Number Banker

1. (a) Ayesha invests Rs 85 000 in a savings scheme that pays simple interest at a rate of 6.5% per year.Calculate the interest she earns in 4 years. [2]
2. (b) Work out the total value of her investment at the end of the 4 years. [1]

1. (a) Daniel invests $3200 at a rate of 2.8% per year compound interest.Calculate the value of his investment after 6 years. Give your answer correct to the nearest cent. [2]
2. (b) Find the number of complete years it takes for the investment to first be worth more than $4500. [2]

1. (a) Mr Qureshi invests Rs 12 000 at r% per year compound interest. After 3 years the investment is worth Rs 13 891.50.Find the value of r. [3]
2. (b) He then changes Rs 13 891.50 into euros when the exchange rate is €1 = Rs 308.70.How many euros does he receive? Give your answer correct to the nearest cent. [2]

1. (a) Without using a calculator, work out 2¾ − 1⅚.Give your answer as a fraction in its simplest form. [2]
2. (b) Without using a calculator, work out 3/8 ÷ 9/10.Give your answer as a fraction in its simplest form. [2]

1. (a) Write the recurring decimal 0.363636… (the digits 36 recur) as a fraction in its simplest form. [2]
2. (b) Show that the recurring decimal 0.4727272… (the digits 72 recur) can be written as 26/55. [3]

1. (a) A school bag costs Rs 2400. In a sale the price is reduced by 15%.Calculate the sale price. [2]
2. (b) The price of a bicycle increases from $250 to $285.Calculate the percentage increase. [2]

1. (a) After an increase of 12%, the population of a town is 63 840.Calculate the population before the increase. [3]
2. (b) The price of a used car increases by 12% and then the new price decreases by 12%.Find the overall percentage change in the price, stating whether it is an increase or a decrease. [2]

1. (a) Write 360 as a product of its prime factors. [2]
2. (b) Find (i) the highest common factor (HCF) of 360 and 84,(ii) the lowest common multiple (LCM) of 360 and 84. [3]

1. (a) At a bus station in Lahore, buses on route A leave every 12 minutes, buses on route B every 18 minutes and buses on route C every 30 minutes.Buses on all three routes leave together at 06 45.Find the next time when buses on all three routes leave together. [3]
2. (b) p = 2³ × 3² × 7 and q = 2 × 3⁴ × 5.Write down, as products of prime factors, (i) the HCF of p and q, (ii) the LCM of p and q. [2]

1. (a) U = {integers from 1 to 15}A = {multiples of 3}B = {odd numbers}List the elements of A ∩ B. [1]
2. (b) Find n(A ∪ B). [1]
3. (c) List the elements of A′. [1]

A sports club has 50 members.C = {members who play cricket} and H = {members who play hockey}.28 members play cricket, 19 play hockey and 9 play neither sport.

1. (a) Find the number of members who play both sports. [2]
2. (b) Find n(C ∩ H′). [1]
3. (c) Find n(C′ ∩ H). [1]
4. (d) Describe in words the members in the set (C ∪ H)′. [1]

1. (a) Three sisters share Rs 36 000 in the ratio 2 : 3 : 7.Calculate the largest share. [2]
2. (b) A recipe for 6 people uses 250 g of flour.How much flour is needed for 15 people? [2]

1. (a) In a school the ratio boys : girls is 5 : 4.When 30 more girls join the school, the ratio becomes 10 : 9. No boys join or leave.Find the number of students in the school before the girls joined. [4]

1. (a) A car travels 186 km in 2 hours 15 minutes.Calculate its average speed in km/h. Give your answer correct to 1 decimal place. [2]
2. (b) Change 25 m/s into km/h. [2]

1. (a) A metal block is a cuboid measuring 8 cm by 5 cm by 4 cm. Its mass is 1270 g.Calculate the density of the metal in g/cm³. Give your answer correct to 3 significant figures. [2]
2. (b) The weight of the block is 12.5 N.The block rests on a table on its largest face.Calculate the pressure on the table in N/m².[Pressure = Force ÷ Area] [2]
3. (c) The block is turned so that it rests on its smallest face.Find the new pressure in N/m². [1]

1. (a) The length of a table is 48 cm, correct to the nearest centimetre.Write down the lower bound and the upper bound of the length. [2]
2. (b) The mass of a bag of rice is 3.6 kg, correct to the nearest 0.1 kg.Complete the statement: …… ≤ mass < …… [2]

1. (a) The area of a rectangular solar panel is 54 cm², correct to the nearest square centimetre.The length of the panel is 9.2 cm, correct to 1 decimal place.Calculate the upper bound of the width of the panel. Give your answer correct to 3 significant figures. [3]
2. (b) Calculate the lower bound of the width. Give your answer correct to 3 significant figures. [2]

1. (a) Work out 7 + 3 × (8 − 2)² ÷ 4. [2]
2. (b) Insert one pair of brackets to make this statement correct.12 − 4 × 2 + 1 = 17 [1]
3. (c) Work out 0.6 × 0.07. [1]

1. (a) Without using a calculator, work out 23.4 × 1.6.Show all your working. [2]
2. (b) Without using a calculator, work out 4.56 ÷ 0.012. [2]
3. (c) Work out −5 − (−8) × 3. [1]

1. (a) Write 0.000 407 in standard form. [1]
2. (b) Write 3.2 × 10⁵ as an ordinary number. [1]
3. (c) Work out (6 × 10³) × (4 × 10⁻⁷).Give your answer in standard form. [2]

1. (a) The mass of the Earth is 5.97 × 10²⁴ kg and the mass of the Moon is 7.35 × 10²² kg.How many times heavier is the Earth than the Moon? Give your answer correct to 3 significant figures. [2]
2. (b) Find the total mass of the Earth and the Moon. Give your answer in standard form, correct to 3 significant figures. [2]
3. (c) The distance from the Sun to the Earth is 1.496 × 10⁸ km. Light travels at 3.00 × 10⁵ km/s.Calculate the time, in seconds, for light to travel from the Sun to the Earth. Give your answer correct to the nearest second. [2]

1. (a) A flight leaves Karachi at 23 10 local time. The flight takes 7 hours 50 minutes.Work out the time in Karachi when the flight lands. [1]
2. (b) The local time in London is 4 hours behind the local time in Karachi.Write down the local time in London when the flight lands. [1]
3. (c) The return flight leaves London at 21 35 local time and lands in Karachi at 11 05 Karachi time the next day.Work out the length of the return flight. [2]

1. (a) Find the value of 27^(−2/3). [2]
2. (b) Find the value of n when 2ⁿ = 1/32. [1]
3. (c) Work out 8^(2/3) × 16^(−3/4), giving your answer as a fraction. [2]

1. (a) Write 0.004 867 2 correct to 3 significant figures. [1]
2. (b) By rounding each number to 1 significant figure, estimate the value of(61.8 × 0.49) ÷ 2.03²Show all your working. [2]

Here is a list of numbers.2 9 15 17 27 36 −4 √5 0.3 π

1. (a) From the list, write down all the prime numbers. [1]
2. (b) From the list, write down all the square numbers. [1]
3. (c) From the list, write down a cube number. [1]
4. (d) From the list, write down all the irrational numbers. [1]

1. (a) A colony of bacteria has 2400 cells. The number of cells increases by 15% every hour.Calculate the number of cells after 6 hours. Give your answer correct to the nearest whole number. [2]
2. (b) A car bought for $18 000 loses 12% of its value every year.Find the number of complete years after which the value of the car is first less than $9000. [2]

1. (a) Use your calculator to work out √(18.4² − 6.3²) ÷ (2.7 + 1.15).Write down all the figures on your calculator display. [1]
2. (b) Write your answer to part (a) correct to 4 significant figures. [1]

1. (a) Simplify √75 − √12. [2]
2. (b) Rationalise the denominator and simplify 6/(3 − √3). [3]
3. (c) Expand and simplify (2 + √5)². [2]

1. (a) Write these numbers in order of size, starting with the smallest.5/8 0.63 62% √0.39 0.666… (the 6 recurs) [2]

1. (a) Write down the value of 13². [1]
2. (b) Write down the value of ∛64. [1]
3. (c) Write down the value of √0.81. [1]
4. (d) Work out 2⁵ − 3³. [1]