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1. End of Unit Test on Bivariate Data for S3 Students
2. End of Unit Test on Inverse and Composite Transformations in 2D for S3 Students
3. End of Unit Test on Collinear Points and Orthogonal Vectors for S3 Students
4. End of Unit Test on Right Angled Triangles for S3 Students
5. End of Unit Test on Percentage Interest and Proportion for S3 Students
6. End of Unit Test on Linear and Quadratic Functions for S3 Students
7. End of Unit Test on Quadratic Equations for S3 Students
8. End of Unit Test on Simultaneous Equations and Inequalities for S3 Students
9. End of Unit Test on Algebraic Fractions for S3 Students
10. End of Unit Test on Number Bases for S3 Students
11. End of Unit Test on Problems on Sets for S3 Students
Enlargement and Similarity in 2D Unit Summary
1. Two triangles are similar if the corresponding sides are in proportion, i.e. have a constant ratio or the corresponding angles are equal. Congruent triangles are also similar.
2. For all shapes, other than triangles, both similarity conditions must be satisfied for them to be similar.
3. The ratio of the corresponding sides in similar figures is called a linear scale factor.
\(L.S.F=\frac{\text{ Length of image }}{\text{ Length of object }}\)
4. For all solids, corresponding angles must be equal and the ratios of corresponding lengths must be equal for the solids to be similar.
5. All cuboids are equiangular since all the faces are either rectangular or squares. However, not all cuboids are similar but all cubes are.
6. If two figures are similar, the ratio of their corresponding areas equals the square of their linear scale factor.
\(A.S.F = (L.S.F)^{2}\)
7. If two solids are similar, then the ratio of their corresponding volumes equals the cube of their linear scale factor.
\(V.S.F = (L.S.F)^{3}\)
8. An enlargement is defined completely if the scale factor and the centre of enlargement are known.
9. In an enlargement the object and its image are similar. If the scale factor is \(\pm 1\), the object and its image are identical. Scale factor of enlargement.
\(\text{ Scale factor of enlargement }=\frac{\text{ Length of image }}{\text{ Length of object }}\)
\(\text{ Scale factor of enlargement }=\frac{\text{ Image distance from centre of enlargement }}{\text{ Object distance from centre of enlargement}}\)
10. To locate the centre of enlargement given an object and its image,
(a) join any two pairs of corresponding points.
(b) produce the lines until they meet at a point, that point is the centre of enlargement.
11. An enlargement scale factor \(k\) centre origin \((0, 0)\) maps a point \(P(a, b)\) onto \(P^{'}(ka , kb)\).