Certificate of Secondary Education (CSE) Mathematics Flashcards

24 sample cards from the Mathematics deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. 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 $x=5$.

2. 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 $x=4$.

3. 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 $r=\frac{C}{2\pi}$.

4. 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. $2,6,18,54$, $\times3$).

5. 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 $3n+1$.

6. 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 $\frac{n(n+1)}{2}$).

7. 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 $360^{\circ}$.

8. 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 $360^{\circ}$.

9. 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).

10. 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 $360^{\circ}$.

11. 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 $90^{\circ}$.

12. 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: $A=b\times h$.

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

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

14. 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).

15. 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.

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

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

17. 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 $90^{\circ}$.

18. 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 $200000\text{ cm}=2\text{ km}$.

19. 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.

20. 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).

21. 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.

22. 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 $\text{speed}=\frac{\text{distance}}{\text{time}}$.

23. 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.

24. 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.

What this deck covers

Mathematics flashcards FAQ