Currently unavailable: for regular students
Degree: Mathematics (Masters) - Durham University
I'm a first year student at Durham University studying for a Masters degree in Mathematics. I've loved Maths and Science for as long as I can remember and I'm hoping my tutorials will inspire the same love and passion in you, or at the very least tolerate it!
I've had experience tutoring students in Maths at both GCSE and A-Level, dealing with students at various levels of understanding. I also have been involved with, as well as running, numerous STEM clubs; so I'm used to leading in addition to planning interactive (and hopefully fun) sessions.
The most important thing about these sessions is you getting some useful out of them. Because of this I’ll let you decide what we’re going to cover in every session.
With Maths especially, it is very important to practice questions and practice the different methods to solve equations. At the same time, Maths becomes a much more interesting subject when you begin to understand the reasoning behind it; so I’ll try to cover both in our sessions. I’m also happy to go through numerous different methods as every has a different approach, and these sessions are about finding the best methods for you.
Can I Help with UCAS?
Definitely! I’m more than happy to help with things like personal statements and how to choose your universities and I’d also be happy to help you with interview style questions and how to answer them. I originally applied for Natural Science before changing to Mathematics, so I can help with applying for most science subjects.
If you have any questions, please book a 'Meet the Tutor Session'! and remember to tell me your exam board, what modules you are studying (if you are an A-Level student) and what you're struggling with.
I look forward to working with you!
|Further Mathematics||A Level||£20 /hr|
|Maths||A Level||£20 /hr|
The first step to solving this problem is to treat it as a normal quadratic equation; if you are struggling with comparing our equation to a normal quadratic, try substituting sin(x) = y into the equation as shown:
sin2(x) + 4sin(x) becomes y2 + 4y
Even though our equation does not equal 0 we can still use the 'complete the square' method to help us find the minimum, after applying this method our equation becomes:
(y + 2)2 - 4
From this we can substitue y for sin(x), giving:
(sin(x) + 2)2 - 4
To find the minimum of our equation we have to take in to account the fact that sin(x) has a range of -1 to 1, which limits (sin(x) + 2) to a range of 1 to 3.
From this you should be able to deduct that the smallest value of (sin(x) + 2)2 - 4 is -3. This occurs when sin(x) = -1.
(-1 + 2)2 - 4 = 12 - 4 = -3
Hence the minimum of sin2(x) + 4sin(x) is -3.see more