The Earth is 93 million miles from the sun.

This distance is called an Astronomical Unit (AU).

Below is a table of the planets in our solar system, their distance from the sun and the length of their years in Earth time.

Planet | Distance from the Sun (AU) | Year length in Earth time |
---|---|---|

Mercury | 0.39 | 88 days |

Venus | 0.723 | 225 days |

Earth | 1 | 365 days |

Mars | 1.524 | 687 days |

Jupiter | 5.203 | 11.86 years |

Saturn | 9.539 | 29.5 years |

Uranus | 19.18 | 84 years |

Neptune | 30.06 | 165 years |

Using this information, whilst assuming all orbits are circular, which planet is moving the fastest and which is the slowest?

speed = distance ÷ time.

orbit/distance = circumference = 2πr (where r = distance from the sun)

Using π = 3.14 and year = 365 days

speed (in AU per day) = circumference ÷ time in days

**Mercury is the fastest planet travelling at 0.28AU a day.**

speed (in AU per day) = circumference ÷ time in days

To make this more challenging, do ** not** use a calculator.

Excel version of the crossword grid for screen readers

ACROSS | DOWN |
---|---|

1. 1790 + 2686 | 1. 40433 x 1 |

4. 8880 ÷ 10 | 2. 94 - 29 |

6. 318 x 161 | 3. 14 - 3 |

9. 480 ÷ 10 | 4. 359 x 247 |

11. 1122 ÷ 17 | 5. 94 x 86 |

12. 415 ÷ 5 | 7. 16 - 4 |

14. 70 x 43 | 8. 3564 + 6061 |

16. 727 x 1 | 10. 32 + 48 |

17. 280 ÷ 7 | 13. 2464 ÷ 8 |

18. 936 - 283 | 15. 390 + 704 |

19. 36 + 63 | 16. 1087 - 319 |

21. 6 +12 | 20. 83 x 11 |

23. 5741 x 1 | 21. 281 - 82 |

24. 3598 -999 | 22. 356 + 535 |

25. 5360 - 1576 | 23. 57780 ÷ 10 |

27. 7304 ÷ 8 | 24. 344 - 104 |

28. 1584 ÷ 22 | 26. 820 ÷ 10 |

30. 19 x 11 | 29. 71 + 135 |

32. 11264 - 3218 | 31. 1683 ÷ 17 |

34. 3378 + 5744 | 33. 23 x 3 |

36. 3533 + 6361 | 35. 29 x 1 |

What is the value of one-half of two-thirds of three-quarters of four-fifths of five-sixths of six-sevenths of seven-eighths of eight-ninths of nine-tenths of one thousand?

The trick is to work backwards through this problem, so start with ^{9}/_{10} of 1000.

nine-tenths of 1000 = 900

eight-ninths of 900 = 800

seven-eighths of 800 = 700

six-sevenths of 700 = 600

five-sixths of 600 = 500

four-fifths of 500 = 400

three-quarters of 400 = 300

two-thirds of 300 = 200

one-half of 200 = 1000

**The answer is 100**

eight-ninths of 900 = 800

seven-eighths of 800 = 700

six-sevenths of 700 = 600

five-sixths of 600 = 500

four-fifths of 500 = 400

three-quarters of 400 = 300

two-thirds of 300 = 200

one-half of 200 = 1000

You need to fill in the empty spaces with integers between 0 and 9.

The numbers in each row add up to the totals on the right.

The numbers in each column add up to the totals along the bottom.

The diagonal lines also add up to the totals on the right-hand corners.

Start with the rows and columns that already have four numbers.

This means the bottom row reads 2, 7, 8, 0, 2 which when added together makes 19.

So, to work out the missing number in the first column (on the left) you need to calculate 18 - (5 + 9 + 2 + 2)

Find the values of ** x** for each of the below

- 8
*x*^{2}-= 0*x* - 9
*x*^{2}- 49 = 0 *x*^{2}- 9+ 20 = 0*x**x*^{2}+ 4- 12 = 0*x*- 8
*x*^{2}+ 15 = 22*x* - 20
*x*^{2}= 9 + 31*x*

Work-through Examples:

Find the values of ** x** when 3

Step 1: Factorise

** x**(3

Step 2: Solve

** x** = 0 or

**Note:** This method only works for the format a*x*^{2} + b** x** = 0. Otherwise, see below.

Find the values of ** x** when 6

Step 1: Factorise

(2** x** + 1)(3

Step 2: Solve

Either 2** x** + 1 = 0 or 3

So, ** x** = -

**Note:** If this didn't help, please visit the Maths is Fun website for a more in-depth tutorial.

- 0 or
^{1}/_{8} ^{7}/_{3}or^{-7}/_{3}- 4 or 5
- 2 or -6
^{5}/_{4}or^{3}/_{2}^{9}/_{5}or^{-1}/_{4}