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Functional Skills Qualifications Functional Skills Maths — Number and the Number System Syllabus

The Functional Skills Maths — Number and the Number System syllabus for Functional Skills Qualifications in full: 3 chapters, 13 topics and 24 sub-topics, every one listed below, plus 51 Functional Skills Maths — Number and the Number System flashcards with answers.

3Chapters
13Topics
24Sub-topics
51Flashcards

Functional Skills Maths — Number and the Number System syllabus: all 3 chapters

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

  1. Whole Numbers and Place Value

     5 topics
    • Reading, writing and ordering whole numbers
      • Place value to millions
      • Comparing and ordering using < and >
    • The four operations with whole numbers
      • Addition and subtraction
      • Multiplication and division
      • Order of operations (BIDMAS)
    • Rounding and estimation
      • Rounding to the nearest 10, 100 and 1000
      • Estimating to check calculations are sensible
    • Negative numbers
      • Negative numbers in context (temperature, money)
      • Calculating with negative numbers
    • Factors, multiples and prime numbers

  2. Fractions, Decimals and Percentages

     4 topics
    • Understanding and working with fractions
      • Equivalent fractions and simplifying
      • Adding, subtracting, multiplying and dividing fractions
      • Finding a fraction of a quantity
    • Decimals and decimal calculations
      • Place value in decimals
      • Calculating with decimals
      • Rounding decimals to a number of decimal places
    • Percentages
      • Finding a percentage of an amount
      • Percentage increase and decrease
      • Expressing one number as a percentage of another
    • Converting between fractions, decimals and percentages
      • Common equivalences (1/2, 1/4, 1/10)
      • Ordering mixed forms of values

  3. Ratio, Proportion and Scaling

     4 topics
    • Understanding and simplifying ratio
      • Expressing and simplifying ratios
      • Sharing a quantity in a given ratio
    • Direct proportion
      • Scaling recipes and quantities up and down
      • Unit pricing and best-value comparisons
    • Scale drawings, maps and models
    • Currency and unit conversions

Functional Skills Qualifications Functional Skills Maths — Number and the Number System flashcards — 51 questions with answers

  1. What is place value, and what is the value of the digit 7 in the number 4{,}763?

    Place value is the value a digit holds because of its position in a number. In $4{,}763$ the digit $7$ is in the hundreds column, so its value is $700$.

  2. How do you compare two whole numbers to decide which is larger?

    First compare the number of digits — more digits means a larger number. If they have the same number of digits, compare digit by digit from the left (highest place value) until they differ.

  3. What do the symbols $<$, $>$ and $=$ mean when ordering numbers?

    $<$ means 'is less than', $>$ means 'is greater than', and $=$ means 'is equal to'. For example $35 < 53$ and $90 > 9$.

  4. Write the number 'two thousand and five' in figures, and explain the role of the zeros.

    It is $2{,}005$. The zeros are placeholders showing there are no hundreds and no tens, keeping the $2$ in the thousands place and the $5$ in the units place.

  5. What are the four basic operations in arithmetic and their symbols?

    Addition ($+$), subtraction ($-$), multiplication ($\times$) and division ($\div$).

  6. What is the order of operations (BIDMAS/BODMAS)?

    Brackets, Indices (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right). For example $2 + 3 \times 4 = 2 + 12 = 14$.

  7. Which pairs of operations are inverses of each other?

    Addition and subtraction are inverse operations, and multiplication and division are inverse operations. They 'undo' each other, e.g. $7 \times 6 = 42$ so $42 \div 6 = 7$.

  8. In a division such as $17 \div 5$, name the dividend, divisor, quotient and remainder.

    In $17 \div 5 = 3$ remainder $2$: the dividend is $17$, the divisor is $5$, the quotient is $3$ and the remainder is $2$.

  9. What does it mean to round a number to the nearest 10, and round 47 and 52 to the nearest 10.

    Look at the units digit: if it is $5$ or more round up, otherwise round down. $47 \to 50$ and $52 \to 50$.

  10. State the rule for rounding to a given decimal place or significant figure.

    Look at the digit immediately after the place you are rounding to. If it is $5$ or more, round the last kept digit up by $1$; if it is $4$ or less, leave it unchanged. Drop or zero out the remaining digits.

  11. What is estimation, and how do you estimate $312 \times 49$?

    Estimation finds an approximate answer by rounding numbers, usually to 1 significant figure. $312 \times 49 \approx 300 \times 50 = 15{,}000$.

  12. Round 3.0467 to (a) 2 decimal places and (b) 2 significant figures.

    (a) $3.05$ (the third decimal digit is $6$, so round up). (b) $3.0$ (the first two significant figures are $3$ and $0$; the next digit $4$ rounds down).

  13. What are negative numbers, and what does the number line tell you about their size?

    Negative numbers are numbers less than zero, written with a minus sign (e.g. $-3$). On a number line they lie to the left of zero, and the further left, the smaller, so $-7 < -2$.

  14. State the rules for adding and subtracting negative numbers.

    Adding a negative is the same as subtracting: $5 + (-3) = 5 - 3 = 2$. Subtracting a negative is the same as adding: $5 - (-3) = 5 + 3 = 8$.

  15. State the sign rules for multiplying and dividing negative numbers.

    Same signs give a positive result, different signs give a negative result. For example $(-4)\times(-3)=12$, $(-4)\times 3 = -12$ and $(-12)\div(-3)=4$.

  16. A temperature rises from $-6^{\circ}\mathrm{C}$ to $5^{\circ}\mathrm{C}$. By how many degrees did it rise?

    The rise is $5 - (-6) = 5 + 6 = 11^{\circ}\mathrm{C}$.

  17. Define factor and multiple.

    A factor of a number divides into it exactly with no remainder (e.g. factors of $12$ are $1,2,3,4,6,12$). A multiple is the result of multiplying a number by a whole number (e.g. multiples of $4$ are $4,8,12,16,\dots$).

  18. What is a prime number, and list the first five primes.

    A prime number has exactly two factors: $1$ and itself. The first five are $2, 3, 5, 7, 11$. Note that $1$ is not prime.

  19. What is the highest common factor (HCF) of 12 and 18?

    The HCF is the largest number that divides both exactly. Factors of $12$: $1,2,3,4,6,12$; factors of $18$: $1,2,3,6,9,18$. The HCF is $6$.

  20. What is the lowest common multiple (LCM) of 4 and 6?

    The LCM is the smallest number that is a multiple of both. Multiples of $4$: $4,8,12,\dots$; of $6$: $6,12,\dots$. The LCM is $12$.

Show the other 31 Functional Skills Maths — Number and the Number System flashcards

  1. What is prime factorisation, and write 60 as a product of prime factors.

    It expresses a number as a product of primes only. $60 = 2 \times 2 \times 3 \times 5 = 2^{2} \times 3 \times 5$.

  2. In the fraction $\frac{3}{8}$, what are the numerator and denominator and what do they represent?

    The numerator $3$ (top) is the number of parts taken; the denominator $8$ (bottom) is the number of equal parts the whole is divided into.

  3. How do you simplify a fraction, and simplify $\frac{12}{18}$.

    Divide the numerator and denominator by their highest common factor. For $\frac{12}{18}$ the HCF is $6$, so $\frac{12}{18}=\frac{2}{3}$.

  4. How do you add fractions with different denominators, e.g. $\frac{1}{4} + \frac{1}{6}$?

    Find a common denominator (the LCM), rewrite each fraction, then add the numerators: $\frac{1}{4}+\frac{1}{6}=\frac{3}{12}+\frac{2}{12}=\frac{5}{12}$.

  5. How do you multiply two fractions, e.g. $\frac{2}{3} \times \frac{3}{5}$?

    Multiply the numerators together and the denominators together, then simplify: $\frac{2}{3}\times\frac{3}{5}=\frac{6}{15}=\frac{2}{5}$.

  6. How do you divide by a fraction, e.g. $\frac{1}{2} \div \frac{3}{4}$?

    Multiply by the reciprocal of the second fraction (turn it upside down): $\frac{1}{2}\div\frac{3}{4}=\frac{1}{2}\times\frac{4}{3}=\frac{4}{6}=\frac{2}{3}$.

  7. How do you find a fraction of an amount, e.g. $\frac{3}{4}$ of £20?

    Divide by the denominator then multiply by the numerator: $20\div 4 = 5$, then $5 \times 3 = 15$, so $\frac{3}{4}$ of £20 is £15.

  8. How do you convert the improper fraction $\frac{17}{5}$ to a mixed number?

    Divide $17$ by $5$: $17 \div 5 = 3$ remainder $2$, so $\frac{17}{5} = 3\frac{2}{5}$.

  9. What does each digit after the decimal point represent in 4.276?

    After the point the places are tenths, hundredths and thousandths: $4.276 = 4 + \frac{2}{10} + \frac{7}{100} + \frac{6}{1000}$.

  10. How do you add or subtract decimals correctly?

    Line up the decimal points (and the place-value columns) one under the other, fill empty places with zeros if needed, then add or subtract as with whole numbers, keeping the decimal point in line.

  11. How do you multiply $0.3 \times 0.4$ using whole-number multiplication?

    Ignore the points: $3 \times 4 = 12$. The two factors have $2$ decimal places in total, so the answer has $2$ decimal places: $0.3 \times 0.4 = 0.12$.

  12. How do you divide a number by a decimal, e.g. $4.8 \div 0.6$?

    Multiply both numbers by a power of $10$ so the divisor becomes a whole number: $\frac{4.8}{0.6}=\frac{48}{6}=8$.

  13. What happens to a decimal when you multiply or divide by 10, 100 or 1000?

    Multiplying moves the digits to the left (the point appears to move right): $3.5 \times 100 = 350$. Dividing moves the digits to the right: $3.5 \div 100 = 0.035$.

  14. What does 'per cent' mean, and what is 1% as a fraction and decimal?

    'Per cent' means 'out of 100'. So $1\% = \frac{1}{100} = 0.01$.

  15. How do you find a percentage of an amount, e.g. 15% of £80?

    Convert the percentage to a decimal and multiply: $0.15 \times 80 = 12$, so $15\%$ of £80 is £12. (Or find $10\% = 8$ and $5\% = 4$, then add to get $12$.)

  16. How do you write one quantity as a percentage of another, e.g. 18 out of 24?

    Write it as a fraction, divide, then multiply by 100: $\frac{18}{24}\times 100 = 75\%$.

  17. How do you increase £200 by 12%?

    Find $12\%$ of $200$: $0.12 \times 200 = 24$, then add it on: $200 + 24 = 224$. (Or multiply by the factor $1.12$: $200 \times 1.12 = 224$.)

  18. What is a percentage decrease, and decrease £50 by 20%.

    It reduces an amount by a given percentage. $20\%$ of $50$ is $10$, so $50 - 10 = 40$. (Or multiply by $0.80$: $50 \times 0.80 = 40$.)

  19. How do you convert a fraction to a decimal, e.g. $\frac{3}{8}$?

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

  20. How do you convert a decimal to a percentage and a percentage to a decimal?

    To get a percentage, multiply the decimal by $100$ (e.g. $0.45 \to 45\%$). To get a decimal, divide the percentage by $100$ (e.g. $45\% \to 0.45$).

  21. How do you convert a percentage to a fraction in simplest form, e.g. 40%?

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

  22. List the common equivalences for $\frac{1}{2}$, $\frac{1}{4}$, $\frac{3}{4}$, $\frac{1}{10}$ and $\frac{1}{5}$ as decimals and percentages.

    $\frac{1}{2}=0.5=50\%$, $\frac{1}{4}=0.25=25\%$, $\frac{3}{4}=0.75=75\%$, $\frac{1}{10}=0.1=10\%$, $\frac{1}{5}=0.2=20\%$.

  23. What is a ratio, and what does the ratio $2:3$ mean?

    A ratio compares quantities of the same kind. $2:3$ means that for every $2$ parts of the first quantity there are $3$ parts of the second, giving $5$ parts in total.

  24. How do you simplify the ratio $12:18$?

    Divide both parts by their highest common factor. The HCF of $12$ and $18$ is $6$, so $12:18 = 2:3$.

  25. How do you share £40 in the ratio $3:5$?

    Add the parts: $3 + 5 = 8$. One part is $40 \div 8 = 5$. So the shares are $3 \times 5 = £15$ and $5 \times 5 = £25$.

  26. What is direct proportion?

    Two quantities are in direct proportion if they increase or decrease at the same rate, so doubling one doubles the other. Their ratio (or $\frac{y}{x}$) stays constant.

  27. Using the unitary method, if 5 pens cost £2.00, what do 8 pens cost?

    Find the cost of one: $£2.00 \div 5 = £0.40$. Then multiply: $8 \times £0.40 = £3.20$.

  28. What does a map scale of $1:50{,}000$ mean, and how far is $4\,\mathrm{cm}$ on the map in real life?

    It means $1\,\mathrm{cm}$ on the map represents $50{,}000\,\mathrm{cm}$ in reality. So $4\,\mathrm{cm}$ represents $4 \times 50{,}000 = 200{,}000\,\mathrm{cm} = 2\,\mathrm{km}$.

  29. On a scale drawing with scale $1:20$, a real wall is $5\,\mathrm{m}$ long. How long is it on the drawing?

    Convert and divide by the scale: real length $= 500\,\mathrm{cm}$, drawing length $= 500 \div 20 = 25\,\mathrm{cm}$.

  30. If the exchange rate is £1 = $1.25, how many dollars do you get for £80, and how many pounds for $50?

    To convert pounds to dollars multiply: $80 \times 1.25 = \$100$. To convert dollars to pounds divide: $50 \div 1.25 = £40$.

  31. State the metric conversions between mm, cm, m and km, and between g and kg, ml and litres.

    $10\,\mathrm{mm}=1\,\mathrm{cm}$, $100\,\mathrm{cm}=1\,\mathrm{m}$, $1000\,\mathrm{m}=1\,\mathrm{km}$; $1000\,\mathrm{g}=1\,\mathrm{kg}$; $1000\,\mathrm{ml}=1\,\mathrm{litre}$. To convert to a larger unit divide; to a smaller unit multiply.

Functional Skills Qualifications Functional Skills Maths — Number and the Number System FAQ

What is in the Functional Skills Qualifications Functional Skills Maths — Number and the Number System syllabus?

Functional Skills Qualifications Functional Skills Maths — Number and the Number System is split into 3 chapters: Whole Numbers and Place Value, Fractions, Decimals and Percentages and Ratio, Proportion and Scaling. Together they contain 13 topics and 24 sub-topics.

How many chapters are in Functional Skills Qualifications Functional Skills Maths — Number and the Number System?

3 chapters, containing 13 topics and 24 sub-topics. The largest chapter is Whole Numbers and Place Value, with 5 topics.

Are there flashcards for Functional Skills Qualifications Functional Skills Maths — Number and the Number System?

Yes — a 51-card Functional Skills Maths — Number and the Number System deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.