CXC Math Topic: GEOMETRY AND TRIGONOMETRY (2010)
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CXC General Proficiency Math Topic: GEOMETRY AND TRIGONOMETRY (2010) |
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GENERAL OBJECTIVES On completion of this section, students should: 1. appreciate the notion of space as a set of points with subsets of that set (space) having properties related to other mathematical systems; 2. understand the properties and relationship among geometrical objects; 3. understand the properties of transformations; 4. demonstrate the ability to use geometrical concepts to model and solve real-world problems; 5. appreciate the power of trigonometrical methods in solving authentic problems. |
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SPECIFIC OBJECTIVES: Students should be able to: |
CONTENT | |
| 1. | explain concepts relating to geometry; |
Point, line, parallel lines, intersecting lines and perpendicular lines, line segment, ray, curve, plane, angle, (acute, reflex, right angle, straight angle), face, edge, vertex. |
| 2. |
draw and measure angles and line segments accurately using appropriate geometrical instruments |
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| 3. |
construct lines, angles, and polygons using appropriate geometrical instruments; |
Parallel and perpendicular lines. Triangles, quadrilaterals, regular and irregular polygons. Angles to be constructed include 30, 45, 60, 90, 120. |
| 4. |
identify the type(s) of symmetry possessed by a given plane figure; |
For example f: x → x 2; or f(x)= x2 as well as y = f(x) for given domains. |
| 5. |
solve geometric problems using properties of: (a) lines, angles, and polygons; (b) circles; (c) congruent triangles; (d) similar figures; (e) faces, edges, and vertices of solids; (f) classes of solids; |
Vertically opposite angles, alternate angles, adjacent angles, corresponding angles, co-interior angles, angles at a point, complementary angles, supplementary angles. Parallel lines and transversals. Equilateral, right, and isosceles triangles. Square, rectangle, rhombus, kite, parallelogram, trapezium. Prisms, pyramids, cylinders, cones sphere. |
| 6. | represent translations in the plane using vectors; |
Column matrix notation [xy]
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| 7. |
determine and represent the location of: (a) the image of an object; (b) an object given the image under a transformation; |
x-intercepts and y-intercepts, graphically and algebraically. |
| 8. |
identify the relationship between an object and its image in the plane after a geometric transformation; |
Similar; Congruent. |
| 9. |
describe a transformation given an object and its image; |
A translation in the plane; a reflection in a line in that plane; a rotation about a point (the center of rotation) through an angle in the plane; an enlargement or reduction in that plane about a center. |
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locate the image of a set of points under a combination of transformations; |
Combination of any two of enlargement/reduction, translation, rotation, reflection, glide reflection. |
| 11 |
state the relations between an object and its image as the result of a combination of two transformations; |
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| 12 |
use Pythagoras' theorem to solve problems; |
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| 13 |
determine the trigonometric ratios of acute angles in a right angled triangle; |
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| 14 |
use trigonometric ratios in the solution of right angled triangles; |
Practical geometry and scale drawing, bearing.
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| 15 |
use trigonometric ratios to solve problems based on measures in the physical world; |
Heights and distances; angles of elevation and depression. |
| 16 |
use the sine and cosine rules in the solution of problems involving triangles; |
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| 17 |
represent the relative position of two points given the bearing of one point with respect to the other; |
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| 18 |
determine the bearing of one point relative to another point given the position of the points. |
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| 19 |
solve problems involving bearings; |
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| 20 |
solve practical problems involving heights and distances in three dimensional situations; |
Optional Specific Objective |
| 21 |
solve geometric problems using properties of circles and circle theorems. |
The angle which an arc of a circle subtends at the center of a circle is twice the angle it subtends at any point on the remaining part of the circumference. The angle in a semicircle is a right angle. Angles in the same segment of a circle and subtended by the same arc are equal. The opposite angles of cyclic quadrilateral are supplementary. The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. A tangent of a circle is perpendicular to the radius of that circle at the point of contact. The lengths of two tangents from an external point to the points of contact on the circle are equal. The angle between an tangent to a circle and a chord through the point of contact is equal to the angle in the alternate segment. The line joining the center of a circle to the midpoint of a chord is perpendicular to the chord. |
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Here are our Geometry and Trigonometry tutorials to help you prepare for this section of the CXC math exam. |
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Re: SBA
We provide SBA guides/templates for some CXC CSEC subjects. These SBA guides can be used to help you in writing your SBAs.
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i) all the information that should be in your SBA,
ii) how the information should be organized and laid out
iii) the mark scheme that is used for grading the SBAs.
If you use the search box, you will be able to find the CXC CSEC SBA guides/templates that we have available.
Help
Hey!! I really need some help. I've done mathematics CXC 2 times already and i really need to past it this time!! I need some help to refresh my memory. I need to start math class next September so i can start college the following year!! N paper 2 is always my problem