
FINAL EXAMINATIONS
CANDYSWEET HIGH SCHOOL
NAME: GRETEL SCORE: 10
CLASS: 5A2 GRADE: A
Describe the graph shown in Fig 1.1 within 20 mathematical formulae, giving a short description/conclusion after each step of your working. (Marks will be awarded based on accuracy of your working and the clarity.) [10]
Let H be Hansel and G for Gretel
Let P be Parents
From Point A to Point B,
P x S = H + G, where S is the speed of sound of P traveling to H and G.
(H + G) refers to the quantity of fear experienced upon hearing P's plan to abandon H and G in the forest.
From Point B to Point C,
Since fear factor G > H,
(G - H)/T = A, where T is the time G spent crying and A is the quantity of pebbles H collected per second during which G cried.
From Point C to Point D,
Let D1 be the distance traveled by P and D2 the distance traveled by H & G
D1 = 2D2 as P walked exactly twice the distance
D2 / A = Distance between every pebble H and G will see all the way till they reach home.
From Point D to Point E,
This portion is identical to from A to B
P x S = H + G
However, fear factor is inversely proportional to time.
Thus for this part, P x S = (H + G) / 2
Since G > H,
[(G - H) / 2] / T = B, where B is the quantity of pebbles H collected per second.
As there is no value for duration of opened door, B = 0
From Point E to Point F,
Let D3 be the distance traveled by P and D4 the distance traveled by H and G
D2 < D1 < D4 < D3 D3 = 2D4 B / D4 = infinity, B = 0, thus H and G are lost and cannot find their way home.
From Point F to Point G,
y= (H + G)x+ Wx where y is the distance H+G wanders in the forest and W is the singing white bird encountered and x an undefined number greater than 0. x is defined after 48 hours and y indicated the distance they walked before reaching a cake house on which they feasted upon. y is also equivalent to the distance from which E, the evil witch, could sense H and G approaching.
From Point G to Point H,
(F x E) / T2 = integratrion of (H + G), where F is the food of the evil witch, T2 being the time taken for H and G to finish the food. The integration of H and G's hunger equates to the amount of food consumed per unit time. Integration(H + G) is incidentally the amount of food E wishes to derive out of H and G by eating them.
From Point H to Point I,
Let h be the hours E is awake in a day in the given month. hE thus refers to the amount of time G spent working as a slave and the equal amount of time H is forced to eat and grow fat. The amount of energy lost by G = The amount of energy gained by H
G - hE < H + hE
From Point I to Point J,
Let T3 be the time lapse since H and G were held captive. T3 approx 1 month T3 is also the time taken for E to grow impatient and wishes to consume H and G. Amount of energy left in G = G - hET3, G > hET3
(G - hET3) = amount of energy required to push E into the burning oven when E tried to show G how to crawl inside.
From Point J to Point K,
m = 2n2 + 6n + 2 , m is the time taken since escaping from E's house, n is the distance covered.
Differentiate m with respect to n.
H and G will reach a dead end when n = -1.5, with n calculated as a displacement unit.
In other words, H & G will reach a dead end when they head 1.5 units in the opposite direction of the forest from which they came from.
At n = -1.5
H + 2ge > G + ge
H + G + 3ge > Z
ge refers to the weight of gems and treasures taken from E
As the inequality show, the total weight of H and G and the gems are much higher than Z, weight of a duck encountered at the river bank at n = -1.5, which has agreed to take them across the river.
Thus the only solution is for Z to bring H + 2ge and G + ge separately.
From Point K to Point L,
Given that H and G current location is (8,4) and their house, where their father is waiting for them is (4,8)
It is deduced that the equation of the straight line they can embark on towards home is
P = 12 - Q, where P is distance from home from riverbank and Q is time taken. The equation is obtained from solving simultaneous equations.
Q is defined when H and G noticed the familiar surrounding, thus P is defined.
From Point L to Point M,
Let S1 be the situation before and S2 be the situation after.
S2 - S1 = 3ge - 0.5P, where ge is the gems from E and P is the parents.
Thus (H + G + 0.5P) tends to infinity , where (H + G + 0.5P) is measured in quantity of joy.
H and G and 0.5P never needed to worry again for the rest of their lives.