Royal Navy Recruiting Test (RT) Numeracy Test Syllabus

Numeracy Test syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Numeracy Test in Royal Navy Recruiting Test (RT), not a summary of it.

1. 1

   Core Arithmetic

   4 topics

   • Addition and subtraction without a calculator
     • Mental arithmetic techniques
     • Carrying and borrowing accuracy
   • Multiplication and division
     • Times tables fluency
     • Long multiplication and division
   • Order of operations (BODMAS)
   • Working with negative numbers
2. 2

   Fractions, Decimals and Percentages

   4 topics

   • Simplifying and comparing fractions
     • Equivalent fractions
     • Adding and subtracting fractions
   • Converting between fractions, decimals and percentages
   • Calculating percentages of amounts
     • Percentage increase and decrease
     • Finding the original amount
   • Decimal place value and rounding
3. 3

   Ratio, Proportion and Averages

   4 topics

   • Simplifying and dividing in a ratio
   • Direct proportion and scaling
     • Recipe and quantity scaling
     • Unit pricing comparisons
   • Calculating the mean, median and mode
   • Range of a data set
4. 4

   Measurement, Time and Money

   4 topics

   • Metric units and conversions
     • Length, mass and capacity
     • Converting between units
   • Time calculations
     • 12-hour and 24-hour clock
     • Duration and elapsed time
   • Money problems and change
   • Speed, distance and time formulae
5. 5

   Data Interpretation

   4 topics

   • Reading tables and timetables
   • Interpreting bar charts and pie charts
     • Extracting values from charts
     • Comparing categories
   • Line graphs and trends
   • Solving worded data problems
6. 6

   Algebra and Number Patterns

   4 topics

   • Solving simple linear equations
   • Substituting values into formulae
   • Number sequences and nth-term reasoning
   • Working with powers and square roots

Numeracy Test flashcards for Royal Navy Recruiting Test (RT)

24 of 50 cards from the Numeracy Test deck — real questions with worked answers.

1. When adding or subtracting multi-digit numbers by hand, how should the digits be arranged and in which direction do you work?

   Align the numbers by place value (units under units, tens under tens, etc.) and work from right to left, carrying when a column total reaches 10 or borrowing when the top digit is too small.

2. What is $4736 + 2589$?

   $4736 + 2589 = 7325$

3. What is $8002 - 3457$?

   $8002 - 3457 = 4545$

4. What is the order of operations remembered by the acronym BODMAS?

   Brackets, Orders (powers and roots), Division and Multiplication (left to right), Addition and Subtraction (left to right).

5. Using BODMAS, evaluate $3 + 4 \times 5$.

   Multiplication first: $4 \times 5 = 20$, then $3 + 20 = 23$.

6. Using BODMAS, evaluate $(6 + 2) \times 3^{2}$.

   Brackets: $6 + 2 = 8$; orders: $3^{2} = 9$; then $8 \times 9 = 72$.

7. What are the four rules for the sign of a result when multiplying or dividing two negative numbers and a positive with a negative?

   $(+)\times(+)=+$, $(-)\times(-)=+$, $(+)\times(-)=-$, $(-)\times(+)=-$. The same sign rules apply to division: like signs give $+$, unlike signs give $-$.

8. What is $-7 + 12$?

   $-7 + 12 = 5$

9. What is $-6 - 9$?

   $-6 - 9 = -15$

10. What is $-4 \times -8$?

    $-4 \times -8 = 32$ (two negatives make a positive).

11. What does it mean to simplify a fraction, and how do you do it?

    To write it in its lowest terms by dividing both numerator and denominator by their highest common factor (HCF). For example $\frac{12}{18} = \frac{2}{3}$ (dividing by 6).

12. How do you compare two fractions such as $\frac{3}{4}$ and $\frac{5}{8}$ to see which is larger?

    Give them a common denominator. $\frac{3}{4} = \frac{6}{8}$, so $\frac{6}{8} > \frac{5}{8}$, meaning $\frac{3}{4}$ is larger.

13. How do you convert the fraction $\frac{3}{8}$ into a decimal?

    Divide the numerator by the denominator: $3 \div 8 = 0.375$.

14. How do you convert a decimal such as $0.45$ into a percentage and then into a fraction in lowest terms?

    Multiply by 100 for the percentage: $0.45 = 45\%$. As a fraction $0.45 = \frac{45}{100} = \frac{9}{20}$.

15. How do you convert a percentage such as $12\%$ into a decimal and a fraction?

    Divide by 100: $12\% = 0.12 = \frac{12}{100} = \frac{3}{25}$.

16. What are the decimal and fraction equivalents of $25\%$, $50\%$ and $75\%$?

    $25\% = 0.25 = \frac{1}{4}$, $50\% = 0.5 = \frac{1}{2}$, $75\% = 0.75 = \frac{3}{4}$.

17. How do you calculate a percentage of an amount, for example $15\%$ of $\pounds240$?

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

18. What is a quick mental method to find $10\%$, $5\%$ and $1\%$ of an amount?

    $10\%$ is the amount divided by 10; $5\%$ is half of $10\%$; $1\%$ is the amount divided by 100. Combine these to build other percentages.

19. In the number $3\,migrated... 47.style 826$ ... what is the place value of the digit 8 in $47.826$?

    The 8 is in the tenths place, so it has a value of $\frac{8}{10} = 0.8$.

20. How do you round $6.4783$ to two decimal places?

    Look at the third decimal digit (8); since it is 5 or more, round up: $6.4783 \approx 6.48$.

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

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

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

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

23. 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 $3 \times 12 = \pounds36$.

24. 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 $\pounds5$.

See more Numeracy Test flashcards →

Planning Numeracy Test for Royal Navy Recruiting Test (RT)

Numeracy Test (Royal Navy Recruiting Test (RT)) FAQ