S4_Mock02_E

1.
(a)
N = h + kx (where h and k are non-zero constant)

When x = 10, N = 40 :
40 = h + 10k ...... [1]

When x = 15, N = 30 :
30 = h + 15k ...... [2]

[2] - [1] :
-10 = 5k
k = -2

Put k = -2 into [1] :
40 = h + 10(-2)
h = 60

N = 60 - 2x

(b) (i)
When x = 10, N = 40

Total gross profit
= $10(40)
= $400

(b) (ii)
When the total gross profit is $400, Gross profit of a hat, N = 400/x

N = 60 - 2x
400/x = 60 - 2x
400 = 60x - 2x²
2x² - 60x + 400 = 0
x² - 30x + 200 = 0
(x - 10)(x - 20) = 0
x = 10 or x = 20

The number of hats sold can be 10 or 20.
The hawker is INCORRECT.

(c)
Let $P be the daily net profit.

P = Nx - 80
P = (60 - 2x)x - 80
P = 60x - 2x² - 80
P = -2(x² - 30x) - 80
P = -2(x² - 30x + 15²) +2(15)²- 80
P = 370 -2(x - 15)²

Since -2(x - 15)² ≤ 0, then P = 370 -2(x - 15)² ≤ 370
The maximum daily net profit = $370


====
2.
The answer is : C. 800

Let $c be the cost of the wallet.
The marked price = $c(1 + 25%) = $1.25c

1.25c(1 - 10%) = c + 100
1.125c = c + 100
0.125c = 100
c = 800


====
3.
The answer is : A. 20

Let r, h and A be the base radius, height and curved surface area of thecylinder respectively.

2 π r h = A ...... [1]

2 π [r(1 + 30%)] [h(1 + y%)] = 1.56 A
2 π r h [1.3(1 + y%) = 1.56 A ...... [2]

[2]/[1] :
1.3(1 + y%) = 1.56
1 + y% = 1.2
y% = 0.2
y = 20


====
4.
The answer is : C
(https://www.flickr.com/photos/130230543@N06/16125867741/in/photostream/)

The graph is y = ax² + k (where a and k are constant, and a isnon-zero.)
The graph of y = ax² + k is a parabola with y-axis as the axis of symmetry.


====
5.
The answer is : D. -6

an+1 = an + an+2
Then, an+2 = an+1 - an

When n = 4: a6 = a5 - a4 = 6 - 3 = 3
When n = 5: a7 = a6 - a5 = 3 - 6 = -3
When n = 6: a8 = a7 - a6 = -3 - 3 = -6