AMO 2015 Secondary 1 Question 25 Geometry Area – Right Triangle Configuration – MIMO 2017 – Upper Primary – Money Same Amount Problem – MIMO 2017 – Upper Primary – Geometrical Construction Proof
AMO 2015 Secondary 1 Question 25 Geometry Area – Right Triangle Configuration
Question (Sample)
Solution
MIMO 2017 – Upper Primary – Money Same Amount Problem
Question 10
Five persons A, B, C, D and E raised the same amount of money to buy the same gifts together. Four of them A, B, C and D bought 8 gifts, 6 gifts, 12 gifts and 9 gifts more than E respectively. When they settled the bill, A paid $7 to B. How much did C and D pay to E respectively?
Solution
(Shown in Image).
I think that the answer is E gets a total of $49 back where $35 is from C while $14 is from D respectively.
MIMO 2017 – Upper Primary – Geometrical Construction Proof
Question 11.
Both Question and two solutions are in images below.
Bonus Questions (Additional Questions):
1) Tangent Circles in Pentagon Sides KMC 2016
Question
Please refer to the first Image
Solution
In Second Image
2) Maximizing Addends in Pyramid Layers KMC 2016 Cadet
Question
In Image
Solution
Since we are going to use 8 numbers and the ninth number at the center,
for maximum
Since the center is MOST repeated in layer calculations,
(i) we minimize the 8 different positive integers
hence choose —> 1 + 2 + 3 + … + 8 = (8 x 9)/2 = 36
(ii) we calculate the remaining center number
Total sum fixed at 50 means,
Center number = 50 – 36 = 14
Cube at bottom configuration
3 7 2
8 (14) 6
4 5 1
Giving the 2nd layer for optimum as
32 29
31 26
Total = 32 + 31 + 29 + 26 = 118 (Answer)
Additive Rates of Decrease
Question (MIMO 2017, Upper Primary, No. 12)
The weather is getting colder, the grass on the field is decreasing at a constant rate every day. Mr McDonald told that the grass on the field could feed 20 goats for 5 days or 16 goats for 6 days. If Mr McDonald has 11 goats, the grass could last for how many days?
Answer: 8 Days.
Solution (Please refer to attached Image).
Number Patterns – International Olympiad of Science
Question – International Olympiad of Science
No. 13 & No. 39 in Image
Possible Solution
No. 39 (in Image too – a possibility).
Perhaps Q13 is like this:
Number Arrangement:
a b
c d
Pattern
(a + b) – (c + d) = d
Example:
(i) First Picture
a = 9, b = 17, c = 8 and d = 9
So,
(9 + 17) – (8 + 9) = 9
(ii) Second Picture
a = 18, b = 37, c = 15 and d = 20
So,
(18 + 37) – (15 + 20) = 20
(iii) Third Picture
a = 26, b = 28, c = 18 and d = y
(26 + 28) – (18 + y) = y
54 – 18 – y = y
36 = 2y
y = 18 (answer)