Math: Algebra, Geometry, and Number Manipulation

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Questions and Answers

In a right-angled triangle, if the two shorter sides are 5 cm and 12 cm, what is the length of the hypotenuse?

13 cm (correct)
60 cm
169 cm
17 cm

Pythagoras' Theorem can only be applied to acute, right triangles.

False (B)

A ladder leans against a wall, forming a right-angled triangle. The ladder is 10m long and its base is 6m away from the wall. How high up the wall does the ladder reach?

In a right-angled triangle, the side opposite the right angle is called the ______.

<p>hypotenuse</p> Signup and view all the answers

A triangle has sides of length 7, 8, and 11. Is it a right-angled triangle?

<p>No, because $7^2 + 8^2$ does not equal $11^2$. (D)</p> Signup and view all the answers

Flashcards

Percentages

Expressing a number as a fraction of 100.

Standard Form

Expressing numbers using powers of 10 for concise representation.

Laws of Indices

Rules for simplifying expressions with exponents.

Algebraic Fractions

Fractions with variables in the numerator, denominator, or both.

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Pythagoras' Theorem

a² + b² = c²: Relates the sides of a right-angled triangle.

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Study Notes

Focus on number manipulation, algebra, and geometry.

Number

Percentages are a way of expressing a number as a fraction of 100
Standard form expresses very large or very small numbers concisely using powers of 10.
Laws of indices govern how to simplify expressions involving exponents.

Algebra

Algebraic fractions involve variables in the numerator and/or denominator.
Solving equations with powers and roots requires inverse operations to isolate the variable.
Solving inequalities involves similar steps to solving equations, but with attention to how the inequality sign changes when multiplying or dividing by a negative number.

Shape and Space

Circle theorems describe the relationships between angles, chords, tangents, and radii in a circle.
Pythagoras' Theorem relates the sides of a right-angled triangle: a² + b² = c².
Trigonometry utilizes ratios of sides in right-angled triangles to find unknown angles or lengths, often in conjunction with Pythagoras' Theorem.

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Description

Explore number manipulation with percentages, standard form, and indices. Learn to solve algebraic fractions, equations, and inequalities. Understand circle theorems, Pythagoras' Theorem, and trigonometry for shape and space.