Civil Service Numerical Reasoning Test Core Numeracy Foundations Syllabus

Core Numeracy Foundations syllabus: all 3 chapters

Expand any chapter to see its topics and sub-topics.

1. 1

   Mental Arithmetic and Number Sense

   4 topics

   • Rapid addition and subtraction
     • Column-free running totals
     • Compensation and rounding to estimate then adjust
     • Adding sequences of figures from a table column
   • Multiplication and division shortcuts
     • Times-table fluency to 12 and beyond
     • Multiplying and dividing by 10, 100, 1000
     • Halving, doubling and factor pairing
   • Order of operations (BIDMAS/BODMAS)
     • Brackets and nested expressions
     • Mixed operations in multi-step calculations
   • Estimation and sense-checking
     • Rounding to significant figures
     • Ballpark answers to eliminate options
     • Spotting implausible results quickly
2. 2

   Working with Decimals, Fractions and Negatives

   4 topics

   • Decimal arithmetic
     • Place value and decimal alignment
     • Multiplying and dividing decimals
   • Fraction operations
     • Simplifying and equivalent fractions
     • Adding and subtracting with unlike denominators
     • Multiplying and dividing fractions
   • Converting between fractions, decimals and percentages
     • Common conversion benchmarks (1/4, 1/3, 1/8 etc.)
   • Negative numbers in context
     • Year-on-year decreases and deficits
     • Arithmetic with signed values
3. 3

   Units, Rounding and Accuracy

   3 topics

   • Metric units and conversions
     • Length, mass, volume and time
     • Currency and large-number scaling (thousands, millions)
   • Rounding conventions
     • Decimal places versus significant figures
     • Rounding in the answer to match option precision
   • Reading values in stated units
     • Figures shown in £000s or £m
     • Percentages versus percentage points

Civil Service Numerical Reasoning Test Core Numeracy Foundations flashcards — 50 questions with answers

1. In BIDMAS/BODMAS, what does each letter stand for and in what order are operations performed?

   Brackets, Indices/Orders (powers and roots), Division and Multiplication (left to right), Addition and Subtraction (left to right). They are evaluated in that priority order.

2. Evaluate $3 + 4 \times 2$ using the order of operations.

   $3 + 4 \times 2 = 3 + 8 = 11$. Multiplication is done before addition.

3. Evaluate $(6 + 2)^{2} \div 4$ step by step.

   Brackets first: $6+2=8$; then index: $8^{2}=64$; then division: $64 \div 4 = 16$.

4. In BIDMAS, do division and multiplication have equal priority? How are they resolved?

   Yes, they share equal priority. When both appear, work strictly from left to right. The same rule applies to addition and subtraction.

5. Evaluate $20 - 6 \div 2 + 1$.

   Division first: $6 \div 2 = 3$, giving $20 - 3 + 1$. Then left to right: $20 - 3 = 17$, $17 + 1 = 18$.

6. What is a quick mental method for adding $47 + 38$ by rounding?

   Round $38$ up to $40$: $47 + 40 = 87$, then subtract the $2$ added: $87 - 2 = 85$.

7. What is the 'counting up' (complementary) method for the subtraction $200 - 137$?

   Count up from $137$ to $200$: $137 \to 140$ is $3$, $140 \to 200$ is $60$. Total $3 + 60 = 63$.

8. How can you add $0.6 + 0.7 + 0.4 + 0.3$ quickly by pairing?

   Pair numbers that make whole tenths: $0.6 + 0.4 = 1.0$ and $0.7 + 0.3 = 1.0$, total $= 2.0$.

9. What is the multiplication shortcut for multiplying any number by $10$, $100$ or $1000$?

   Shift the decimal point right by the number of zeros: $\times 10$ moves it one place, $\times 100$ two places, $\times 1000$ three places. E.g. $4.7 \times 100 = 470$.

10. What is the shortcut for dividing a number by $10$, $100$ or $1000$?

    Shift the decimal point left by the number of zeros: $\div 10$ one place, $\div 100$ two places. E.g. $35 \div 100 = 0.35$.

11. Give a quick method to multiply a number by $5$.

    Multiply by $10$ and halve the result (or halve then multiply by $10$). E.g. $46 \times 5 = \frac{460}{2} = 230$.

12. Give a quick method to multiply a number by $50$.

    Multiply by $100$ and halve: $50 = \frac{100}{2}$. E.g. $18 \times 50 = \frac{1800}{2} = 900$.

13. What shortcut multiplies a number by $9$?

    Multiply by $10$ then subtract the original number: $n \times 9 = 10n - n$. E.g. $7 \times 9 = 70 - 7 = 63$.

14. What shortcut multiplies a number by $11$ (e.g. $11 \times 23$)?

    $n \times 11 = 10n + n$. For a two-digit number, add the two digits and place the sum between them: $23 \to 2\,(2{+}3)\,3 = 253$.

15. How can you multiply by $25$ quickly?

    Multiply by $100$ and divide by $4$, since $25 = \frac{100}{4}$. E.g. $16 \times 25 = \frac{1600}{4} = 400$.

16. What is the doubling-and-halving trick for $16 \times 25$?

    Halve one factor and double the other repeatedly: $16 \times 25 = 8 \times 50 = 4 \times 100 = 400$.

17. How do you estimate $312 \times 48$ quickly?

    Round to convenient figures: $300 \times 50 = 15000$. The exact answer ($14976$) is close, confirming the estimate.

18. What is 'sense-checking' an answer, and why is it useful?

    It is verifying that a result is reasonable in size and sign before trusting it — e.g. checking order of magnitude or comparing to an estimate — to catch errors like a misplaced decimal point.

19. Estimate $\frac{597}{29}$ by rounding.

    Round to $\frac{600}{30} = 20$. So the answer is about $20$ (exactly $\approx 20.6$).

20. When estimating, what is the difference between rounding both numbers up versus one up and one down in a product?

    Rounding both up overestimates the product; rounding both down underestimates it. Rounding one up and one down tends to give a closer, more balanced estimate.

Civil Service Numerical Reasoning Test Core Numeracy Foundations FAQ