55&57 | Geometry and Trigonometry | Multiple Choice 5 | CXC CSEC Mathematics
CXC CSEC Mathematics Multiple Choice 5 – In this Caribbean Examination Council (CXC) Caribbean Secondary Education Certificate (CSEC) Mathematics Multiple Choice Examination, questions 55 and 57 are based on the topic Geometry and Trigonometry.
Related videos:
Laws of Indices: • Laws of indices | Algebra
This topic:
GEOMETRY AND TRIGONOMETRY (Playlist: • 4. Geometry and Trigonometry )
Upon completion of this series of videos on this topic, you will understand/be able to:
1. explain concepts relating to geometry;
a. Points, lines, parallel lines, intersecting lines, perpendicular lines, line segments, rays, curves, planes; types of angles; number of faces, edges and vertices.
2. identify the type(s) of symmetry possessed by a given plane figure;
a. Line(s) of symmetry, rotational symmetry, order of rotational symmetry.
3. solve geometric problems using properties of:
a. lines, angles, and polygons;
i. Determining and justifying the measure of angles: adjacent angles, angles at a point, supplementary angles, complementary angles, vertically opposite angles.
ii. Parallel lines and transversals, alternate angles, corresponding angles, co-interior angles.
iii. Triangles: equilateral, isosceles, scalene, obtuse, right, acute.
iv. Quadrilaterals: Square, rectangle, rhombus, kite, parallelogram, trapezium.
v. Other polygons.
b. congruent triangles;
i. Cases of congruency.
c. similar figures;
i. Properties of similar triangles
d. faces, edges and vertices of solids; and,
e. classes of solids;
i. Prisms, pyramids, cylinders, cones, sphere.
4. solve geometric problems using properties of circles and circle theorems;
a. Radius, diameter, chord, circumference, arc, tangent, segment, sector, semicircle, pi.
b. Determining and justifying angles using the circle theorems:
i. The angle which an arc of a circle subtends at the centre of a circle is twice the angle it subtends at any point on the remaining part of the circumference.
ii. Angles at the circumference in the same segment of a circle and subtended by the same arc/chord are equal.
iii. The angle at the circumference subtended by the diameter is a right angle.
iv. The opposite angles of a cyclic quadrilateral are supplementary.
v. The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
vi. The angle between a tangent to a circle and a chord through the point of contact is equal to the angle in the alternate segment.
vii. A tangent of a circle is perpendicular to the radius/diameter of that circle at the point of contact.
viii. The lengths of two tangents from an external point to the points of contact on the circle are equal.
ix. The line joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.
5. use Pythagoras’ theorem to solve problems;
6. define the trigonometric ratios of acute angles in a right triangle;
a. Sine, Cosine, Tangent.
7. relate objects in the physical world to geometric objects;
a. Angle of elevation, angle of depression, bearing.
8. apply the trigonometric ratios to solve problems;
a. Spatial geometry and scale drawing, angles of elevation and depression.
9. use the sine and cosine rules to solve problems involving triangles; and,
10. solve problems involving bearings.
a. Relative position of two points given the bearing of one point with respect to the other; bearing of one point relative to another point given the position of the points. Bearings written in 3-digit format, for example 060°.
11. represent translations in a plane using vectors;
a. Column matrix notation
12. determine and represent the location of the image of an object under a transformation and an object given the image under a transformation;
a. Translation in the plane.
b. Reflection in a line in that plane.
c. Rotation about a point (the centre of rotation) in that plane.
d. Enlargement in the plane.
13. state the relationship between an object and its image in the plane under geometric transformations;
a. Orientation, similarity, congruency.
14. describe a transformation given an object and its image;
a. Translation: vector notation.
b. Reflection: mirror line/ axis of symmetry.
c. Rotation: centre of rotation, angle of rotation, direction of rotation.
d. Enlargement: centre, scale factor 𝑘
15. locate the image of an object under a combination of transformations; Combination of any two of :
a. enlargement;
b. translation;
c. rotation; and,
d. reflection.
16. draw and measure angles and line segments accurately using appropriate instruments;
17. construct lines, angles, and polygons using appropriate instruments;
a. Parallel and perpendicular lines.
b. Bisecting line segments and angles.
c. Constructing a line perpendicular to another line, L, from a point that is not on the line, L.
d. Triangles, quadrilaterals, regular and irregular polygons.
e. Angles include 30°, 45°, 60°, 90°, 120° and their combinations.