Curriculum

Course: Mathematics — Second Preparatory

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Curriculum

Mathematics — Second Preparatory

Unit 1: Real Numbers

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Unit 2: Algebra

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Unit 3: Geometry

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Unit 4: Statistics

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Text lesson

The Pythagorean Theorem

Mathematics — Second Preparatory

The Pythagorean Theorem

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	A right triangle has legs of 6 cm and 8 cm. Find the hypotenuse	righttrianglelegsFind
Solution	c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm.
Example 2	A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the other leg	righttrianglehypotenuseFind
Solution	The unknown leg = √(13² − 5²) = √(169 − 25) = √144 = 12 cm. Check: 5² + 12² = 25 + 144 = 169 = 13².	unknownCheck
Example 3	A ladder 13 m long leans with its top against a vertical wall and its foot is 5 m from the wall. How high on the wall does the ladder reach?	ladderlongleansagainst
Solution	The height = √(13² − 5²) = √144 = 12 m. The wall, the ground and the ladder form a right triangle at the foot of the wall.	heightwallgroundladder
Example 4	A rectangle has sides 9 cm and 12 cm. Find its diagonal. Then find approximately the diagonal of a square with side 5 cm	rectanglesidesFinddiagonal

Solution→The diagonal of the rectangle = √(9² + 12²) = √(81 + 144) = √225 = 15 cm. The diagonal of the square = √(5² + 5²) = √50 = 5√2 ≈ 7.07 cm.

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