Grade 10

Mathematics · Unit 1 · Trigonometric Ratios and Identities

• I can name the opposite side, the adjacent side and the hypotenuse for any acute angle.
• I can write the sine, cosine, tangent and cotangent of an angle in a right triangle.
• I can give the exact ratios of 30, 45 and 60 degrees without a calculator.
• I can explain why the ratios stay the same when the triangle changes size.
• I can prove the identities that come from the Pythagorean theorem.
• I can read the ratios of an angle larger than 90 degrees from the unit circle.

Mathematics · Unit 1 · Pythagoras and the Primary Ratios

• I can find a missing side of a right triangle with the Pythagorean theorem.
• I can test three lengths to decide whether a triangle has a right angle.
• I can choose the ratio a question needs and say why I chose it.
• I can find a missing side whether the unknown is above or below the line.
• I can find an acute angle from a ratio of two sides.
• I can solve a right triangle completely and check my answer.

Mathematics · Unit 1 · Indirect Measurement

• I can say which lengths I can measure directly and which I must calculate.
• I can turn a written situation into a labelled right triangle.
• I can add the height of my own eye at the right moment.
• I can solve a problem that needs two triangles sharing one side.
• I can find the distance between two viewing points, not only the height.
• I can explain how an error of one degree changes the answer.

Mathematics · Unit 1 · Auxiliary Elements of a Triangle

• I can name the four auxiliary elements of a triangle.
• I can use the angle bisector as the set of points at equal distance from two arms.
• I can use the interior and the exterior angle bisector theorems.
• I can find the angle between two bisectors.
• I can use the centroid and the two to one ratio on a median.
• I can say where the circumcentre and the orthocentre lie in any triangle.

Mathematics · Unit 1 · The Area of a Triangle

• I can find an area from any of the three base and height pairs.
• I can compare two areas that have the same height.
• I can split an area with a line drawn from a corner.
• I can show that sliding the top corner along a parallel line does not change the area.
• I can use the medians to cut a triangle into equal parts.
• I can scale an area by the square of the similarity ratio.

Mathematics · Unit 1 · The Sine and Cosine Theorems

• I can find an area from two sides and the angle between them.
• I can compare two areas in the case where the sine cancels.
• I can build the law of sines from the three area expressions.
• I can prove the cosine theorem when the angle is acute and when it is obtuse.
• I can use the sign of the cosine to say what kind of angle it is.
• I can find the length of a median.