Examius

🇬🇧 Certificate of Secondary Education (CSE) · subject

Certificate of Secondary Education (CSE) Mathematics Syllabus

The Mathematics syllabus for Certificate of Secondary Education (CSE) in full: 5 chapters, 22 topics and 42 sub-topics, every one listed below, plus 50 Mathematics flashcards with answers.

5Chapters
22Topics
42Sub-topics
50Flashcards

Mathematics syllabus: all 5 chapters

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

  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. 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. 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. 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. 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

Certificate of Secondary Education (CSE) Mathematics flashcards — 50 questions with 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 $x=4$: $2(4)+3=8+3=11$.

Show the other 30 Mathematics flashcards

  1. 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. $A=lw$).

  2. How do you collect like terms to simplify $5a+3b-2a+b$?

    Combine terms with the same letters: $5a-2a=3a$ and $3b+b=4b$, giving $3a+4b$. Unlike terms cannot be combined.

  3. What are the three index laws for multiplying, dividing and raising powers?

    $a^{m}\times a^{n}=a^{m+n}$; $a^{m}\div a^{n}=a^{m-n}$; $\left(a^{m}\right)^{n}=a^{mn}$.

  4. How do you expand a single bracket such as $3(2x+5)$?

    Multiply each term inside the bracket by the term outside: $3\times2x+3\times5=6x+15$.

  5. How do you factorise an expression like $6x+9$?

    Take out the highest common factor. The HCF of $6x$ and $9$ is $3$, so $6x+9=3(2x+3)$.

  6. How do you expand two brackets $(x+2)(x+3)$?

    Multiply every term in the first bracket by every term in the second (FOIL): $x^{2}+3x+2x+6=x^{2}+5x+6$.

  7. What is the balance method for solving a linear equation such as $3x+4=19$?

    Do the same to both sides to isolate $x$: subtract $4$ to get $3x=15$, then divide by $3$ to get $x=5$.

  8. How do you solve an equation with the unknown on both sides, e.g. $5x-3=2x+9$?

    Gather the unknowns on one side and numbers on the other: $5x-2x=9+3$, so $3x=12$ and $x=4$.

  9. How do you rearrange a formula to make a different variable the subject, e.g. make $r$ the subject of $C=2\pi r$?

    Use inverse operations to isolate the variable: divide both sides by $2\pi$ to get $r=\frac{C}{2\pi}$.

  10. What is the difference between an arithmetic sequence and a geometric sequence?

    In an arithmetic sequence each term increases by a constant difference (e.g. $2,5,8,11$, add $3$). In a geometric sequence each term is multiplied by a constant ratio (e.g. $2,6,18,54$, $\times3$).

  11. How do you find the $n$th-term rule of a linear sequence like $4,7,10,13$?

    The common difference is the coefficient of $n$. Here the difference is $3$, so start with $3n$; adjust by comparing: $3(1)=3$ but first term is $4$, so add $1$. The rule is $3n+1$.

  12. What are the first five terms of the square numbers and the triangular numbers?

    Square numbers: $1,4,9,16,25$ (from $n^{2}$). Triangular numbers: $1,3,6,10,15$ (from $\frac{n(n+1)}{2}$).

  13. What is the sum of angles on a straight line and the sum of angles around a point?

    Angles on a straight line add to $180^{\circ}$; angles around a point add to $360^{\circ}$.

  14. Define acute, right, obtuse and reflex angles by their size.

    Acute: less than $90^{\circ}$. Right: exactly $90^{\circ}$. Obtuse: between $90^{\circ}$ and $180^{\circ}$. Reflex: between $180^{\circ}$ and $360^{\circ}$.

  15. When a transversal crosses parallel lines, what are corresponding, alternate and co-interior angle facts?

    Corresponding angles are equal (F-shape); alternate angles are equal (Z-shape); co-interior (allied) angles add to $180^{\circ}$ (C-shape).

  16. What do the interior angles of a triangle and of a quadrilateral add up to?

    The interior angles of a triangle sum to $180^{\circ}$, and the interior angles of a quadrilateral sum to $360^{\circ}$.

  17. Compare the properties of a square, a rectangle and a rhombus.

    All have four sides and opposite sides parallel. A square has $4$ equal sides and $4$ right angles; a rectangle has equal opposite sides and $4$ right angles; a rhombus has $4$ equal sides but angles need not be $90^{\circ}$.

  18. State the formulae for the area of a rectangle, a triangle and a parallelogram.

    Rectangle: $A=l\times w$. Triangle: $A=\frac{1}{2}\times b\times h$. Parallelogram: $A=b\times h$.

  19. What are the formulae for the circumference and area of a circle of radius $r$?

    Circumference $C=2\pi r$ (or $\pi d$); area $A=\pi r^{2}$.

  20. How do you find the volume of a cuboid and the volume of a cylinder?

    Cuboid: $V=l\times w\times h$. Cylinder: $V=\pi r^{2}h$ (base area times height).

  21. State Pythagoras' theorem and what it relates.

    In a right-angled triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (the longest side, opposite the right angle) and $a$, $b$ are the other two sides.

  22. Using Pythagoras' theorem, find the hypotenuse of a right-angled triangle with legs $3$ and $4$.

    $c=\sqrt{3^{2}+4^{2}}=\sqrt{9+16}=\sqrt{25}=5$.

  23. How do you construct the perpendicular bisector of a line segment?

    Open a compass to more than half the segment's length; draw arcs from each endpoint above and below the line; the arcs cross at two points; join those points with a straight line, which bisects the segment at $90^{\circ}$.

  24. What does a scale of $1:50000$ mean on a map, and how do you convert map distance to real distance?

    Each unit on the map represents $50000$ of the same units in reality. Multiply the measured map distance by $50000$. E.g. $4\text{ cm}$ represents $200000\text{ cm}=2\text{ km}$.

  25. In coordinates $(x,y)$, what do the two values represent and where is the origin?

    The first value $x$ is the horizontal distance and the second $y$ is the vertical distance from the origin, which is the point $(0,0)$ where the axes cross.

  26. What does the equation $y=mx+c$ represent, and what do $m$ and $c$ stand for?

    It is the equation of a straight line; $m$ is the gradient (steepness) and $c$ is the $y$-intercept (where the line crosses the $y$-axis).

  27. How do you calculate the gradient of a straight line between two points?

    Gradient $=\frac{\text{change in }y}{\text{change in }x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$. A positive gradient slopes up, a negative gradient slopes down.

  28. On a distance-time graph, what do a straight sloped line, a horizontal line and the gradient represent?

    A sloped straight line shows constant speed; a horizontal line shows the object is stationary; the gradient represents the speed, since $\text{speed}=\frac{\text{distance}}{\text{time}}$.

  29. What is the difference between discrete and continuous data, and between primary and secondary data?

    Discrete data take separate countable values (e.g. number of pets); continuous data can take any value in a range (e.g. height). Primary data is collected yourself; secondary data comes from an existing source.

  30. How do you calculate the mean, median, mode and range of a data set?

    Mean: add all values and divide by how many there are. Median: the middle value when ordered. Mode: the most frequent value. Range: largest value minus smallest value, a measure of spread.

Certificate of Secondary Education (CSE) Mathematics FAQ

What is in the Certificate of Secondary Education (CSE) Mathematics syllabus?

Certificate of Secondary Education (CSE) Mathematics is split into 5 chapters: Number and Arithmetic, Algebra, Geometry and Measurement, Graphs and Coordinates and Statistics and Probability. Together they contain 22 topics and 42 sub-topics.

How many chapters are in Certificate of Secondary Education (CSE) Mathematics?

5 chapters, containing 22 topics and 42 sub-topics. The largest chapter is Number and Arithmetic, with 5 topics.

Are there flashcards for Certificate of Secondary Education (CSE) Mathematics?

Yes — a 50-card Mathematics 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.