What is the inverse to the function g\left(x\right)=2x+1

g^{-1}\left(x\right)=\frac{x-1}{2}

What function is represented by this graph?

f\left(x\right)=\left|x+2\right|

Which of these is a true identity?

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

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)}

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

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

Which of these is an even function?

m\left(x\right)=\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 true trigonometric identity?

1+\tan^2\theta\equiv\sec^2\theta

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Year 13 Pure Maths Revision

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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 20

Answers

1
What is the derivative of4\cos\left(x\right)
4\sin\left(x\right)\cos\left(x\right)
-4\cos\left(x\right)
4\sin\left(x\right)
-4\sin\left(x\right)
2
What function is represented by this graph?
f\left(x\right)=e^x+3
f\left(x\right)=e^x
f\left(x\right)=e^x+1
f\left(x\right)=e^x+2
3
For radians, arc length (s) can be calculated using what formula?
s=r\cos\left(\theta\right)
s=\pi r\theta
s=d\theta
s=r\theta
4
Using radians, which of these is the correct formula to work out Area of a Sector (A):
A=2r^2\theta
A=\frac{1}{2}r^2\theta
A=\frac{r^2\theta}{360}
A=r^2\theta
5
What is the inverse to the function g\left(x\right)=2x+1
g^{-1}\left(x\right)=2x-1
g^{-1}\left(x\right)=\frac{1}{2x+1}
g^{-1}\left(x\right)=\frac{x-1}{2}
g^{-1}\left(x\right)=\frac{2}{x+1}
6
What set of numbers is represented by the symbol ℚ
Rational Numbers
Complex Numbers
Transcendental Numbers
Natural Numbers
7
What function is represented by this graph?
f\left(x\right)=\left|x\right|-2
f\left(x\right)=\left|x\right|+2
f\left(x\right)=\left|x-2\right|
f\left(x\right)=\left|x+2\right|
8
Which of these is another way of representing \sec\left(x\right)
\frac{1}{\cos\left(x\right)}
\cot\left(x\right)
\sqrt{1-x}
\operatorname{cosec}\left(x\right)-1
9
Which of these is the quotient rule for a function \frac{u}{v}
\frac{uv'-vu'}{v^2}
\frac{vu'-uv'}{v^2}
\frac{uv-u'v'}{v^2}
\frac{uv'+vu'}{v^2}
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)\equiv\cos^2\theta-\sin^2\theta
\cos\left(2\theta\right)\equiv2\sin^2\theta+1
11
What is the small angle approximation for \tan\left(\theta\right)
1-\frac{\theta^2}{2}
\frac{\theta}{1-\theta}
\theta
1-\theta^2
12
Which of these is a general rule for the derivative of \ln\left(f\left(x\right)\right)
\frac{1}{f\left(x\right)}
\frac{f'\left(x\right)}{f\left(x\right)}
f'\left(x\right)\ln\left(f\left(x\right)\right)
f'\left(x\right)e^{f\left(x\right)}
13
The following identity has what name: \cos^2\theta+\sin^2\theta\equiv1
Pythagorean identity
Bézout's identity
Lagrange's identity
Euler's identity
14
Differentiate and simplify x\sin\left(x\right)
x\sin^{-1}\left(x\right)
x\sin\left(x\right)+\cos\left(x\right)
\sin\left(x\right)+x\cos\left(x\right)
x\cos\left(x\right)\sin\left(x\right)
15
Which of these is the derivative of \sin\left(e^x\right)
\cos\left(e^x\right)
e\cos\left(x\right)
e^x\cos\left(x\right)
e^x\cos\left(e^x\right)
16
Which of these functions is an example of a 'one-to-one' function?
f\left(x\right)=\cos\left(x\right)
f\left(x\right)=\sin\left(x\right)
f\left(x\right)=x^4
f\left(x\right)=x
17
Which of these is an even function?
f\left(x\right)=e^x
h\left(x\right)=x^3+x
g\left(x\right)=\sin\left(x\right)
m\left(x\right)=\cos\left(x\right)
18
Which of these is used to differentiate functions from first principles?
\lim_{\left(x\to0\right)=\frac{f\left(x+h\right)-f\left(h-x\right)}{h}}
\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}}
19
What transformation of a function has taken place in this graph?
\left|f\left(x\right)\right|
f\left(\right|x\left|\right)
f\left(x\right)^2
\sqrt{f\left(x\right)}
20
Which of these is a true trigonometric identity?
1+\tan^2\theta\equiv\sec^2\theta
\cos^2\left(\theta\right)-\sin^2\left(\theta\right)\equiv1
\cos2\theta\equiv2\sin\theta\cos\theta
\cot^2\theta+\operatorname{cosec}^2\theta\equiv1

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