1. Evaluate: $\frac{6}{11} \div \left(-\frac{3}{5}\right)$. Use the rule: dividing by a fraction is the same as multiplying by its reciprocal. $$\frac{6}{11} \div \left(-\frac{3}{5}\right) = \frac{6}{11} \times \left(-\frac{5}{3}\right)$$ 2. Multiply numerators and denominators: $$\frac{6 \times (-5)}{11 \times 3} = \frac{-30}{33}$$ 3. Simplify the fraction by dividing numerator and denominator by 3: $$\frac{\cancel{-30}^{-10}}{\cancel{33}^{11}} = -\frac{10}{11}$$ Answer: A. $-\frac{10}{11}$ --- 1. Compare $0.65$ and $\frac{2}{3}$. 2. Convert $\frac{2}{3}$ to decimal: $$\frac{2}{3} = 0.666\ldots$$ 3. Compare decimals: $0.65 < 0.666\ldots$ Answer: C. $0.65 < \frac{2}{3}$ --- 1. Evaluate: $(-4)^2 + \left(\frac{1}{5} \times 15\right)$. 2. Calculate each term: $$(-4)^2 = 16$$ $$\frac{1}{5} \times 15 = 3$$ 3. Add results: $$16 + 3 = 19$$ Answer: B. 19 --- 1. Expand and simplify: $3(a + 2b - 5) + 2(4a - b + 1)$. 2. Distribute: $$3a + 6b - 15 + 8a - 2b + 2$$ 3. Combine like terms: $$3a + 8a = 11a$$ $$6b - 2b = 4b$$ $$-15 + 2 = -13$$ 4. Final expression: $$11a + 4b - 13$$ Answer: A. $11a + 4b - 13$ --- 1. Simplify: $9p - 3(2p - 4q + 1) + 5q$. 2. Distribute: $$9p - 6p + 12q - 3 + 5q$$ 3. Combine like terms: $$9p - 6p = 3p$$ $$12q + 5q = 17q$$ 4. Final expression: $$3p + 17q - 3$$ Answer: A. $3p + 17q - 3$ --- 1. Arrange in ascending order: $-0.6, \frac{3}{10}, -\frac{1}{4}, 0.75$. 2. Convert fractions to decimals: $$\frac{3}{10} = 0.3$$ $$-\frac{1}{4} = -0.25$$ 3. Order from smallest to largest: $$-0.6, -0.25, 0.3, 0.75$$ Answer: A. $-0.6, -\frac{1}{4}, \frac{3}{10}, 0.75$ --- 1. Can a triangle be formed with sides 5 cm, 6 cm, and 12 cm? 2. Triangle inequality: sum of any two sides must be greater than the third. Check $5 + 6 = 11 < 12$. 3. Since $5 + 6 < 12$, triangle cannot be formed. Answer: B. No, because $5 + 6 < 12$ --- 1. Ladder problem: ladder is 6 m from wall, reaches 8 m high. Find length. 2. Use Pythagoras theorem: $$\text{length} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$$ Answer: A. 10 m --- 1. Two circles with radii 15 cm and 6 cm touch internally. Find distance between centers. 2. Distance between centers = difference of radii: $$15 - 6 = 9$$ Answer: A. 9 cm --- 1. Two circles with radii 10 cm and 4 cm touch internally. Find distance between centers. 2. Distance = difference of radii: $$10 - 4 = 6$$ Answer: A. 6 cm --- 1. Right triangle legs 9 cm and 12 cm. Find height to hypotenuse. 2. Hypotenuse: $$c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15$$ 3. Area: $$\frac{1}{2} \times 9 \times 12 = 54$$ 4. Height to hypotenuse $h$: $$h = \frac{2 \times \text{area}}{c} = \frac{2 \times 54}{15} = \frac{108}{15} = 7.2$$ Answer: C. 7.2 cm --- 1. Evaluate $M = (4x - 3) + (x^2 - y)$ for $x=4$, $y=6$. 2. Substitute: $$M = (4 \times 4 - 3) + (4^2 - 6) = (16 - 3) + (16 - 6) = 13 + 10 = 23$$ Answer: D. 23 --- 1. Expand and simplify: $4(m - 2n + 3) + 2(3m + n - 5)$. 2. Distribute: $$4m - 8n + 12 + 6m + 2n - 10$$ 3. Combine like terms: $$4m + 6m = 10m$$ $$-8n + 2n = -6n$$ $$12 - 10 = 2$$ 4. Final expression: $$10m - 6n + 2$$ Answer: A. $10m - 6n + 2$ --- 1. Right triangle legs 10 cm and 24 cm. Find height to hypotenuse. 2. Hypotenuse: $$c = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26$$ 3. Area: $$\frac{1}{2} \times 10 \times 24 = 120$$ 4. Height to hypotenuse $h$: $$h = \frac{2 \times 120}{26} = \frac{240}{26} \approx 9.23$$ Closest answer: 9.6 cm Answer: A. 9.6 cm --- 1. Right triangle hypotenuse 20 cm, one side 12 cm. Find other side. 2. Use Pythagoras: $$b = \sqrt{20^2 - 12^2} = \sqrt{400 - 144} = \sqrt{256} = 16$$ Answer: C. 16 cm --- 1. Point N is 18 cm from a line along slanted line; perpendicular distance is 11 cm. Which is true distance? 2. True distance is the perpendicular distance. Answer: B. 11 cm