Certificate of Secondary Education (CSE) Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in Certificate of Secondary Education (CSE), not a summary of it.

1. 1

   Number and Arithmetic

   5 topics

   • The four operations
     • Whole numbers and integers
     • Order of operations
   • Fractions, decimals and percentages
     • Converting between forms
     • Calculating percentages of quantities
   • Ratio and proportion
     • Sharing in a given ratio
     • Direct proportion problems
   • Approximation and estimation
     • Rounding and decimal places
     • Significant figures
   • Money and everyday calculations
     • Interest, profit and loss
     • Wages, bills and best buys
2. 2

   Algebra

   5 topics

   • Algebraic notation and substitution
     • Using letters for numbers
     • Evaluating expressions
   • Simplifying and manipulating expressions
     • Collecting like terms
     • Expanding brackets
   • Solving equations
     • Linear equations
     • Forming equations from problems
   • Formulae and rearrangement
     • Substituting into formulae
     • Changing the subject
   • Sequences and patterns
     • Continuing number patterns
     • Finding the rule
3. 3

   Geometry and Measurement

   5 topics

   • Angles and lines
     • Angles on a line and at a point
     • Parallel lines and transversals
   • Properties of shapes
     • Triangles and quadrilaterals
     • Polygons and symmetry
   • Perimeter, area and volume
     • Rectangles, triangles and circles
     • Cuboids and prisms
   • Pythagoras' theorem
     • Finding the hypotenuse
     • Finding a shorter side
   • Construction and scale drawing
     • Using ruler, compass and protractor
     • Maps, plans and bearings
4. 4

   Graphs and Coordinates

   3 topics

   • Coordinates and plotting points
     • The four quadrants
   • Straight-line graphs
     • Plotting from a table of values
     • Gradient and intercept
   • Conversion and travel graphs
     • Distance-time graphs
     • Reading conversion graphs
5. 5

   Statistics and Probability

   4 topics

   • Collecting and recording data
     • Tally charts and frequency tables
   • Representing data
     • Bar charts and pictograms
     • Pie charts
   • Averages and spread
     • Mean, median and mode
     • Range
   • Introduction to probability
     • The probability scale
     • Simple events and outcomes

Mathematics flashcards for Certificate of Secondary Education (CSE)

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. What are the four basic operations of arithmetic, and what symbols represent them?

   Addition ($+$), subtraction ($-$), multiplication ($\times$) and division ($\div$). They are the foundation of all number calculations.

2. State the correct order of operations and the memory aid used to recall it.

   BIDMAS (or BODMAS): Brackets, Indices (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

3. How do you convert a fraction to a decimal, and a decimal to a percentage?

   Divide the numerator by the denominator to get a decimal (e.g. $\frac{3}{4}=0.75$). Multiply a decimal by $100$ to get a percentage (e.g. $0.75=75\%$).

4. How do you add or subtract two fractions with different denominators?

   Find a common denominator (often the LCM), rewrite each fraction over it, then add or subtract the numerators. For example $\frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$.

5. How do you multiply and how do you divide two fractions?

   Multiply: multiply numerators and denominators, $\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}$. Divide: multiply by the reciprocal of the second fraction, $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$.

6. How do you find a percentage of an amount, for example $15\%$ of $\pounds80$?

   Convert the percentage to a decimal and multiply: $0.15\times80=\pounds12$.

7. What is the multiplier method for increasing or decreasing a quantity by a percentage?

   Increase by $p\%$: multiply by $\left(1+\frac{p}{100}\right)$. Decrease by $p\%$: multiply by $\left(1-\frac{p}{100}\right)$. E.g. a $20\%$ rise uses $\times1.2$, a $20\%$ fall uses $\times0.8$.

8. How do you express one quantity as a percentage of another?

   Divide the part by the whole and multiply by $100$: $\text{percentage}=\frac{\text{part}}{\text{whole}}\times100\%$. For example $18$ out of $24$ is $\frac{18}{24}\times100=75\%$.

9. What is the difference between a ratio and a proportion?

   A ratio compares two or more quantities (e.g. $3:2$), showing relative size. A proportion is a statement that two ratios are equal, often used to scale quantities up or down.

10. How do you share an amount in a given ratio, e.g. share $\pounds60$ in the ratio $2:3$?

    Add the parts: $2+3=5$. Divide the amount by the total parts: $\pounds60\div5=\pounds12$ per part. Multiply: $2\times12=\pounds24$ and $3\times12=\pounds36$.

11. What is the unitary method for solving proportion problems?

    Find the value of one unit first, then scale up to the required amount. E.g. if $5$ pens cost $\pounds2$, one pen costs $\pounds0.40$, so $8$ pens cost $8\times0.40=\pounds3.20$.

12. What is the difference between direct and inverse proportion?

    Direct: as one quantity increases, the other increases at the same rate ($y=kx$). Inverse: as one increases, the other decreases ($y=\frac{k}{x}$, so their product is constant).

13. What does it mean to round a number to a given number of decimal places?

    Keep the stated number of digits after the decimal point; look at the next digit and round up if it is $5$ or more, otherwise round down. E.g. $3.146$ to $2$ d.p. is $3.15$.

14. How do you round a number to a given number of significant figures?

    Count significant figures starting from the first non-zero digit; round using the next digit. E.g. $0.04826$ to $2$ s.f. is $0.048$, and $5274$ to $2$ s.f. is $5300$.

15. How do you estimate the answer to a calculation?

    Round each number to $1$ significant figure, then calculate. E.g. $\frac{29\times4.8}{6.1}\approx\frac{30\times5}{6}=25$.

16. What are the upper and lower bounds of a measurement given to the nearest unit?

    They are half a unit below and above the value. E.g. a length of $24\text{ cm}$ to the nearest cm has lower bound $23.5\text{ cm}$ and upper bound $24.5\text{ cm}$.

17. How do you calculate change and check it in everyday money calculations?

    Subtract the total cost from the amount paid: $\text{change}=\text{paid}-\text{cost}$. E.g. paying $\pounds20$ for goods costing $\pounds13.45$ gives change $\pounds6.55$.

18. What is the formula linking simple interest, principal, rate and time?

    $I=\frac{P\times R\times T}{100}$, where $P$ is the principal, $R$ the percentage rate per year, and $T$ the time in years.

19. In algebraic notation, how are $3\times a$, $a\times a$ and $a\div b$ written?

    $3\times a$ is written $3a$; $a\times a$ is written $a^{2}$; $a\div b$ is written $\frac{a}{b}$.

20. What does it mean to substitute into an expression, and what is the value of $2x+3$ when $x=4$?

    Substitution means replacing each letter with its given number and evaluating. With $x=4$: $2(4)+3=8+3=11$.

21. What is the difference between a term, an expression, an equation and a formula?

    A term is a single number/letter product (e.g. $3x$); an expression is terms combined (e.g. $3x+2$); an equation contains an equals sign and can be solved (e.g. $3x+2=8$); a formula relates variables (e.g. $A=lw$).

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