Mathematics ignite year 9 (Mid term 2 2025 test)

Identifying and recalling the formula

Topic: The sine rule (6F)

Formula: \frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}

Topic: Cosine rule (6G)

Formula: a^2 = b^2 + c^2 - 2bc \cdot cosA

Topic: Irrational numbers including surds (4A)

Concept: Numbers that cannot be expressed as a simple fraction \frac{p}{q}. Surds are irrational numbers involving the root of an integer (e.g., \sqrt{2}, \sqrt{3}, \sqrt{5}).

Topic: Adding and subtracting surds (4B)

Concept: a\sqrt{x} + b\sqrt{x} = (a+b)\sqrt{x}. Simplify surds first.

Topic: Multiplying and dividing surds (4C)

Concept: \sqrt{a} \times \sqrt{b} = \sqrt{ab}, \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}

Example: In triangle ABC, a=5 cm, \angleA=30^{\circ}, and \angleB=45^{\circ}. Find the length of side b.

Formula/Topic: The sine rule (6F)

Example: In triangle PQR, p=8 m, q=7 m, and \angleR=60^{\circ}. Find the length of side r.

Formula/Topic: Cosine rule (6G)

Example: Is \sqrt{7} a rational or irrational number? Explain your reasoning.

Formula/Topic: Irrational numbers including surds (4A) (\sqrt{7} is irrational.)

Example: Simplify 3\sqrt{5}+7\sqrt{5}-2\sqrt{5}.

Formula/Topic: Adding and subtracting surds (4B)

Example: Simplify \sqrt{3} \times \sqrt{12}.

Formula/Topic: Multiplying and dividing surds (4C)