978-1-4730-1188-5 (.epub)

Word/phrase | Mathematical meaning | Example of use |
---|---|---|

Even number | A whole number that is exactly divisible by two (that is, it results in a whole number when divided by two). | 432 is an even number. |

Odd number | A whole number that is not exactly divisible by two. | 321 is an odd number. |

Sum | The addition of numbers. | The sum of 123 and 456 is 579. |

Difference | The numerical difference between two numbers, or the positive result of subtracting one number from the other. | The difference between 24 and 42 is 18. The difference between 5 and ^{−}2 is 7. |

Product | The result of multiplying numbers together. | The product of 3, 4 and 5 is 60. |

Quotient | One number divided by another. | The quotient 60 ÷ 12 is 5. |

Exponent | The power to which a number is raised. | In the expression (2.6)^{4}, 4 is the exponent. |

Perimeter | The outer boundary of a geometric figure (also the length of that boundary). | The perimeter of the figure was drawn in red. |

Circle | A geometric figure in which every point on its perimeter is the same distance (the radius) from its centre. | The circle has a radius of 4 cm. |

Equation | One expression equaling another. | The equation 9 − 6 = 3. |

Inequality | One expression being less than or greater than another. | 3 < 6 is an inequality, which reads ‘3 is less than 6’. |

Word | Mathematical meaning | Example of use |
---|---|---|

Decimal | A number expressed in terms of tenths, hundredths, etc. | A quarter expressed as a decimal is 0.25. |

Fraction | One whole number over another. | 0.75 expressed as a fraction is |

Positive | Greater than zero. | 2 is a positive number. |

Negative | Less than zero. | ^{−}2 is a negative number. |

Write down … | Determine … | Show … |

What is… | Find … | Prove … |

Calculate … | ||

A simple answer will do but generally give some working. | Justification for your answer is required. This will be reflected in the marks. | The answer is given to you. All marks awarded for a convincing argument. |

(a) Write down one billion as a power of 10. | [3] |

(b) Consider how far a billion centimetres (cm) is. Determine what one billion cm is in kilometres (km). How does it compare with the distance between Saturn and the Sun, which is 1427000 000 km? | [5] |

(c) Now consider one billion seconds. Determine how long this is in years (round your answer to the nearest whole number). | [7] |

(d) Finally, if there are 4 980 000 grains in 1 kilogram (kg) of sugar, show that one billion grains of sugar are approximately equivalent to 2 × 10^{2} kg of sugar. | [5] |

(a) Write down one billion as a power of 10. | [3] |

(b) Consider how far a billion centimetres (cm) is. Determine what one billion cm is in kilometres (km). How does it compare with the distance between Saturn and the Sun, which is 1427000 000 km? | [5] |

(c) Now consider one billion seconds. Determine how long this is in years (round your answer to the nearest whole number). | [7] |

(d) Finally, if there are 4 980 000 grains in 1 kilogram (kg) of sugar, show that one billion grains of sugar are approximately equivalent to 2 × 10^{2} kg of sugar. | [5] |

(a) Write down the people I met. | [2] |

(b) Find the number of wives, sacks, cats and kits. | [4] |

(c) Show that the number of kits is 7^{4}. | [4] |

(d) What is the answer to the riddle? | [2] |

(a) Write down the people I met. | [2] |

(b) Find the number of wives, sacks, cats and kits. | [4] |

(c) Show that the number of kits is 7^{4}. | [4] |

(d) What is the answer to the riddle? | [2] |

(a) Write down the area of the lawn. | [3] |

(b) The turf they can lay is sold in pieces, each of which is a square of grass measuring ½ m by ½ m. How many pieces of turf are needed to cover the lawn? | [4] |

(c) If a piece of turf costs 50p, write down how much it will cost to turf the lawn. | [3] |

(d) Grass seed is sold in boxes. Each box contains enough seed for 10 m^{2}, and costs £5.15. Find the cost of sowing seed. | [5] |

(e) Which method is cheaper? Why might your friends choose the more expensive method? | [3] |

(a) Write down the area of the lawn. | [3] |

(b) The turf they can lay is sold in pieces, each of which is a square of grass measuring ½ m by ½ m. How many pieces of turf are needed to cover the lawn? | [4] |

(c) If a piece of turf costs 50p, write down how much it will cost to turf the lawn. | [3] |

(d) Grass seed is sold in boxes. Each box contains enough seed for 10 m^{2}, and costs £5.15. Find the cost of sowing seed. | [5] |

(e) Which method is cheaper? Why might your friends choose the more expensive method? | [3] |

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