Two walls of a bathroom need tiling. The walls are shown below.

One wall is 3 metres by 3 metres.

The other wall is 3 metres by 4 metres with a window which is 1 metre by ½ metre.

a) Work out the area that needs tiling

Tiles are squares measuring 25cm by 25 cm. They cost £3.00 each

b) Calculate the costs of tiling the bathroom

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a) Expand y (y – 5)

b) Expand and simplify (5x – 2)( x + 3)

c) Simplify 10a^{2} – 6b – 3a^{2} + 3b - b

d) Factorise 9x^{2} – 4

e) Solve 21a^{2} +5a = 4

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For a qualification 2/5 of the marks were given for coursework.

The rest of the marks were given for a written paper of which 3/8 were given for a mental test.

Total marks were out of 120.

How many marks were given for the mental test.

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Two mathematically similar cylinders are shown .

The volume of the smaller cylinder is 50 cm^{3}
Calculate the volume of the larger cylinder.

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Cyril had a pack of playing cards.

Each card in the pack was either green or blue with a circle, square, triangle or rectangle symbol. The table shows the probability of picking different cards.

Cyril picked two cards at random without replacement.

a) What is the probability of picking a blue card *and* a green card.

Cyril put the cards back, then picked two cards at random without replacement.

b) What is the probability of not picking a card with the square symbol

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A bag contained some blue and green balls. Two balls are picked at random without replacement

The probability of picking a blue ball on the first selection is

The probability of picking two blue balls is

How many blue balls were in the bag

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Poppy had an internet business selling socks. She starts by charging £5.00 for each pair plus postage of £3 for each order.

a) Get some graph paper and plot the equation y = 5x + 3

In a special offer, Poppy reduced the price for a pair of socks to £4, but increased postage to £6. On the same graph plot the equation for this special offer.

b) Use the graphs to compare both offers and work out for how many pairs of socks they charge the same.

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Matt looked at his yearly income statement and noticed some missing values.

Copy the statement and use the formula below to complete it

His taxable pay is worked out using the tax code 747L.

This means, he doesn't pay tax on £7475 of his gross pay.

a) Taxable Pay = Gross Pay – £7475.

Work out Matt's Taxable Pay.

b) Matt's Income tax = 20% of Taxable Pay.

Work out Matt's Income tax.

c) Matt's Total Deductions = Income Tax + NI (national Insurance)

Work out Matt's Total Deductions.

d) Net Pay = Gross pay – Total deductions.

Work out Matt's Net Pay.

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Peter made some bricklaying mortars using the proportions:

1 part cement ¼ part lime 3 parts sand |

He made 34 kg of mortar. Work out the proportions in kg for each.

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The formula

v^{2} = u^{2} + 2as |

gives the velocity v of an object dropped from a height.

u is the starting velocity of an object

v is the final velocity of an object

a is the acceleration due to gravity. a = 9.8 on Earth.

s is the height dropped in metres.

a) An object is dropped from rest and reaches a final velocity of 10m/s

Calculate the height dropped to 1 decimal place.

Another object has an initial velocity of 20 m/s and falls 25m

u = 20m/s; s = 25m

b) Calculate the final velocity v to 1 decimal place.

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Chantelle wants to buy two pairs of trainers.

Three shops sell the trainers she wants, as shown below

DW Shoes | CB Sport | Joggers |

Normally £40 1/5th off |
Normally £38 15% off |
Normally £43 Buy one pair get 2nd pair half price |

Calculate which shop is the cheapest for **two** pairs of trainers

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a) Make y the subject of the formula .

b) Simplify

c) Simplify

d) Solve the simultaneous equations

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The sale price for a coat was £108.

The normal price was reduced by 20%.

Work out the normal price for the coat.

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Given that x^{2} – 8x – 4 = (x – a)^{2} + b

find a and b

Hence solve x^{2} – 8x – 4 = 0

Give your answer in the form c ± d√5

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The amount of energy (E) released when matter is converted to energy is proportional to mass of that object (m).

When E = 9 × 10^{13} Joules, m = 1 × 10^{–3} kg

a) Find a formula for E in terms of m giving your answer in standard form

b) Calculate the mass, in kg when E = 1.8 × 10^{15} Joules

Give your answer in standard form

c) Calculate the energy, in joules when m = 0.00000015 kg

Give your answer in standard form

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ACDE is a rectangle with:

M is the midpoint of AC

ABC is a right angled triangle

Write each of the following vectors in terms of a and b

a)

b)

c) Show that M is the midpoint of the line BE

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A survey of 100 trainee teachers was made to see how long they spent revising for their QTS numeracy test

The table below shows how long in hours the trainee teachers spent.

Time (t hours) | Frequency |

0 ≤ t ≤ 4 | 8 |

4 ≤ t ≤ 8 | 23 |

8 ≤ t ≤ 12 | 37 |

12 ≤ t ≤ 16 | 25 |

16 ≤ t ≤ 20 | 7 |

a) Complete the cumulative frequency table

Time (t hours) | Cumulative Frequency |

0 ≤ t ≤ 4 | 8 |

0 ≤ t ≤ 8 | |

0 ≤ t ≤ 12 | |

0 ≤ t ≤ 16 | |

0 ≤ t ≤ 20 |

Get some graph paper and use your completed table to draw a cumulative frequency graph

c) One quarter of the trainee teachers spent x hours or more revising.

Using the cumulative frequency graph estimate the value of x.

The diagram shows a sketch of y = f(x).

a) For a graph of y = f(2x) what are the co-ordinates of points A and B.

b) For a graph of y = –2f(x) what are the co-ordinates of points A and B.

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