Mathletics 2013

1. Mathletics 2013 Seniors – Grades 7 & 8 Session 1

2. Q1. Numeration (20+2)/(2+9)+15×3 = ? Answer

3. Q2. Fraction I Which is NOT equal to 15/4? (A) 3.75; (B) (14+1)/(3+1); (C) 3/4 + 3; (D) 5/4 × 3/4; (E) 21/4 - 5/4 -1/4. Answer

4. Q3. Driving Day 1: 8 hrs Day 2: 10 hrs Day 3: 7 hrs Day 4: 8 hrs Day 5: 9 hrs Day 6: 9 hrs Day 7: only 5 hrs due to sickness Calculate mean for first 6 days and then for all 7 days. A) 8.5 and 8.25 B) 8.5 and 8 C)8.25 and 8 D) 8 and 8.5 Answer

5. Q4. Parts of the Song How many bytes in the fifth part? • 2048 bytes in total, divided in 5 parts • The first 4 parts take up 1/2, 1/4, 1/8, and 1/16 of the total size Answer

6. Q5. Median What is the median score? Answer

7. Q6. Similar Triangles • Triangle ABC is similar to triangle PQR; certain edges are in proportion Answer

8. Q7. Cutting Loaf • Size: 30 × 6 × 5 (cm) • Two cuts from the top, dividing the loaf into 3 parts • New surfaces generated by the two cuts • Increase by 30 cm2 • Increase by 60 cm2 • Increase by 120 cm2 • Decrease by 30 cm2 Answer

9. Q8. Electrical Circuit • Bulb can be on by closing certain switches • Closed loop is necessary to light the bulb Answer

10. Q9. Sports Survey 20 people watch Baseball, 25 people said watch Basketball, 40 people watch Ice Hockey and 15 people watch soccer. Angle of basketball in the pie chart? Hint: 100% ↔ 360° Answer

11. Q10. Comics on the Wall How many posters (25cm×50cm) can be fit on the wall (4m×10m)? Answer

12. Q11. 2D & 3D Find the 3D shape representing the front, right side and top views shown. • Exclude any impossibilities! A B C D Answer

13. Q12. Parterre & Flowerpots • Round parterre with perimeter = 36m • 1 flowerpot every 3 m • 10 • 11 • 12 • 13 Answer

14. Q13. Sequence What is the next number in the sequence: 2, 5, 10, 17, ? Answer

15. Q14. Trapezoid Backyard Roomy backyard! • a, b, h are given. Fence Answer House

16. Q15. Cube • What is the minimum number of small cubes required to form a LARGER cube ? Answer

17. Q16. Factor • 2012 = 4 × 503 • 503 is a prime number (A) 2 (B) 3 (C) 7 (D) 6 (E) 8 Answer

18. Q17. Mass of the Sand Pile • Cone shape: diameter of surface = 40cm, height = 20cm • Density of sand: 1200kg/m3 • Mass = Density X Volume • 3 kg • 100 kg • 300 kg • 10 kg Answer

19. Q18. Area Calculation What is the area of the figure? Answer

20. Q19. Coins A collection of coins includes only pennies (1¢), nickels (5¢), dimes (10¢) and quarters (25¢). Using the coins in this collection, it is possible to create any amount of money less than one dollar (0-99¢). What is the smallest possible number of coins in the collection? (A) 10 (B) 7 (C) 11 (D) 13 (E) 12 Answer

21. Q20. Photo Shrinker How many steps must be experienced to retrieve 1 pixel photo? • 512 → 256 → 128 → … Answer

22. Numeration Solution: 47. Next Question

23. Fraction I Solution: D. 5/4 × 3/4 = 15/16 ≠ 5/4 Next Question

24. Driving Solution: (B) 8.5 and 8. • First 6 days: (8+10+7+8+9+9)/6=8.5; • All 7 days: (8+10+7+8+9+9+5)/7=8. Next Question

25. Parts of the Song Solution: 128 bytes. The fifth part takes up (1 – ½ – ¼ – 1/8 – 1/16) = 1/16 of the total song. = (1/16)X2048 = 128 Next Question

26. Median Solution: 7 points. 4, 6, 6, 6, 7, 8, 8, 9, 9 in order from small to large; median is the middle number. Next Question

27. Similar Triangles Solution: (C) Next Question

28. Cutting Loaf Solution: (C) Increased by 120 cm2. 4 new cross sections generated with the 2 cuts; area of each 5cm × 6cm = 30 cm2 Next Question

29. Electrical Circuit Solution: 4 ways. Next Question

30. Sport Survey Solution: 90 degrees. 25 / 100 × 360 = 90 Next Question

31. Comics on the Wall Solution: 320 posters in total. 4m / 0.25m = 16 10m / 0.5m = 20 16 × 20 = 320. Next Question

32. 2D & 3D Solution: A. The right view doesn’t belong to B The top view doesn’t belong to C and D The front view doesn’t belong to D Next Question

33. Parterre & Flowerpots Solution: (C) 12 flowerpots needed. 36 / 3 =12 3 m Next Question

34. Sequence (solution 1) Answer: 26 2 5 = 2 + 2 X 1 + 1 10 = 5 + 2 X 2 + 1 17 = 10 + 2 X 3 + 1 So the final number is 17 + 2 X 4 + 1 = 26 Continued…

35. Sequence (solution 2) Answer: 26 2 = 12 + 1 5 = 22 + 1 10 = 32 + 1 17 = 42 + 1 So the final number is 52 + 1 = 26 Next Question

36. Trapezoid Backyard Solution: 2400m2. A= (a+b) / 2 × h = (50 + 70) / 2 × 40 = 2400 Next Question

37. Cube Solution: (C) 8 small cubes. The next size cube is 2 X 2 X 2. Next Question

38. Factors Solution: Both 1 and 2012 are obvious positive integer factors of 2012. Since 2012 is an even number and 2012 ÷ 2 = 1006, then both 2 and 1006 are factors of 2012. Since 1006 is also even then 2012 is divisible by 4. Since 2012 ÷ 4 = 503, then both 4 and 503 are factors of 2012. We are given that 503 is a prime number; thus there are no additional factors of 503 and hence there are no additional factors of 2012. The factors of 2012 are 1 and 2012, 2 and 1006, 4 and 503. Therefore, there are 6 positive integers that are factors of 2012. Next Question

39. Mass of the Sand Pile Solution: (D) 10 kg. Radius r = 40cm/2 = 20cm = 0.2m; Height h = 20cm = 0.2m; Density of sand ρ= 1200 kg/m3; Volume of cone V = πr2h / 3 = 0.008π/3 m3; Mass of sand m = Density X Volume= 9.6π/3 kg ≈ 10 kg. Next Question

40. Area Calculation (solution 1) Solution: 264 km2. Calculate the larger rectangle and subtract the smaller one. (36 × 11) – (22 × 6) = 264 Continued…

41. Area Calculation (solution 2) Solution: 264 km2. Split into two rectangles and add together. 5 × 22 = 110 km2 14 × 11 = 154 km2 110 + 154 = 264 km2 Next Question

42. Coins Solution: (A) 10 coins needed. • 4 pennies to cover 1 ~ 4 cents • 1 nickel to cover 5 ~ 9 cents • 2 dimes to cover 10 ~ 24 cents • 3 quarters to cover 25 ~ 99 cents Next Question

43. Photo Shrinker Solution: 9 times.