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

Functional Skills Maths — Number and the Number System syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Functional Skills Maths — Number and the Number System in Functional Skills Qualifications, not a summary of it.

1. 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. 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. 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 Maths — Number and the Number System flashcards for Functional Skills Qualifications

21 of 51 cards from the Functional Skills Maths — Number and the Number System deck — real questions with worked 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 $12$.

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

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

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