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

Numerical Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Numerical Reasoning in RAF Airman/Airwoman Selection Test (AST), not a summary of it.

1. 1

   Core Arithmetic (Non-calculator)

   4 topics

   • Addition, subtraction, multiplication and division
     • Long multiplication and division by hand
     • Mental arithmetic shortcuts
   • Order of operations (BODMAS)
   • Working with negative numbers
   • Estimation and rounding for quick checks
2. 2

   Fractions, Decimals and Percentages

   4 topics

   • Converting between fractions, decimals and percentages
   • Calculating a percentage of a quantity
     • Percentage increase and decrease
   • Simplifying and ordering fractions
   • Ratio and proportion
     • Sharing a quantity in a given ratio
     • Scaling recipes and quantities
3. 3

   Applied Word Problems

   4 topics

   • Speed, distance and time
     • Average speed calculations
     • Unit conversion (mph, km/h, minutes)
   • Currency and money calculations
     • Change, profit and discounts
   • Time and timetable problems
     • 24-hour clock and elapsed time
   • Averages (mean, median, mode)
4. 4

   Data Interpretation

   4 topics

   • Reading tables of figures
   • Bar charts and pie charts
     • Extracting values from a chart
     • Comparing categories
   • Line graphs and trends
   • Multi-step calculations from a data source
5. 5

   Algebra and Number Patterns

   4 topics

   • Solving simple linear equations
   • Substituting values into formulae
   • Number sequences and the next term
     • Arithmetic and geometric progressions
   • Powers, squares and square roots

Numerical Reasoning flashcards for RAF Airman/Airwoman Selection Test (AST)

22 of 50 cards from the Numerical Reasoning deck — real questions with worked answers.

1. In the four basic operations, what are the names for the result of (a) addition, (b) subtraction, (c) multiplication and (d) division?

   (a) Sum, (b) difference, (c) product, (d) quotient.

2. What does the acronym BODMAS stand for, in order?

   Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Division and multiplication rank equally (left to right), as do addition and subtraction.

3. Evaluate using BODMAS: $6 + 2 \times 3$

   $12$. Multiplication first: $2 \times 3 = 6$, then $6 + 6 = 12$ (not $24$).

4. Evaluate using BODMAS: $(8 - 3)^{2} \times 2$

   $50$. Brackets: $8-3=5$; order: $5^{2}=25$; multiply: $25 \times 2 = 50$.

5. What are the sign rules for multiplying or dividing two numbers with different signs versus the same sign?

   Same signs give a positive result; different signs give a negative result. E.g. $(-)\times(-)=+$ and $(+)\times(-)=-$.

6. Evaluate: $-7 - (-4)$

   $-3$. Subtracting a negative is the same as adding: $-7 + 4 = -3$.

7. Evaluate: $-6 \times (-5)$

   $30$. A negative times a negative gives a positive.

8. To estimate quickly, what is a good way to check $312 \times 49$ without exact calculation?

   Round to convenient numbers: $300 \times 50 = 15{,}000$. The exact answer ($15{,}288$) should be close to this estimate.

9. What is the rule for rounding a number when the digit to be dropped is exactly 5?

   Conventional rounding rounds half up: a trailing 5 (or more) rounds the preceding digit up. E.g. $2.5 \to 3$ and $0.45 \to 0.5$ (to 1 d.p.).

10. Round $47{,}382$ to (a) the nearest hundred and (b) the nearest thousand.

    (a) $47{,}400$; (b) $47{,}000$.

11. How do you convert a fraction to a decimal, and a decimal to a percentage?

    Fraction to decimal: divide numerator by denominator. Decimal to percentage: multiply by $100$ (move the decimal two places right). E.g. $\frac{3}{4}=0.75=75\%$.

12. How do you convert a percentage to a fraction in simplest form? Convert $40\%$.

    Write it over $100$ and simplify: $40\% = \frac{40}{100} = \frac{2}{5}$.

13. State the decimal and percentage equivalents of $\frac{1}{8}$.

    $\frac{1}{8} = 0.125 = 12.5\%$.

14. What is the method to find a percentage of a quantity? Find $15\%$ of $\pounds240$.

    Convert the percentage to a decimal and multiply: $0.15 \times 240 = \pounds36$.

15. Find $30\%$ of $\pounds90$ using the '10% method'.

    $10\%$ of $90 = 9$, so $30\% = 3 \times 9 = \pounds27$.

16. A price of $\pounds80$ increases by $25\%$. What is the new price?

    $\pounds100$. Increase $= 0.25 \times 80 = 20$; new price $= 80 + 20 = \pounds100$ (or $1.25 \times 80$).

17. How do you simplify a fraction such as $\frac{18}{24}$?

    Divide numerator and denominator by their highest common factor. $\gcd(18,24)=6$, so $\frac{18}{24}=\frac{3}{4}$.

18. To compare or order fractions with different denominators, what must you do first? Which is larger, $\frac{2}{3}$ or $\frac{3}{5}$?

    Convert to a common denominator (or to decimals). With denominator $15$: $\frac{2}{3}=\frac{10}{15}$, $\frac{3}{5}=\frac{9}{15}$, so $\frac{2}{3}$ is larger.

19. What does a ratio express, and how do you simplify the ratio $12:18$?

    A ratio compares quantities of the same kind. Divide both parts by their common factor: $12:18 = 2:3$ (dividing by $6$).

20. Share $\pounds60$ in the ratio $2:3$. How much is each part?

    Total parts $= 2+3 = 5$; one part $= 60 \div 5 = 12$. Shares are $2\times12=\pounds24$ and $3\times12=\pounds36$.

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

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

22. 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 $\text{time} = \dfrac{\text{distance}}{\text{speed}}$.

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