MEP Practice Book ES1. (h) (l) Simplify each of the following, leaving your answer in index notation.

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1 Indices MEP Practice Book ES. Inde Notation. Write in a form using indices: a) b) c) d) e) f) g) h) i) j) k) l). Find the value of the following: a) 7 b) c) d) 8 e) 7 0 f) g) h) i) 7 j) 0 k) 0 l). Simplify each of the following, leaving your answer in inde notation. 7 a) b) c) 7 d) e) f) g) h) i) 7. Simplify each of the following, leaving your answer in inde notation. ) 8 a) b) 7 7 c) 7 d) 8 8 e) g) ) f) ) 0 ) h) 0 ) i) 0 0 ) 0 7 ) k) ) l) 8 ) j). Epress each of the following numbers as a number to a power, e.g. = 8. a) 0 b) c) d) e) f) 9 g) h) 000 i) j) 08 k) 89 l)

2 MEP Practice Book ES. Fill in the missing numbers. ) = b) ) = c) ) = a) ) = 8 d) ) = 9 g) 0 0 ) = f) ) = e) h) 7 7 ) = i) ) = 7 ) = k) ) = j) ) = l) 0 7. Simplify the following epressions, leaving your answers in inde notation. ) e) f) ) ) h) a ) a ) i) ) ) k) b ) b ) l) a a ) 8 a a) a a b) c) b b b d) a a g) a a a j) b b m) 7 n) a ) a 8 a o) [ ] 8. a) Fill in the missing number. 0 = b) 0 is approimately equal to is approimately equal to. Prime Factors. Which of the numbers,,, 7,, are prime factors of the following numbers a) 89 b) c) 90 d) 770 e) f) 88 g) 87 h) 0 i) 0 j) 00 k) 9 l) 8. Use the Sieve of Eratosthenes to find all prime numbers between 00 and 00.. Epress the following numbers as products of prime numbers. a) 0 b) 0 c) 7 d) e) f) 0 g) 8 h) 80 i) 70 j) k) 0 l) 00 m) 70 n) o) 8008 p) 890

3 MEP Practice Book ES. Find the highest common factor of the following. a) and b) and c) and 70 d) 90 and e), and 78 f) 8, 98 and g) 89 and 8 h) and 70 i) and 9 j) 0, 0 and k), and 80 l), 00 and. a) Copy and put {9, 7, 8, 0} into the correct boes. Is it odd Yes No Is it a Is it a prime number square number Yes No Yes No Does it have eactly si factors Yes No b) Write down a number that could go into the empty bo.. a) Epress the following numbers as products of their prime factors. i) 7 ii) 80 b) Two cars go round a race track. The first car takes minute seconds to complete a circuit and the second car takes minute 0 seconds. They start level. Find the length of time before they are net level with one another.. Further Inde Notation. Without using a calculator, find the value of each of the following. a) 9 b) 7 c) d) 8 e) 00 f) 9. g) h) i) j) k) l)

4 MEP Practice Book ES m) 7 n) 8 o) 000 p) 0. q). r). s) 8 0. t) u) v) 8 y) 08. z). w) 9 0. ) 0.. What is the value of each of the following epressions Do not use a calculator. a) b) 8 c) ). d) g) 7 j) e) 7 0 f) h) i) k) l) 78. Epress each of the following in inde form. a) a ) b) a ) c) 7 9 a ) d) ) ) f) a a a ) j) a a e) 0 i) g) a a h) a ) k) a l) a ). Solve the following equations for. a) = 8 b) = c) = d) 7 = 9 e) = f) = g) = 7 h) = i) = j) = k) = l) = m) = 0 n) = o) = p) = q) = r) =. Simplify the following: a) a a b) a ) c) a a d) a a e) a a f) ab a b g) a b a b h) a a a ) ) 7 ) i) a a

5 MEP Practice Book ES. Write these numbers in order of size, starting with the smallest.,,. 7. Evaluate a) b) c) 7 8. a) Calculate n when n =. b) Calculate n when c) Work out 9 n = 9. Solve the following equations. a) n = b) n = 8 c) n n n = d) + = 97.7 Standard Form. Write the following numbers in standard form, A 0, where A < 0 and n is an integer. a) 000 b) 0 c) d) 0 e) f) 700 g) h) 0 i) 0. j) k) l) m) million n) 0. million o) 00 p).00 q) 70. r) n. Epress the following in ordinary notation. a). 0 b) 7. 0 c) 0. 0 d). 0 e) 7. 0 f). 0 g). 0 j) 7. 0 m) 0 7 h) 7. 0 k). 0 n). 8 0 i). 0 l). 0 o) p) q) 7. 0 r). 0

6 MEP Practice Book ES. State whether or not the following numbers are in standard form. If not, rewrite them in standard form. a). 7 0 b). 7 0 c). 7 0 d) g) e) 0 h) f) 7. 0 i) The area of the surface of the earth is about km. Epress this in standard form.. The population of the UK is estimated as Write this in standard form.. The speed of light is approimately km/s. a) Epress this speed in m/s in standard form. b) The speed of sound is 00 m/s. How many times more than the speed of sound is the speed of light 7. The population of Singapore in a given year was. 0. Its total land area is estimated as 8 km. What was the average population per square km in that year Give your answer in standard form, correct to significant figures..8 Calculations with Standard Form. Without using a calculator, work out the following calculations. Epress your answers in standard form. ) + ) b). 8 0 ) 0 ). ) +. ) d) ) ) ) ) f) 0 ) 0 ) ) ) h). 0 ) 0 ). ) ) j) 9 0 ) 0 ). ). ) l) 8. 0 ). 0 ). ) ) n). 0 ) 0 ) ) ) p). 0 ) 0 ) a) c) e) 0 0 g) i) 0 0 k) 0 0 m) 0 0 o) 0 0 ) + ). Write as a single number epressed in standard form.. Given that = 0 and y = 7 0, epress + 8 y in standard form.

7 MEP Practice Book ES ) 7. Epress 0. 0 in standard form.. Given that =. 0 and y = 0 7, epress in standard form: a) y b) y c) y d) y. In the formula R M =, substitute EI M = 0, E =. 0 8, I = 0 and evaluate R, giving your answer in standard form. 7. The radius of a circular micro-organism is cm. Calculate the circumference and area of the micro-organism, giving your answer in standard form. 8.* Evaluate each of the following epressions, giving your answers in standard form. a) b).. c) d) e) f). 0 g) h) i) [ ) )] j) Given that.... and epress it in standard form. =., without using a calculator find the value of 0.* If =. 0, evaluate and epress your answer in standard form: a) + b) +. Given that = 0, find the value of each of the following, giving your answer in standard form. a) b) c) d) 00 7

8 MEP Practice Book ES 8. Work out Saturn is approimately. 0 9 km from the Sun. Venus is approimately km from the Sun. How much further from the Sun is Saturn than Venus. A light year is the distance travelled by light in days. The speed of light is 9. 0 kilometres per second. a) Calculate the number of kilometres in one light year. b) The distance to the nearest star is 0. 0 kilometres. How many light years is this c) One kilometre = 0. miles. Calculate the speed of light in miles per second.. The mass, M, of the planet Mars is. 0 kg. The planet is a sphere with radius, r, equal to 8. 0 m. Use this formula to find its density: M Density = π r Epress your answer in standard form, correct to three significant figures.. The surface area of the Earth is approimately square miles. The surface area of the Earth covered by water is approimately square miles. a) Calculate the surface area of the Earth not covered by water. b) What percentage of the Earth's surface is not covered by water 7. The mass of a neutron is. 7 0 grams. Calculate the total mass of 00 neutrons. LON) LON) 8