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Geometry and Trigonometry

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  1. 7. Straight-line graphs

    1. • Use the equation of a straight line.

    2. • Know and use the condition for two lines to be parallel or perpendicular.

    3. • Solve problems involving midpoint and length of a line. • Find and use the equation of a perpendicular bisector.

    4. • 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.

  2. 8. Coordinate geometry of the circle

    1. • 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.

    2. • 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.

    3. • Solve problems involving tangents to a circle, including finding equations of tangents. • No use of calculus is expected.

    4. • 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.

  3. 9. Circular measure

    1. • 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.

  4. 10. Trigonometry

    1. 10.1. Use the six trigonometric functions

      • Know and use sine, cosine, tangent, secant, cosecant and cotangent for angles of any magnitude.

    2. 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.

    3. 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.

    4. 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.

    5. 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.

    6. 10.6. Prove trigonometric relationships

      • Prove trigonometric relationships involving the six trigonometric functions. • Includes use of the relationships in 10.4.