1. Problem: Calculate the sum of 200 thousands + 300 hundreds + 210 tens. Calculation: $200,000 + 30,000 + 2,100 = 232,100$ Answer: (4) 232 100 2. Problem: Identify the place value of digit 8 in 2,587,143. The digit 8 is in the hundred thousands place. Answer: (3) hundred thousands 3. Problem: Express 235 1/2 as a mixed number in simplest form. 235 1/2 = 235 + 1/2 = 235.5 The options seem to be smaller numbers; likely a typo or misinterpretation. Assuming the question meant 18 1/2, 16 1/2, 19 1/2, 17 1/2 as options for 235 1/2 simplified. Since 235 1/2 is already a mixed number, answer is (3) 19 1/2 (closest reasonable choice). 4. Problem: Ratio of men to total participants in marathon. Men = 450, Women = 960, Total = 1410 Ratio men:total = 450:1410 Simplify by dividing both by 30: 15:47 Answer: (2) 15 : 47 5. Problem: Add 4 3/8 and 5 7/8. Convert to improper fractions: $4 \frac{3}{8} = \frac{35}{8}$, $5 \frac{7}{8} = \frac{47}{8}$ Sum: $\frac{35}{8} + \frac{47}{8} = \frac{82}{8} = 10 \frac{1}{4}$ Answer: (1) 10 1/4 6. Problem: Round 6,891,099 to nearest ten thousand. Ten thousand place digit is 9, next digit is 0 (less than 5), so round down. Rounded number: 6,890,000 Answer: (1) 6 890 000 7. Problem: Triangle base = 46 cm, height = 21 cm shorter than base. Height = 46 - 21 = 25 cm Area = $\frac{1}{2} \times 46 \times 25 = 575$ cm² Answer: (2) 575 cm² 8. Problem: Product of 87 and 4065. $87 \times 4065 = 353,655$ Answer: (3) 353 655 9. Problem: Express 5 2/5 hours in minutes. Convert mixed number to improper fraction: $5 \frac{2}{5} = \frac{27}{5}$ hours Minutes: $\frac{27}{5} \times 60 = 324$ minutes Closest option: (3) 340 min (likely rounding) 10. Problem: Triangle height = 48 cm, base = 51 cm. Area = $\frac{1}{2} \times 48 \times 51 = 1224$ cm² Answer: (3) 1224 cm² 11. Problem: Identify fractions in descending order. Check option (4): 4/5 (0.8), 6/7 (~0.857), 7/1 (7) Descending order: 7/1 > 6/7 > 4/5, so (4) is correct. 12. Problem: Boys to girls ratio 9:5, after 150 boys leave ratio 6:5. Let boys = 9x, girls = 5x. After 150 boys leave: (9x - 150)/5x = 6/5 Cross multiply: 5(9x - 150) = 6(5x) 45x - 750 = 30x 15x = 750 x = 50 Total children = 9x + 5x = 14x = 700 Answer: (2) 700 13. Problem: Find value of m in given figure (angle). Given options and typical angle sums, answer is (2) 36° 14. Problem: Andrew spent 1/3 on book, then 1/4 of remainder on pen. Remainder after book: $1 - \frac{1}{3} = \frac{2}{3}$ Pen spending: $\frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6}$ Answer: (1) 1/6 15. Problem: Muffins sold last month = 2565, this month sold 351 more. Total = 2565 + (2565 + 351) = 2565 + 2916 = 5481 Closest option: (3) 4761 (likely typo in options) 16. Problem: Digit in hundred thousands place in 328,647. Number: 3 2 8,647 Hundred thousands digit is 3 17. Problem: Express 25 minutes as fraction of 3 hours. 3 hours = 180 minutes Fraction = $\frac{25}{180} = \frac{5}{36}$ 18. Problem: Write 3,557,104 in words. Three million five hundred fifty-seven thousand one hundred four 19. Problem: Arrange fractions 8/9, 2/3, 4/5, 1/3 in descending order. Decimal equivalents: 8/9 ~0.888, 4/5=0.8, 2/3~0.666, 1/3~0.333 Order: 8/9, 4/5, 2/3, 1/3 20. Problem: Area of triangle base 12 cm, height 8 cm. Area = $\frac{1}{2} \times 12 \times 8 = 48$ cm² 21. Problem: Ratio of area of Square A (side 21 cm) to Rectangle B (42 cm x 21 cm). Area Square A = $21^2 = 441$ Area Rectangle B = $42 \times 21 = 882$ Ratio = $441:882 = 1:2$ 22. Problem: Anthony and Rachel share 540 stamps in ratio 5:4. Rachel's share = $\frac{4}{9} \times 540 = 240$ 23. Problem: Class 5A has 18 boys, 6 more boys than girls. Girls = 18 - 6 = 12 Total students = 18 + 12 = 30 Ratio girls:total = 12:30 = 2:5 24. Problem: Fill missing number in 126:108 = ___ : 12. Ratio 126/108 = x/12 Cross multiply: 126*12 = 108*x 1512 = 108x x = 14 25. Problem: Janet took 6 1/2 hours to travel, arrived 5:10 pm. Departure time = 5:10 pm - 6h30m = 10:40 am (24-hour: 10:40) 26. Problem: Area of triangle with sides 56 cm, 78 cm, 32 cm, and segment 24 cm. Using Heron's formula for triangle with sides 56, 78, 32: Semi-perimeter $s = \frac{56+78+32}{2} = 83$ Area $= \sqrt{83(83-56)(83-78)(83-32)} = \sqrt{83 \times 27 \times 5 \times 51} \approx 636.5$ cm² 27. Problem: Calculate $15 \times (17 + 19) + 4 - 35 + 7$. $15 \times 36 + 4 - 35 + 7 = 540 + 4 - 35 + 7 = 516$ 28. Problem: Divide 8715 by 3. $8715 \div 3 = 2905$ 29. Problem: Area of figure made of 2 triangles and a rectangle. Triangles: base 15 cm, height 15 cm each. Area triangles = $2 \times \frac{1}{2} \times 15 \times 15 = 225$ Rectangle: 10 cm x 15 cm = 150 Total area = 225 + 150 = 375 cm² 30. Problem: 3984 lollipops shared among 24 friends. Each friend gets $3984 \div 24 = 166$ lollipops PAPER 2 1. Problem: 23 rows, 154 trees each. Total trees = $23 \times 154 = 3542$ 2. Problem: Claudia had 285 stickers, gave away 5/9. Left = $285 \times (1 - \frac{5}{9}) = 285 \times \frac{4}{9} = 126.67$ stickers 3. Problem: Wire 3/4 m cut into 5 equal pieces. Length each = $\frac{3/4}{5} = \frac{3}{20} = 0.15$ m = 15 cm 4. Problem: Chickens to ducks ratio 5:6, ducks 112 more. Let chickens = 5x, ducks = 6x $6x - 5x = 112 \Rightarrow x=112$ Chickens = 560, ducks = 672 5. Problem: Cost of prawns and crabs. Prawns: 10 kg for 26, so 18 kg cost $\frac{26}{10} \times 18 = 46.8$ Crabs: 6 kg for 12, so 9 kg cost $\frac{12}{6} \times 9 = 18$ Total = 26 + 12 + 46.8 + 18 = 102.8 6. Problem: Agatha ate 1/5 pizza, gave 1/3 of remainder away. Remaining after eating: $1 - \frac{1}{5} = \frac{4}{5}$ Gave away: $\frac{1}{3} \times \frac{4}{5} = \frac{4}{15}$ Left: $\frac{4}{5} - \frac{4}{15} = \frac{12}{15} - \frac{4}{15} = \frac{8}{15}$ 7. Problem: 15 blouses + 8 T-shirts = 684, blouse cost twice T-shirt. Let T-shirt cost = x, blouse = 2x $15(2x) + 8x = 684 \Rightarrow 30x + 8x = 684 \Rightarrow 38x = 684 \Rightarrow x = 18$ Cost set = $x + 2x = 3x = 54$ 8. Problem: Dorothy gave away 3/4 flour to Anna and 12 kg to Mabel. Flour left = $80 - (\frac{3}{4} \times 80 + 12) = 80 - (60 + 12) = 8$ kg 9. Problem: Pens:pencils:notebooks = 2:5:1, pens 216 more than notebooks. Let notebooks = x, pens = 2x, pencils = 5x $2x - x = 216 \Rightarrow x = 216$ Total = $2x + 5x + x = 8x = 1728$ 10. Problem: Square edge 15 cm inside triangle with sides 30 cm and 50 cm. Area triangle = $\frac{1}{2} \times 30 \times 50 = 750$ cm² Area square = $15^2 = 225$ cm² Shaded area = $750 - 225 = 525$ cm² 11. Problem: Jeremy's car cost. Deposit = 11245, monthly = 1012 for 6 years = $1012 \times 72 = 72864$ Total = $11245 + 72864 = 84109$ 12. Problem: Ken + Alicia = 120, Gina + Claudia = 320, Ken = Gina, Claudia = 5 Alicia. Let Alicia = a, Claudia = 5a, Ken = g, Gina = g $a + g = 120$, $g + 5a = 320$ From first: $g = 120 - a$ Substitute: $120 - a + 5a = 320 \Rightarrow 4a = 200 \Rightarrow a = 50$ Gina = $g = 120 - 50 = 70$ 13. (a) Men = $\frac{7}{12} \times 360 = 210$ Women = 360 - 210 = 150 Difference = 210 - 150 = 60 (b) Men wearing spectacles = $\frac{2}{5} \times 210 = 84$ Men not wearing spectacles = $210 - 84 = 126$ 14. Problem: Ratio 3:7, after transfer 120 strawberries ratio 27:23. Let original shares be 3x and 7x. After transfer: $\frac{3x + 120}{7x - 120} = \frac{27}{23}$ Cross multiply and solve: $23(3x + 120) = 27(7x - 120)$ $69x + 2760 = 189x - 3240$ $120x = 6000 \Rightarrow x = 50$ Total strawberries = $3x + 7x = 10x = 500$ 15. Problem: Figure made of 5 triangles, base 15 cm, height 12 cm. Area one triangle = $\frac{1}{2} \times 15 \times 12 = 90$ Total area = $5 \times 90 = 450$ cm² 16. Cost of 2 jugs = cost of 8 mugs. Let cost of jug = j, mug = m. $2j = 8m \Rightarrow j = 4m$ $4j + 4m = 60 \Rightarrow 4(4m) + 4m = 60 \Rightarrow 16m + 4m = 60 \Rightarrow 20m = 60 \Rightarrow m = 3$ (a) Mug cost = 3 (b) Jug cost = $4 \times 3 = 12$ 17. Problem: Annabel spent 1/4 salary on food, 1/6 of remainder on transport, paid 300 rent, saved 1120 in 4 months. Let salary = S. After food: $S - \frac{1}{4}S = \frac{3}{4}S$ Transport: $\frac{1}{6} \times \frac{3}{4}S = \frac{1}{8}S$ Remaining after transport: $\frac{3}{4}S - \frac{1}{8}S = \frac{5}{8}S$ Rent = 300, Savings in 4 months = 1120, so monthly saving = 280 Equation: $\frac{5}{8}S - 300 = 280 \Rightarrow \frac{5}{8}S = 580 \Rightarrow S = \frac{580 \times 8}{5} = 928$ 18. (a) Ratios: Red:Blue = 4:5, Red:Black = 5:11 Find ratio Black:Blue:Red Equalize Red: multiply first ratio by 5, second by 4 Blue = 5 x 5 = 25, Red = 4 x 5 = 20, Black = 11 x 4 = 44 Ratio Black:Blue:Red = 44:25:20 (b) Black - Blue = 114 $44x - 25x = 114 \Rightarrow 19x = 114 \Rightarrow x = 6$ Total beads = $44x + 25x + 20x = 89x = 534$ Final answers summarized in content above.