The service tax charged by restaurant abc is 9 a family

Question

Question 1:

Simplify the following expressions.

(a) 3y³ x 12z⁵ x 2^-3 

(b) 4a³x6⁴/24a 

(c) (b⁸)^-3

(d) (x³ y^-3) x x^-5 /y^-2

(e) (3x³ y⁵) + 9x⁵y³)² / x³y³ x 3²

(f) (2x⁴ + 4x³ + 4x² + 4x + 2) / x² + 1

Question 2:

Evaluate the following arithmetic expressions:

(a) |3-[5 + 7(1)^-1]|
(b)  √[(3)³ - (-3)² + 2 x 12 -7³)]²
(c)  3 - |[5/2 - 6(1)^-1]| x 2
(d)  3/4 x 100/24 - 6(3)^-1 x 7
(e) 7/4 + (84/44) / (6(11))^-1 + 7/8

Question 3:

(a) Convert the following fraction to be in percentage (correct up to 2 decimal places)
(i) 7/8
(ii) 7/18

(b) The service tax charged by Restaurant ABC is 9%. A family paid RM81 for the service tax. Calculate the total amount payable by the family.

(c) A batch of students took the University Mathematics test. 299 students passed the test, which translates to 92% passing rate. Determine the total number of students sat for this test. 

(d) The petrol price went up by 20%. The petrol price before the price hike was RM1.80 per litre. Ben pumped 40 litres of petrol after the price hike. Calculate the total amount he needs to pay.

(e) The sugar price went up by 21% in May 2014. Alice used to spend RM10 to purchase 5kg of sugar in April 2014. In May 2014, Alice is still spending RM10 to purchase the sugar. Calculate

(i) Sugar price (per kg) in May 2014.

(ii) Amount of sugar purchased by Alice and the difference between the amount purchased in April 2014 and May 2014. 

Question 4:

(a) Let ??(??) =??²+1 and, let a>0 and h be real number. Find and simplify the following:
(i) f(-α)
(ii) f(α^0.5)
(iii) f(α + h)

(b) If f(x) = x² + 4 and g(x) = 1/x²+4, find the following:

(i) f(g(x))
(ii) g(f(x))

(c) Find the domain and range of the following functions, explain briefly and sketch the graphs:
(i) y = 5x/x-4
(ii) y = 5/log₁₀(x-1)

Question 5:

a) Write and simplify an algebraic expression to represent the area of the figure shown above.

b) Find the range of x.

c) Given that the Area is 204 cm², find the perimeter.