British Army Cognitive Test (BARB) Foundational Numeracy and Literacy Skills Syllabus

Foundational Numeracy and Literacy Skills syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Foundational Numeracy and Literacy Skills in British Army Cognitive Test (BARB), not a summary of it.

1. 1

   Core Numeracy Refresher

   3 topics

   • Mental arithmetic fundamentals
     • Rapid addition and subtraction
     • Times tables and quick multiplication
   • Number comparison and estimation
     • Ordering and comparing values
     • Rounding and approximation
   • Place value and number structure
     • Tens, hundreds and reading multi-digit numbers
2. 2

   Core Literacy Refresher

   3 topics

   • Reading and interpreting short statements
     • Extracting meaning quickly and accurately
   • Spelling and word recognition
     • Recognising correct word forms at speed
   • Following written instructions precisely
     • Acting on exactly what is asked
3. 3

   Concentration and Working Memory

   3 topics

   • Sustained attention drills
     • Maintaining focus during repetitive tasks
   • Holding information in mind
     • Keeping counts and orderings without writing
   • Reducing distraction and improving speed
     • Building processing speed through practice

Foundational Numeracy and Literacy Skills flashcards for British Army Cognitive Test (BARB)

25 of 51 cards from the Foundational Numeracy and Literacy Skills deck — real questions with worked answers.

1. In the BARB context, what does 'mental arithmetic' mean, and why is it tested?

   Mental arithmetic is performing calculations (add, subtract, multiply, divide) in your head without a calculator or written working. BARB tests it because soldiers must process numbers quickly and accurately under time pressure.

2. What is the correct order of operations for mental arithmetic, and what acronym summarises it?

   BODMAS (or BIDMAS): Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right). For example, $2 + 3 \times 4 = 14$, not $20$.

3. How can you quickly add two-digit numbers like $47 + 38$ mentally?

   Split into tens and units: $40 + 30 = 70$ and $7 + 8 = 15$, then combine: $70 + 15 = 85$. This 'partitioning' method reduces errors.

4. What is a fast mental method to subtract, e.g. $83 - 47$?

   Count up from the smaller number: from $47$ to $50$ is $3$, from $50$ to $83$ is $33$, so $3 + 33 = 36$. This 'shopkeeper' method avoids borrowing.

5. State the multiplication facts for the $9$ times table up to $9 \times 10$.

   $9, 18, 27, 36, 45, 54, 63, 72, 81, 90$. Tip: the digits of each product always sum to $9$ (e.g. $54 \to 5+4=9$).

6. What is a quick trick to multiply any number by $10$, $100$ or $1000$?

   Shift the digits left and add zeros (for whole numbers): $\times 10$ adds one zero, $\times 100$ adds two, $\times 1000$ adds three. E.g. $46 \times 100 = 4600$.

7. How do you multiply a number by $5$ quickly in your head?

   Multiply by $10$ then halve, or halve then multiply by $10$. E.g. $5 \times 18 = \frac{18 \times 10}{2} = \frac{180}{2} = 90$.

8. How do you divide a number by $5$ quickly?

   Double the number then divide by $10$. E.g. $\frac{85}{5} = \frac{85 \times 2}{10} = \frac{170}{10} = 17$.

9. What is the doubling and halving method for multiplication, with an example?

   Halve one factor and double the other to simplify. E.g. $16 \times 25 = 8 \times 50 = 4 \times 100 = 400$.

10. What is a 'number bond' and why are bonds to $10$ and $100$ useful?

    A number bond is a pair that sums to a target. Bonds to $10$ ($3+7$, $4+6$) and to $100$ ($35+65$) let you add and subtract instantly, e.g. $100 - 28 = 72$.

11. Define 'estimation' and give the main reason to estimate before calculating.

    Estimation is finding an approximate answer using rounded numbers. It gives a quick sanity check so you can spot if a precise answer is wildly wrong.

12. How do you estimate $312 \times 19$ using rounding?

    Round to convenient numbers: $300 \times 20 = 6000$. The estimate $\approx 6000$ is close to the exact value $5928$.

13. What are the standard rounding rules for the digit $5$ and above?

    Look at the digit to the right of the rounding place: if it is $5$ or more, round up; if it is $4$ or less, round down. E.g. $47 \to 50$ to the nearest ten; $43 \to 40$.

14. What symbols mean 'greater than', 'less than', and 'approximately equal to'?

    $>$ means greater than, $<$ means less than, $\geq$ means greater than or equal to, $\leq$ means less than or equal to, and $\approx$ means approximately equal to.

15. How do you compare which is larger, $0.7$ or $0.65$?

    Give them the same number of decimal places: $0.70$ vs $0.65$. Since $70 > 65$, we get $0.7 > 0.65$.

16. How do you compare two fractions such as $\frac{3}{5}$ and $\frac{2}{3}$?

    Cross-multiply or use a common denominator. $\frac{3}{5} = \frac{9}{15}$ and $\frac{2}{3} = \frac{10}{15}$, so $\frac{2}{3} > \frac{3}{5}$.

17. When comparing whole numbers, why does the number of digits matter first?

    A whole number with more digits is larger (ignoring leading zeros). E.g. $1000 > 999$ because it has four digits versus three. Only when digit counts match do you compare digit by digit from the left.

18. Define 'place value' and identify the place values in the number $4{,}572$.

    Place value is the value a digit holds based on its position. In $4{,}572$: $4$ = thousands ($4000$), $5$ = hundreds ($500$), $7$ = tens ($70$), $2$ = units ($2$).

19. What is the place value of the digit $8$ in $3{,}826$?

    The $8$ is in the hundreds place, so its value is $800$.

20. Write the number 'six thousand and forty' in digits, and explain the role of the zero.

    $6040$. The zero is a place holder in the hundreds column, showing there are no hundreds while keeping the other digits in their correct positions.

21. How does multiplying a whole number by $10$ affect each digit's place value?

    Every digit moves one place to the left, increasing its value tenfold. E.g. $57 \times 10 = 570$: the $5$ moves from tens to hundreds and the $7$ from units to tens.

22. What is the value of $2$ in the number $20{,}913$, and how is the structure read?

    The $2$ is in the ten-thousands place, value $20000$. The number reads 'twenty thousand, nine hundred and thirteen'.

23. In BARB-style instructions test items, what does 'reading and interpreting a short statement' require you to do?

    Read the statement carefully, identify the key facts and relationships (who, what, order, position), and answer a question based only on the information given, not assumptions.

24. If a statement says 'John is taller than Mike, and Mike is taller than Sam', who is shortest?

    Sam. The chain is John > Mike > Sam, so Sam is the shortest.

25. What is the key strategy for interpreting a positional statement like 'The red box is to the left of the blue box'?

    Fix the described relationship exactly as stated and visualise the layout: red on the left, blue on the right. Do not reverse the relationship or add extra items.

See more Foundational Numeracy and Literacy Skills flashcards →

Planning Foundational Numeracy and Literacy Skills for British Army Cognitive Test (BARB)

Foundational Numeracy and Literacy Skills (British Army Cognitive Test (BARB)) FAQ