (or length) of each bar represent, and what is plotted on each axis?

The height/length represents the frequency or value for each category. Categories are usually on the horizontal axis; the measured value (frequency) is on the vertical axis.

In a pie chart, how do you convert a category's share into a sector angle, and what does the whole circle represent?

The whole circle ($360^{\circ}$) represents the total. A category's angle $= \dfrac{\text{category}}{\text{total}} \times 360^{\circ}$ (equivalently, its percentage of $360^{\circ}$).

A pie chart category represents $25\%$ of the total. What angle does its sector occupy?

$90^{\circ}$. $25\%$ of $360^{\circ} = 0.25 \times 360 = 90^{\circ}$.

On a line graph, how do you identify an upward trend versus a downward trend?

An upward trend is a line rising from left to right (values increasing over time); a downward trend is a line falling from left to right (values decreasing).

On a line graph, what does a flat (horizontal) section of the line indicate?

No change in the measured value over that period — the quantity stays constant.

What is the general strategy for a multi-step calculation from a chart or table?

Read off each required value separately, perform the operations in the correct order (BODMAS), keep units consistent, and only round at the final step.

From a table, sales were $120$ in January and $150$ in February. What was the percentage increase?

$25\%$. Increase $= 30$; $\dfrac{30}{120} \times 100 = 25\%$.

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

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

Solve for $x$: $\dfrac{x}{4} - 2 = 3$.

$x = 20$. Add $2$: $\dfrac{x}{4} = 5$; multiply by $4$: $x = 20$.

What is the golden rule when solving an equation by performing operations on both sides?

Whatever operation you do to one side you must do to the other, so the two sides stay equal (keep the equation balanced).

What does it mean to substitute values into a formula? Find $A$ when $A = l \times w$, $l = 6$, $w = 4$.

Replace each letter with its given number and evaluate. $A = 6 \times 4 = 24$.

Using $v = u + at$, find $v$ when $u = 5$, $a = 2$, $t = 3$.

$v = 11$. $v = 5 + (2 \times 3) = 5 + 6 = 11$.

For the sequence $3, 7, 11, 15, \dots$, what is the rule and the next term?

It is arithmetic with common difference $+4$; the next term is $15 + 4 = 19$.

What kind of sequence is $2, 6, 18, 54, \dots$ and what is the next term?

A geometric sequence with common ratio $\times 3$; the next term is $54 \times 3 = 162$.

Identify the rule and next term of the sequence $1, 4, 9, 16, \dots$

These are the square numbers $n^{2}$; the next term is $5^{2} = 25$.

What does 'squaring' a number mean and what is $7^{2}$? What does the square root sign ask for, and what is $\sqrt{49}$?

Squaring means multiplying a number by itself: $7^{2} = 49$. A square root asks which number squared gives the value: $\sqrt{49} = 7$.

State the first five perfect squares and evaluate $\sqrt{144}$.

$1, 4, 9, 16, 25$ (i.e. $1^2$ to $5^2$). $\sqrt{144} = 12$ since $12^{2} = 144$.