Geometry and Trigonometry
- Syllabus
- 0606–2028–2029
- Section
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- Level
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In this section
Topic 7
7. Straight-line graphs
Objectives in this topic
7.1. Use straight-line equations
- Use the equation of a straight line.
7.2. Use parallel and perpendicular gradients
- Know and use the condition for two lines to be parallel or perpendicular.
7.3. Solve midpoint, length and bisector problems
- Solve problems involving midpoint and length of a line.
- Find and use the equation of a perpendicular bisector.
7.4. Transform relationships to straight-line form
- Transform given relationships to and from straight-line form.
- Determine unknown constants by calculating the gradient or intercept of the transformed graph.
- Includes forms such as y = Ax^n, y = Ab^x, y^2 = Ax^3 + B, e^(2y) = Ax^2 + B and y^3 = A ln x + B.
Topic 8
8. Coordinate geometry of the circle
Objectives in this topic
8.1. Use circle equations
- Know and use the equation of a circle with radius r and centre (a, b).
- Identify the centre and radius from circle equations in any form, including (x - a)^2 + (y - b)^2 = r^2 and x^2 + y^2 + 2gx + 2fy + c = 0.
- The formula is given in the List of formulas.
8.2. Solve line-circle intersection problems
- Solve problems involving the intersection of a circle and a straight line.
- Find points of intersection and determine whether a line is a tangent, a chord or does not intersect the circle.
8.3. Solve tangent problems
- Solve problems involving tangents to a circle, including finding equations of tangents.
- No use of calculus is expected.
8.4. Solve circle-circle intersection problems
- Solve problems involving the intersection of two circles.
- Find points of intersection, find the equation of a common chord, and determine whether two circles intersect, touch or do not intersect.
Topic 9
9. Circular measure
Objectives in this topic
9.1. Solve arc length and sector area problems
- Solve problems involving arc length and sector area of a circle, including knowledge and use of radian measure.
- Use radian measure in problems that may involve compound shapes.
- Formulas are not given.
Topic 10
10. Trigonometry
Objectives in this topic
10.1. Use the six trigonometric functions
- Know and use sine, cosine, tangent, secant, cosecant and cotangent for angles of any magnitude.
10.2. Use amplitude and period
- Understand and use the amplitude and period of a trigonometric function.
- Understand relationships between graphs of related trigonometric functions, such as y = sin x and y = 3 sin 2x.
- The period may be in degrees or radians.
10.3. Draw and use trigonometric graphs
- Draw and use graphs of y = a sin bx + c, y = a cos bx + c and y = a tan bx + c.
- Graphs are drawn over a given domain, in degrees or radians.
- For y = a tan bx + c, clearly label the x-coordinate of any asymptote.
- Use a as a positive integer, b as a simple fraction or integer, and c as an integer; simple fractions have denominator 2, 3, 4, 6 or 8 only.
10.4. Use trigonometric identities
- Use the relationships sin^2 A + cos^2 A = 1, sec^2 A = 1 + tan^2 A and cosec^2 A = 1 + cot^2 A.
- Trigonometric identities are given in the List of formulas.
10.5. Solve trigonometric equations
- Solve trigonometric equations over a given domain involving the six trigonometric functions.
- Includes use of the relationships in 10.4.
10.6. Prove trigonometric relationships
- Prove trigonometric relationships involving the six trigonometric functions.
- Includes use of the relationships in 10.4.