(A)   Evaluate:

(i)   \(\dfrac {\left(5 \dfrac 12 \right)^2 – 3 \dfrac 14}{\left(-1 + \dfrac 14 \right)^3}\) [1]

(ii)  \(\sqrt [3] {12.022 – \pi – 0.88}\) [1]

(B)   The table below shows the temperature in a number of cities at noon at a particular day.

(i)   Find the temperature in London if the temperature in Taipei was exactly midway between the temperatures in Singapore and London? [1]

(ii)  The temperature in Paris at 6 pm on the same day was −7ºC. Given that the temperature increased at a constant rate, what time was the temperature at 0ºC? [2]

(A)   Evaluate:

(i)   \(\dfrac {\left(5 \dfrac 12 \right)^2 – 3 \dfrac 14}{\left(-1 + \dfrac 14 \right)^3}\) [1]

(ii)  \(\sqrt [3] {12.022 – \pi – 0.88}\) [1]

(B)   The table below shows the temperature in a number of cities at noon at a particular day.

(i)   Find the temperature in London if the temperature in Taipei was exactly midway between the temperatures in Singapore and London? [1]

(ii)  The temperature in Paris at 6 pm on the same day was −7ºC. Given that the temperature increased at a constant rate, what time was the temperature at 0ºC? [2]

Solution: 

Abby weighs \(4x\) kg and Betty weighs 8 kg more than Abby. Cassandra’s weight is half the total weight of Abby and Betty. Write an expression, in terms of \(x\), for

(i)   Betty’s weight, [1]

(ii)  average weight of the 3 girls. [2]

Abby weighs \(4x\) kg and Betty weighs 8 kg more than Abby. Cassandra’s weight is half the total weight of Abby and Betty. Write an expression, in terms of \(x\), for

(i)   Betty’s weight, [1]

(ii)  average weight of the 3 girls. [2]

Solution: 

(A)   Factorise \(3ac – 9c + 6ab – 18b\) completely. [2]

(B)   Simplify \(\dfrac x5 – \dfrac {x – 2}{15}\) [2]

(A)   Factorise \(3ac – 9c + 6ab – 18b\) completely. [2]

(B)   Simplify \(\dfrac x5 – \dfrac {x – 2}{15}\) [2]

Solution: 

Alaric and Damon each purchased the latest tablet computer, ePad, during its launch day. The poster below shows the deals offered by the shop they went to.

(A)   Calculate the amount of GST paid by Alaric ifhe bought an ePad using cash. [2]

(B)   Alaric decides to sell away the ePad for $1280.79. Find the percentage profit made. [2]

(C)   Damon bought the ePad using his credit card. However, as he is a VIP member, he ends up paying the price as Alaric. What is the percentage discount offered to VIP members? [2]

Alaric and Damon each purchased the latest tablet computer, ePad, during its launch day. The poster below shows the deals offered by the shop they went to.

(A)   Calculate the amount of GST paid by Alaric ifhe bought an ePad using cash. [2]

(B)   Alaric decides to sell away the ePad for $1280.79. Find the percentage profit made. [2]

(C)   Damon bought the ePad using his credit card. However, as he is a VIP member, he ends up paying the price as Alaric. What is the percentage discount offered to VIP members? [2]

Solution: 

A laundry company provides cleaning of clothing such as shirts, jackets, skirts and trousers. In one particular week, \(\dfrac 25\) of the clothing sent in for washing are shirts, \(\dfrac 38\) of the clothing are jackets and the remaining of the clothing are skirts and trousers in the ratio of \(2 : 1\).

(A)   If there are 108 skirts, find the total number of pieces of clothing [2]

(B)   Given that it takes \(\dfrac {6}{125}\) kg of washing powder to wash each piece of clothing, how many pieces of clothing will be left unwashed if the shop only has 20 kg of washing powder? [2]

A laundry company provides cleaning of clothing such as shirts, jackets, skirts and trousers. In one particular week, \(\dfrac 25\) of the clothing sent in for washing are shirts, \(\dfrac 38\) of the clothing are jackets and the remaining of the clothing are skirts and trousers in the ratio of \(2 : 1\).

(A)   If there are 108 skirts, find the total number of pieces of clothing [2]

(B)   Given that it takes \(\dfrac {6}{125}\) kg of washing powder to wash each piece of clothing, how many pieces of clothing will be left unwashed if the shop only has 20 kg of washing powder? [2]

Solution: 

The line graph below shows the number of tickets sold for the movie The Starvation Games from Monday to Thursday on a certain week.

(A)   Calculate total amount of money collected from ticket sales from Monday to Thursday if each ticket is priced at $7.50. [2]

The pictogram below shows the number of tickets sold on Thursday and Friday from the same week.

(B)   Calculate the number of tickets sold on Friday. [2]

(C)   Find the number of tickets sold on Friday as a percentage of the total number of tickets sold from Monday to Friday. [2]

(D)   Find the total number of tickets sold on both Saturday and Sunday if they formed \(\dfrac {8}{13}\) of all tickets sold for the whole week. [2]

The line graph below shows the number of tickets sold for the movie The Starvation Games from Monday to Thursday on a certain week.

(A)   Calculate total amount of money collected from ticket sales from Monday to Thursday if each ticket is priced at $7.50. [2]

The pictogram below shows the number of tickets sold on Thursday and Friday from the same week.

(B)   Calculate the number of tickets sold on Friday. [2]

(C)   Find the number of tickets sold on Friday as a percentage of the total number of tickets sold from Monday to Friday. [2]

(D)   Find the total number of tickets sold on both Saturday and Sunday if they formed \(\dfrac {8}{13}\) of all tickets sold for the whole week. [2]

Solution: 

(A)   During AMKSS Alumni Homecoming Day, 540 fish balls and 432 chicken wings are catered for the guests. Given that the food is to be shared equally among the guests, find

(i)   the largest possible number of guests that can be invited. [2]

(ii)  the number of chicken wings each guest will receive. [1]

(B)   The diagram below shows a concrete block measuring 45 cm by 18 cm by 20 cm. An engineer wants to build cubes using these concrete blocks.

Find

(i)   the smallest possible length of side of a cube that can be built, [2]

(ii)  the number of blocks needed to build 5 such cubes. [1]

(A)   During AMKSS Alumni Homecoming Day, 540 fish balls and 432 chicken wings are catered for the guests. Given that the food is to be shared equally among the guests, find

(i)   the largest possible number of guests that can be invited. [2]

(ii)  the number of chicken wings each guest will receive. [1]

(B)   The diagram below shows a concrete block measuring 45 cm by 18 cm by 20 cm. An engineer wants to build cubes using these concrete blocks.

Find

(i)   the smallest possible length of side of a cube that can be built, [2]

(ii)  the number of blocks needed to build 5 such cubes. [1]

Solution: 

The above diagram shows the design (not drawn to scale) for a new water reservoir, Lagoon Barrage. It is made up of trapezium ABDE of height 80 m, semicircles BCD and APE with semicircle GHI cut out of it. It is given that AB = ED, AE = 84 m, GH = 21 m and BD = 56 m. (Take \(\pi = \dfrac {22}{7})\)

(A)   Given that the outer perimeter of Lagoon Barrage is 420 m, find the length of AB. [3]

(B)      (i)   The shaded region shows the area of Lagoon Barrage. Calculate the area of Lagoon Barrage. [3]

(ii)  A contractor is employed to plant grass on the shaded region indicated on the diagram. Given that he charges $0.50 for each 0.25 m² of grass, calculate the total cost of grass needed. [2]

The above diagram shows the design (not drawn to scale) for a new water reservoir, Lagoon Barrage. It is made up of trapezium ABDE of height 80 m, semicircles BCD and APE with semicircle GHI cut out of it. It is given that AB = ED, AE = 84 m, GH = 21 m and BD = 56 m. (Take \(\pi = \dfrac {22}{7})\)

(A)   Given that the outer perimeter of Lagoon Barrage is 420 m, find the length of AB. [3]

(B)      (i)   The shaded region shows the area of Lagoon Barrage. Calculate the area of Lagoon Barrage. [3]

(ii)  A contractor is employed to plant grass on the shaded region indicated on the diagram. Given that he charges $0.50 for each 0.25 m² of grass, calculate the total cost of grass needed. [2]

Solution: 

A plane travelling from Singapore to Sydney was supposed to leave Singapore at 2250 h Monday and travel at a constant speed of 825 km/h to reach Sydney at 0610 h Tuesday.

(A)   Find the distance between Singapore and Sydney. [2]

(B)   On the actual day, the plane stopped over at Jakarta along the journey to repair a technical problem after travelling for 770 km. At what time did the plane reach Jakarta? [2]

(C)   The stop-over at Jakarta took 1 hour and 24 minutes. The plane then continued the rest of the journey to Sydney at a faster speed. At what speed did the plane travel from Jakarta to Sydney if it still reached Sydney at the schedule time? [2]

A plane travelling from Singapore to Sydney was supposed to leave Singapore at 2250 h Monday and travel at a constant speed of 825 km/h to reach Sydney at 0610 h Tuesday.

(A)   Find the distance between Singapore and Sydney. [2]

(B)   On the actual day, the plane stopped over at Jakarta along the journey to repair a technical problem after travelling for 770 km. At what time did the plane reach Jakarta? [2]

(C)   The stop-over at Jakarta took 1 hour and 24 minutes. The plane then continued the rest of the journey to Sydney at a faster speed. At what speed did the plane travel from Jakarta to Sydney if it still reached Sydney at the schedule time? [2]

Solution: