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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 (e.g diffe...
HP
Answered by Hanesh P. • Maths tutor
2904 Views

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 that the f(...
HB
Answered by Hannah B. • Maths tutor
9913 Views

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 on t...
DL
Answered by Daniel L. • Maths tutor
3567 Views

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

(1) x 2 + y 2 = 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 this example, we have squ...
MO
Answered by Maria O. • Maths tutor
3947 Views

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 can ...
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Answered by Angus M. • Maths tutor
3180 Views