Differentiate and simplify x\sin\left(x\right)

\sin\left(x\right)+x\cos\left(x\right)

Which of these is used to differentiate functions from first principles?

\lim_{\left(h\to0\right)=\frac{f\left(x+h\right)-f\left(x\right)}{h}}

Which of these is a general rule for the derivative of \ln\left(f\left(x\right)\right)

\frac{f'\left(x\right)}{f\left(x\right)}

Which of these is a true identity?

\cos\left(2\theta\right)\equiv\cos^2\theta-\sin^2\theta

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CF Year 13 Pure Maths Revision b

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Year 13 A Level Pure Maths Core Maths Differentiation Trigonometry Double Angle Compound Functions Modulus Radians

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Questions 10

Answers

1
Differentiate and simplify x\sin\left(x\right)
x\sin\left(x\right)+\cos\left(x\right)
x\cos\left(x\right)\sin\left(x\right)
\sin\left(x\right)+x\cos\left(x\right)
x\sin^{-1}\left(x\right)
2
Which of these functions is an example of a 'one-to-one' function?
f\left(x\right)=x
f\left(x\right)=x^4
f\left(x\right)=\cos\left(x\right)
f\left(x\right)=\sin\left(x\right)
3
What is the small angle approximation for \tan\left(\theta\right)
1-\frac{\theta^2}{2}
1-\theta^2
\frac{\theta}{1-\theta}
\theta
4
Which of these is used to differentiate functions from first principles?
\lim_{\left(h\to0\right)=\frac{f\left(x\right)-f\left(x+h\right)}{h}}
\lim_{\left(x\to0\right)=\frac{f\left(x\right)-f\left(h\right)}{h}}
\lim_{\left(h\to0\right)=\frac{f\left(x+h\right)-f\left(x\right)}{h}}
\lim_{\left(x\to0\right)=\frac{f\left(x+h\right)-f\left(h-x\right)}{h}}
5
What set of numbers is represented by the symbol ℚ
Transcendental Numbers
Complex Numbers
Rational Numbers
Natural Numbers
6
The following identity has what name: \cos^2\theta+\sin^2\theta\equiv1
Euler's identity
Pythagorean identity
Lagrange's identity
Bézout's identity
7
Which of these is a general rule for the derivative of \ln\left(f\left(x\right)\right)
\frac{f'\left(x\right)}{f\left(x\right)}
f'\left(x\right)e^{f\left(x\right)}
\frac{1}{f\left(x\right)}
f'\left(x\right)\ln\left(f\left(x\right)\right)
8
Using radians, which of these is the correct formula to work out Area of a Sector (A):
A=\frac{r^2\theta}{360}
A=r^2\theta
A=2r^2\theta
A=\frac{1}{2}r^2\theta
9
Which of these is another way of representing \sec\left(x\right)
\operatorname{cosec}\left(x\right)-1
\frac{1}{\cos\left(x\right)}
\cot\left(x\right)
\sqrt{1-x}
10
Which of these is a true identity?
\cos\left(2\theta\right)=2\cos^2\theta+1
\cos\left(2\theta\right)\equiv\sin^2\theta-1
\cos\left(2\theta\right)\equiv2\sin^2\theta+1
\cos\left(2\theta\right)\equiv\cos^2\theta-\sin^2\theta

CF Year 13 Pure Maths Revision b Flashcards | StudBud