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Prove that the square of an odd number is always 1 more than a multiple of 4.

First we consider how to represent an odd number. We know that any even number can be represented as 2k for some integer k since, by definition, all even numbers are multiples of 2. We also know that all ...

Answered by Josh L. • Maths tutor

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We have 2 spinners: spinner A and spinner B. Spinner A can land on 2, 3, 5 or 7. Spinner B can land on 2, 3, 4, 5 or 6. Spin both. Win if one spinner lands on odd and the other lands on even. Play game twice, what is the probability of winning both games?

P(win 2 out of 2 games) = P(win first game and win second game) = P(win first game)^2. So want to find the probability of winning a game.To win, either we need A odd and B even or we need A even and B odd...

Answered by Henry C. • Maths tutor

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Simplify (2x+3)^2 - (2x +3)(x-5). Give your answer in the form ax^2 +bx +c

Break this down into two parts.
a. Multiply out the 1st bracket, (2x+3)^2: This goes to (2x+3)(2x+3) which is equal to 4x^2 + 9 +6x+6x . Collect the like terms to get 4x^2 +12x +9.
b. Multiply...

Answered by Kenji S. • Maths tutor

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A square based pyramid with corners ABCD has side length 6 cm. The distance from the centre of the square (C) to the top vertex of the pyramid (V) is 4 cm. Work out the total surface area of the pyramid.

The first thing I would do with this question is to draw it out to help visualise the shape.From this drawing you can see that the shape has 4 triangle shaped faces (let's call this triangle T1) and 1 squ...

Answered by Matthew E. • Maths tutor

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There are 10 boys and 20 girls in a class. The class has a test. The mean mark for all the class is 60. The mean mark for the girls is 54. Work out the mean mark for the boys

Find the total number of people in the class 10+20=30
find the total number of marks achieved by the class 60x30=1800
since the mean mark for the girls is 54, you can work out the total marks ac...

Answered by Dessi T. • Maths tutor

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