MEP Practice Book SA1

Transcription

1 1 Indices MEP Practice Book SA1 1.1 Multiplication and Division 1. Calculate the following mentally: a) b) c) d) e) f) g) h) i) j) k) 5 1 l) 7 18 m) n) o) Calculate the following mentally: a) 5 7 b) 9 7 c) 8 8 d) 6 8 e) 7 f) 7 8 g) 8 9 h) 5 8 i) 9 6 j) 7 8 k) 5 7 l) 81 9 m) 6 n) 6 9 o) 9 7 p) 56 8 q) 5 5 r) 8 6. Simplify the following epressions without using a calculator. a) d) ) b) 7 7) 8 c) ) ) e) ) 9 f) ) ) + h) ) i) 7 8) 5 g) j) ) k) 7 + ) 5 l) 9 9) 7 ) + ) n) 6 9) 5 o) 7 6) 5 9) m) Pens cost 1 p each. How much will 8 pens cost? 5. A crate of small lemonade bottles has 8 rows with 6 bottles in each row. How many bottles are there in the crate? 6. A chocolate bar has 5 rows with chunks in each row. How many chunks are there in total? 7. In snooker, potting a RED counts as one point and a BLACK as seven points. What do you score if you pot 6 REDS and 6 BLACKS? 8. A syndicate of 7 teachers won 6 on the national lottery. How much does each teacher win? 9. There are 8 stamps in a booklet. How many stamps are there in total in 7 booklets? 1

2 1.1 MEP Practice Book SA1 10. There are 6 runners entered for 100 m races. If there are 8 runners in each race in the first round of heats, how many first round heats are there? 11. You need to divide a class of 5 pupils into five-a-side teams. How many teams will there be? 1. Copy and complete this diagram by filling in each bo with the correct number Tony has a hot-dog stall. He uses sauce from a bottle which holds ml. He puts about 7 ml of sauce on each hot-dog. a) How many hot-dogs can he put sauce on from one bottle? b) Tony buys the sauce in boes of bottles. One full bottle weighs 56 g. The empty bo weighs 750 g. What is the total weight of a bo full of sauce bottles? NEAB) 1. Write down three multiplication sums, each of which has an answer equal to 0. Do not use any number more than once. LON) 15. Look at these numbers. 5, 10, 15, 0, 5, 0, 5, 0 a) b) Which number is a multiple of si? Which number is a square number? 1. Squares, Cubes, Square Roots and Cube Roots 1. Find, without using a calculator: a) 5 b) c) d) e) 7 f) 1 g) h) 5 i) 9 j) 10 k) 10 l) 8 m) 7 n) 6 o)

3 MEP Practice Book SA1. Find, without using a calculator: a) b) 7 c) 6 d) 8 e) 81 f) 9 g) 100 h) 6 i) 1 j) 6 k) 11 l) 5 m) 15 n) 1000 o) 169. Calculate, with or without a calculator, a) b) c) d) 1 + e) f) 9 7 g) + 9 h) 6 i) 8 16 j) k) l) m) 6 6 n) 81 o) 65. Find the net 5 terms in the sequence.,,,,...,... How many terms are needed before the value reaches one million? 1. Inde Notation 1. Write in a form using indices: a) b) c) d) e) f) 5 5 g) h) i) j) 5 5 k) 5 5 l) Find the value of the following: a) 7 b) c) 5 d) 8 e) 7 0 f) 5 g) h) 6 i) 1 7 j) 10 6 k) 10 l) 6

4 1. MEP Practice Book SA1. Simplify each of the following, leaving your answer in inde notation a) b) c) d) e) f) g) 5 5 h) i) Simplify each of the following, leaving your answer in inde notation. ) 5 a) b) 7 7 c) 1 7 d) 8 8 e) g) ) f) ) 10 ) 6 h) ) 6 i) ) 10 7 ) k) 1 ) l) ) j) 5. Epress each of the following numbers as a number to a power, e.g. 56 = 8. a) 10 b) c) 15 d) 16 e) 51 f) 169 g) h) 1000 i) 65 j) 08 k) 89 l) Fill in the missing numbers. ) =? b) ) =?? c) 5 ) = 5 a) 1 ) =? 8 d) ) =? 9 g) ) =?? f) ) = e) 5 5 h) ) =?? 6 i) ) = 1? 7 1? 16 ) = k) ) = j)? ) = l) Simplify the following epressions, leaving your answers in inde notation. ) 5 e) 5 f) 5 ) 5 ) h) a ) a ) i) ) ) k) b ) b ) l) a a ) 8 a 5 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) [ ] 5 8. a) What is the missing number?? 10 =

5 MEP Practice Book SA1 b) 10 is approimately equal to is approimately equal to? Write as a power of 7: i) 7 7 ii) 7 7 Edecel) 1. Factors 1. Which of the following numbers are divisible by, or 5? a) 10 b) c) 60 d) 108 e) 15 f) 189 g) 0 h) 15 i) 68 j) 756 k 10 l) 10. Which of the following numbers are divisible by, 9 or 11? a) 18 b) 7 c) 16 d) 1 e) 69 f) 85 g) 119 h) 97. List all factors of these numbers. a) 0 b) c) d) 8 e) 60 f) 10 g) 81 h) 98. Copy and fill in the missing factors in each of the following. a) 5 = 5? b) 77 = 7? c) 96 = 8? d) =? e) 66 =? f) 7 =? g) 10 =? h) 15 = 5 5? i) 0 = 5? 5. Copy and complete the following factor trees. a) 8 b) 6 8 =??? 6 =???? c) 0 d) 7 0 =??? 7 =????? 5

6 MEP Practice Book SA1 1.5 Prime Factors 1. Which of the numbers,, 5, 7, 11, 1 are prime factors of the following numbers? a) 189 b) 6 c) 90 d) 70 e) 165 f) 88 g) 87 h) 10 i) 60 j) 6006 k) 195 l) Use the Sieve of Eratosthenes to find all prime numbers between 100 and 00.. Epress the following numbers as products of prime numbers. a) 150 b) 60 c) 7 d) 1 e) 15 f) 10 g) 8 h) 180 i) 70 j) 1 k) 06 l) 500 m) 70 n) o) 8008 p) Find the highest common factor of the following. a) 16 and b) 5 and 6 c) 56 and 70 d) 90 and 16 e), 66 and 78 f) 8, 98 and 15 g) 189 and 8 h) 15 and 70 i) 616 and 9 j) 560, 10 and k) 1, 156 and 180 l) 55, 100 and a) Copy and put {9, 17, 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. 6

7 MEP Practice Book SA1 6. 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 1 minute 1 seconds to complete a circuit and the second car takes 1 minute 0 seconds. They start level. Find the length of time before they are net level with one another. 7. a) Write 18 as the product of its prime factors. b) What is the least common multiple LCM) of 1 and 18? 1.7 Standard Form AQA) 1. Write the following numbers in standard form, A 10, where 1 A < 10 and n is an integer. a) 000 b) 560 c) d) 50 e) 1 f) 700 g) 6 h) 60 i) 0.1 j) k) l) m) million n) 0.1 million o) p).006 q) 70. r) n. Epress the following in ordinary notation. a). 10 b) c) d) e) f) g) j) m) h) k) n) i) l) o) p) q) r) State whether or not the following numbers are in standard form. If not, rewrite them in standard form. a) b) c) d) g) e) h) f) i) The area of the surface of the earth is about km. Epress this in standard form. 7

8 1.7 MEP Practice Book SA1 5. The population of the UK is estimated as Write this in standard form. 6. 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? Give your answer in standard form. 7. The population of Singapore in a given year was Its total land area is estimated as 618 km. What was the average population per square km in that year? Give your answer in standard form, correct to significant figures. 8. Astronomers measure distances in the solar system in astronomical units AU). One AU is kilometres. The distance from the Sun to Pluto is 9.5 AU. How many kilometres is the Sun from Pluto? Give your answer in standard form to a sensible degree of accuracy. AQA) 1.8 Calculations with Standard Form 1. Without using a calculator, work out the following calculations. Epress your answer in standard form. ) + ) b) ) 10 ). ) +. ) d) ) ) ) ) f) 5 10 ) 10 ) ) ) h) ) 10 ). ) ) j) 9 10 ) 10 ). 6). ) l) ) ). 6) ) n). 10 ) 10 ) ) ) p). 10 ) 5 10 ) a) c) e) g) i) k) m) o) ) + ). Write as a single number epressed in standard form.. Given that = 10 and y = 7 10, epress + 8 y in standard form. ) 6 7. Epress in standard form. 5. Given that = and y = , epress in standard form: a) y b) y c) y d) y 8

9 MEP Practice Book SA1 6. In the formula R M =, substitute EI M = 6 10, E = , I = 10 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 answer in standard form. 6 a) b) c) d) e) f) g) h) i) [ ) )] j) Given that and epress it in standard form. = 1., without using a calculator, find the value of 10.* If = 6. 10, evaluate and epress your answer in standard form: a) + b) Given that = , find the value of each of the following, giving your answer in standard form. a) 5 b) c) d) Work out Give your answer in standard form. LON) 1. Saturn is approimately km from the Sun. Venus is approimately km from the Sun. How much further from the Sun is Saturn than Venus? Give your answer in standard form. 9

10 1.8 MEP Practice Book SA1 1. A light year is the distance travelled by light in 65 days. The speed of light is kilometres per second. a) Calculate the number of kilometres in one light year. Give your answer in standard form. b) The distance to the nearest star is kilometres. How many light years is this? c) One kilometre = 0.65 miles. Calculate the speed of light in miles per second. 15. The mass, M, of the planet Mars is kg. The planet is a sphere with radius, r, equal to m. Use this formula to find its density: M Density = π r Epress your answer in standard form, correct to three significant figures. 16. The surface 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. Give your answer in standard form. b) What percentage of the Earth's surface is not covered by water? 17. The mass of a neutron is grams. Calculate the total mass of 1500 neutrons. Give your answer in standard form. LON) 18. a) i) Write sity thousand in standard form. ii) Hence, or otherwise, find the value of the square of sity thousand. Give your answer in standard form. b) Work out Give your answer in standard form. OCR) 19. Some large numbers are 1 million = 10 6 written opposite. 1 billion = trillion = 10 1 a) b) c) How many millions are there in one trillion? Write 8 billion in standard form. Work out 8 billion multiplied by trillion. Give your answer in standard form. AQA) 10