Mathematics Geometry Syllabus

Geometry syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Geometry in Mathematics, not a summary of it.

1. 1

   Lines and Angles

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

2. 2

   Triangles

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

3. 3

   Quadrilaterals

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

4. 4

   Circles

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

5. 5

   Polygons

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

6. 6

   Coordinate Geometry

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

7. 7

   Transformations

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

8. 8

   Area and Perimeter

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

9. 9

   Volume and Surface Area

   overview

   Examined as a single unit within Geometry — no further topic split in the official outline.

Geometry flashcards for Mathematics

19 of 50 cards from the Geometry deck — real questions with worked answers.

1. What is the sum of the interior angles of a triangle?

   $180^{\circ}$ (or $\pi$ radians).

2. State the Pythagorean theorem for a right triangle with legs $a$, $b$ and hypotenuse $c$.

   $$a^{2} + b^{2} = c^{2}$$

3. What is the area of a triangle with base $b$ and height $h$?

   $A = \frac{1}{2} b h$

4. State Heron's formula for the area of a triangle with sides $a$, $b$, $c$ and semiperimeter $s = \frac{a+b+c}{2}$.

   $$A = \sqrt{s(s-a)(s-b)(s-c)}$$

5. What is the area of a circle of radius $r$?

   $A = \pi r^{2}$

6. What is the circumference of a circle of radius $r$?

   $C = 2\pi r$ (equivalently $\pi d$).

7. Define a right angle, acute angle, and obtuse angle by their measures.

   Right angle $= 90^{\circ}$; acute angle is between $0^{\circ}$ and $90^{\circ}$; obtuse angle is between $90^{\circ}$ and $180^{\circ}$.

8. What is the sum of the interior angles of a polygon with $n$ sides?

   $(n-2)\times 180^{\circ}$

9. What is the measure of each interior angle of a regular $n$-gon?

   $\frac{(n-2)\times 180^{\circ}}{n}$

10. What is the sum of the exterior angles of any convex polygon (one per vertex)?

    $360^{\circ}$

11. Classify triangles by their sides.

    Equilateral (all three sides equal), isosceles (exactly two sides equal), and scalene (no sides equal).

12. Classify triangles by their angles.

    Acute (all angles $< 90^{\circ}$), right (one angle $= 90^{\circ}$), and obtuse (one angle $> 90^{\circ}$).

13. What is the area of a rectangle with length $l$ and width $w$?

    $A = l w$

14. What is the area of a parallelogram with base $b$ and height $h$?

    $A = b h$

15. What is the area of a trapezoid with parallel sides $a$ and $b$ and height $h$?

    $A = \frac{1}{2}(a + b) h$

16. What is the area of a rhombus with diagonals $d_{1}$ and $d_{2}$?

    $A = \frac{1}{2} d_{1} d_{2}$

17. State the distance formula between points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$.

    $$d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}$$

18. State the midpoint formula for the segment from $(x_{1}, y_{1})$ to $(x_{2}, y_{2})$.

    $\left( \frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2} \right)$

19. What is the slope of the line through $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$?

    $m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

See more Geometry flashcards →

Planning Geometry for Mathematics

Geometry (Mathematics) FAQ