Comprehensive assessment covering all 20 lessons, from place value and rational numbers to prime factorisation, roots and index laws.
Question 21 3 marks
(a) Write 4,506,070 in words. 1 mark
(b) What is the value of the digit 5 in 4,506,070? 1 mark
(c) Round 4,506,070 to the nearest hundred thousand. 1 mark
(a) Four million, five hundred and six thousand and seventy [1]
(b) The 5 is in the hundred-thousands place, so its value is 500,000 [1]
(c) 4,500,000 [1]
Question 22 4 marks
(a) Evaluate: $-8 + 15 - (-3)$ 2 marks
(b) Evaluate: $(-4) \times (-5) \div (-2)$ 2 marks
(a) $-8 + 15 = 7$ [1]. $7 - (-3) = 7 + 3 = 10$ [1]
(b) $(-4) \times (-5) = 20$ [1]. $20 \div (-2) = -10$ [1]
Question 23 4 marks
(a) Simplify $\frac{24}{36}$ to lowest terms. 1 mark
(b) Evaluate: $\frac{2}{3} + \frac{3}{4}$ 2 marks
(c) Evaluate: $\frac{5}{6} \div \frac{2}{3}$ 1 mark
(a) $\frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}$ [1]
(b) LCD = 12. $\frac{2}{3} = \frac{8}{12}$, $\frac{3}{4} = \frac{9}{12}$ [1]. $\frac{8}{12} + \frac{9}{12} = \frac{17}{12} = 1\frac{5}{12}$ [1]
(c) $\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}$ [1]
Question 24 4 marks
(a) Convert 0.375 to a fraction in lowest terms. 1 mark
(b) Convert $\frac{2}{5}$ to a percentage. 1 mark
(c) A $250 bicycle has 20% off. What is the sale price? 2 marks
(a) $0.375 = \frac{375}{1000} = \frac{3}{8}$ [1]
(b) $\frac{2}{5} = 0.4 = 40\%$ [1]
(c) Discount = $20\%$ of $\$250 = \$50$ [1]. Sale price = $\$250 - \$50 = \$200$ [1]
Question 25 5 marks
(a) Simplify the ratio 18:24. 1 mark
(b) Divide $72 in the ratio 5:4. 2 marks
(c) A car travels 420 km in 6 hours. What is its average speed? 1 mark
(d) Which is better value: 400 g for $\$5$ or 1 kg for $\$12$? 1 mark
(a) $18:24 = 3:4$ [1]
(b) Total parts = 9. Each part = $\$72 \div 9 = \$8$ [1]. Shares are $\$40$ and $\$32$ [1]
(c) Speed = $420 \div 6 = 70$ km/h [1]
(d) 400 g for $\$5 = \$12.50$/kg. 1 kg for $\$12 = \$12$/kg. The 1 kg for $\$12$ is better value [1]
Question 26 5 marks
(a) Write 360 as a product of prime powers. 2 marks
(b) Simplify $(2^3)^2 \times 2^4 \div 2^7$. 2 marks
(c) Explain why $11^0=1$. 1 mark
(a) $360 = 36 \times 10 = 2^3 \times 3^2 \times 5$ [2]
(b) $(2^3)^2 \times 2^4 \div 2^7 = 2^6 \times 2^4 \div 2^7 = 2^{6+4-7}=2^3=8$ [2]
(c) $11^3 \div 11^3=11^0$, and a non-zero number divided by itself is 1 [1]