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There are 30 yellow sweets and 10 black sweets in a bag. Two sweets are taken out at random without replacement. Work out the probability that the two sweets are the same colour.

It is important before proceeding with the question to note down a few key facts. As can be seen by the question there are 40 sweets in total. With probability questions in general it can be easy to remember...
JT
Answered by James T. • Maths tutor
9683 Views

Write y = x^2 + 4x + 6 in the form y = (x + a)^2 + b. What is the minimum value of y?

This is an example of completing the square. Notice that when we expand y = (x + a)^2 + b we get y = x^2 + 2ax + a^2 + b. By comparing coefficients (ie, making sure the number x is multiplied by and the cons...
NS
Answered by Naomi S. • Maths tutor
8402 Views

Find INT{2,1}{x^4 + 3x^2 + 2}

This is a typical AS-level Maths question. We see it’s a definite integral so start by drawing some big square brackets with the “limits” (2 and 1). We go through the expression inside the integral (the “int...
AF
Answered by Andrew F. • Maths tutor
4341 Views

How could I sketch a graph of y=2x^3-3x^2?

To sketch a graph of an equation, there are several key features to consider. Firstly, we can consider where the graph crosses the x- and y-axes. When x=0, y=0, so the graph goes through the origin. If y=0, ...
LH
Answered by Lawrence H. • Maths tutor
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Let f(x)=x^2-ax+a-1 and g(x)=x-5. The graphs of f and g intersect at one distinct point. Find the possible values of a.

If the two graphs intersect, it means that they will share the same y and x coordinates at one particular point. (I will draw diagram to show point). Therefore, you can set f(x)=g(x) so that x^2 -ax +a -1 = ...
AO
Answered by Andres O. • Maths tutor
8219 Views