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Nadia has £5 to buy pencils and rulers. Pencils are 8p each. Rulers are 30p each. She says “I will buy 15 pencils. Then I will buy as many rulers as possible. With my change I will buy more pencils.” How many pencils and how many rulers does she buy?

Read the question carefully to understand what it is asking2) Consider how to approach the question - is there more than one way of getting the answer, are there any things that could trick me out (...

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For all values of x, f(x)=(x+1)^2 and g(x)=2(x-1). Show that gf(x)=2x(x+2)

The question is asking us to find gf(x).
When approaching this question, the first thing I tend to look for is what information we have that we can break down. In this case, I can immediately see tha...

Answered by Hannah B. • Maths tutor

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Determine the nature of the roots of the quadratic equation x^2 + 6x + 8 = 0, and plot the graph of this function.

The graph has two distinct real roots (x=-4 and x = -2), which we can see by factorising the equation, which gives (x+4)(x+2) = 0. We can then plot the function y = x^2 + 6x + 8, first marking the roots o...

Answered by Daniel L. • Maths tutor

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Solve algebraically the simultaneous equations: x^2 + y^2 = 25 and y – 3x = 13

(1) x²+ y²= 25 (2) y - 3x = 13 To solve simultaneous equations algebraically we want to rearrange one of the equations to be able to substitute this in to the other equation. In th...

Answered by Maria O. • Maths tutor

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How do I solve simultaneous equations when one is quadratic? For example 3x^2 -2y = 19, 6x-y-14=0

The aim of this question is to find the two solutions which satisfy the quadratic equation. The approach to this can be broken down into a few principle steps: 1) Express y in terms of x. Here 6x-y-14=0 c...

Answered by Angus M. • Maths tutor

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