Free Printable CAPE Pure Math Unit 2 Module 1 Revision

1.

In the expression

z= x+iy

which letter represents the real part?

a)

z

b)

x

c)

y

d)

i

2.

The conjugate form of z=x-iy is

a)

z*= x+iy

b)

z*= -x-iy

c)

z*= -x+iy

d)

z*= x-iy

3.

The modulus of

\left|z\right|

is

a)

r= $\sqrt{\left(x+y\right)^2-\left(x-y\right)^2}$

b)

$r=\sqrt{x^2+y^2}$

c)

r= $\sqrt{x+y}$

4.

The quadratic equation with imaginary roots is

a)

$x^2-\left(\alpha\beta\right)x+\alpha\beta=0$

b)

$x^2+\left(\alpha+\beta\right)x\ -\alpha\beta=0$

c)

$x^2-\left(\alpha+\beta\right)x+\alpha\beta=0$

d)

$x^2+\left(\alpha\beta\right)-\left(\alpha+\beta\right)=0$

5.

Step 1 in finding the Square Root of a Complex Number

a)

Square both sides

b)

Equate Real and Imaginary Parts

c)

Express square root in the form

\sqrt{a+bi}=x+yi

d)

Solve for x and y

6.

Step 2 in finding the square root of a Complex Number

a)

Square both sides

b)

Equate real and imaginary parts

c)

Solve for x and y

d)

Express square root in the form

\sqrt{a+bi}=x+yi

7.

Step 3 in finding the Square Root of a Complex Number

a)

Solve for x and y

b)

Equate real and imaginary parts

c)

Square both sides

d)

Express square root in the form

\sqrt{a+bi}=x+yi

8.

Step 4 when finding the square root of a Complex Number

a)

$\sqrt{a+bi}=x+yi$ Express square root in the form

b)

Equate real and imaginary parts

c)

Square both sides

d)

Solve for x and y

9.

How is zero represented as a Complex Number?

z=

(a)

10.

Quadratic Equations of Complex Numbers with Non-real Coefficients can be solved using the Quadratic Formula. If the Quadratic Equation is given as

z^2+iz+2=0

, what are the respective constants?

a)

a=1, b=1, c=2

b)

a=0, b=1, c=2

c)

a=1, b=i, c=2

d)

a=0, b=-1, c=2

11.

On the Argand Diagram, what are the respective labels of the axes?

Choose the two correct answers below.

a)

The horizontal is the Imaginary Axis [Im(z)]

b)

The horizontal is the Real Axis [Re(z)]

c)

The vertical is the Real Axis [Re(z)]

d)

The vertical is the Imaginary Axis [Im(z)]

12.

Which of the following correctly represents the locus of a circle?

a)

$\left|z-c\right|=r$

b)

$\left|z-a\right|=\left|z-b\right|$

c)

$\arg\left(z-a\right)=0$

d)

$\left|z-z_1\right|=k\left|z-z_2\right|$

13.

Which of the following correctly represents the locus of a perpendicular bisector of a line segment?

a)

$\left|z-a\right|=\left|z-b\right|$

b)

$\left|z-z_1\right|=k\left|z-z_2\right|$

c)

$\arg\left(z-a\right)=0$

d)

$\left|z-c\right|=r$

14.

Which of the following correctly represents the locus of Half lines?

a)

$\left|z-c\right|=r$

b)

$\left|z-a\right|=\left|z-b\right|$

c)

$\arg\left(z-a\right)=0$

d)

$\left|z-z_1\right|=k\left|z-z_2\right|$

15.

Which of the following correctly represents the locus straight lines?

a)

\left|z-c\right|=r

b)

$\left|z-a\right|=\left|z-b\right|$

c)

$\arg\left(z-a\right)=0$

d)

$\left|z-z_1\right|=k\left|z-z_2\right|$

16.

Which of the following represents the correct formula related to De Moivre's Theorem?

a)

$z^n=\left(\cos\theta\pm\sin\theta\right)^n=\left(\cos n\theta\pm i\sin n\theta\right)$

b)

$z^n=\left(\sin\theta\pm i\cos\theta\right)^n=\left(\sin n\theta\pm i\cos n\theta\right)$

c)

$z^n=\left(\cos n\theta\pm i\sin n\theta\right)^n$

17.

$\cos\theta=$

a)

$\sin\theta$

b)

$\cos^2\theta$

c)

$\cos\left(-\theta\right)$

d)

$-\sin\left(-\theta\right)$

18.

$\sin\theta$

a)

$\cos\theta$

b)

$\sin^2\theta$

c)

$-\sin\left(-\theta\right)$

d)

$\frac{1}{\sin\theta}$

19.

$\frac{d}{dx}\left(x^n\right)=$

a)

$x^{n+1}$

b)

$nx^{n-1}$

c)

$nx^{n+1}$

20.

$\frac{d}{dx}\left(ax+b\right)=0$

a)

$na\left(ax+b\right)^{n-1}$

b)

$\frac{a}{n}\left(ax+b\right)^{n+1}$

c)

$na\left(ax+b\right)^{n+1}$

d)

$\frac{\left(ax+b\right)^{n-1}}{a\left(n-1\right)}$

21.

$\frac{d}{dx}\left(e^{ax+b}\right)$

a)

$ax+b\left(e^{ax+b}\right)$

b)

$ax\left(e^{ax+b}\right)$

c)

$a\left(e^{ax+b}\right)$

22.

\frac{d}{dx}\ln\left(ax+b\right)=

a)

$\ln ax$

b)

$ax\ln ax$

c)

$\frac{a}{ax+b}$

23.

\frac{d}{dx}\sin x=

a)

-sinx

b)

-cosx

c)

cosx

d)

sinxcosx

24.

\frac{d}{dx}\cos x=

a)

sinx

b)

cosx

c)

-sinx

d)

-sinxcosx

25.

\frac{d}{dx\ }\tan x=

a)

$\sec x$

b)

$\frac{\sin x}{\cos x}$

c)

-cosecx

d)

$\sec^2x$

26.

\frac{d}{dx}\sec x=

a)

tan x

b)

$\tan^2x$

c)

$\sec x\tan x$

d)

$\sec^2\tan x$

27.

\frac{d}{dx}\operatorname{cosec}x=

a)

-cot x

b)

cot x

c)

cosec x

d)

-cosec x cot x

28.

\frac{d}{dx}\cot x=

a)

$\frac{\cos x}{\sin x}$

b)

$\operatorname{cosec}^2x$

c)

$-\operatorname{cosec}^2x$

d)

tan x

29.

\frac{d}{dx\ }\sin^{-1}=

a)

$-\frac{1}{\sqrt{1+x}}$

b)

$\frac{1}{\sqrt{1-x^2}}$

c)

$\frac{1}{\sqrt{1+x^2}}$

d)

$-\frac{1}{\sqrt{1-x^2}}$

30.

\frac{d}{dx\ }\cos^{-1}=

a)

$\frac{1}{\sqrt{1-x^2}}$

b)

$-\frac{1}{\sqrt{1-x^2}}$

c)

$-\frac{1}{\sqrt{1+x^2}}$

d)

$\frac{1}{\sqrt{1+x^2}}$

31.

\frac{d}{dx}\tan^{-1}=

a)

$\frac{1}{\sqrt{1-x^2}}$

b)

$-\frac{1}{\sqrt{1+x^2}}$

c)

$-\frac{1}{\sqrt{1-x^2}}$

d)

$\frac{1}{\sqrt{1+x^2}}$

32.

$\frac{d}{dx}a^x=$

a)

$a^x\ln x$

b)

$a\ln x$

c)

$\ln ax$

d)

$\ln\ \frac{a}{x}$

33.

Which of the following correctly represents the Product Rule?

$\frac{dy}{dx}=$

a)

$UV+\frac{du}{dx}\left(\frac{dv}{dx}\right)$

b)

$U\left(\frac{dv}{dx}\right)+V\left(\frac{du}{dx}\right)$

c)

$U\left(\frac{dv}{dx}\right)-V\left(\frac{du}{dx}\right)$

34.

Which of the following correctly represents the Quotient Rule?

a)

\frac{U\left(\frac{dv}{dx}\right)}{V\left(\frac{du}{dx}\right)}

b)

$\frac{\left(V\left(\frac{du}{\left(dx\right)}\right)-U\left(\frac{dv}{dx}\right)\right)}{V^2}$

c)

$\frac{\left(U\left(\frac{dv}{dx}\right)-V\left(\frac{du}{dx}\right)\right)}{V^2}$

35.

$\frac{dy}{dx}$ represents the gradient of
a) Tangent
b) Normal

(a)

36.

$-\frac{dy}{dx}$ represents the gradient of

a) Normal

b) Tangent

(a)

37.

The Parametric Equations are defined as:

$x=f\left(t\right)$ and $y=g\left(t\right)$

The parametric differential is represented as;

\frac{dy}{dx}=\frac{dy}{dt}\times\frac{dx}{dt}

True or False?

(a)

38.

$\frac{d}{dx}\ y=$

a)

$\frac{dy}{dx}$

b)

$\frac{dx}{dy}$

c)

y

d)

xy

39.

$\frac{d}{dx\ }\ y^2=$

a)

2y

b)

$2\ \frac{dy}{dx}$

c)

$2\ \frac{d^2y}{dx^2}$

d)

$2\ y\ \frac{dy}{dx}$

40.

$\frac{P\left(x\right)}{\left(ax+b\right)\left(cx+d\right)}=$

a)

$\frac{A}{\left(ax+b\right)}+\frac{B}{\left(cx+d\right)}$

b)

$\frac{A}{\left(ax+b\right)}+\frac{B}{\left(cx+d\right)}+\frac{C}{\left(cx+d\right)^2}$

c)

$\frac{A}{\left(ax+b\right)}+\frac{\left(Bx+C\right)}{\left(cx^2+dx+e\right)}$

d)

$\frac{A}{\left(ax+b\right)}+\frac{\left(Bx+C\right)}{\left(cx^2+dx+e\right)}+\frac{\left(Dx+E\right)}{\left(cx^2+dx+e\right)^2}$

41.

$\frac{P\left(x\right)}{\left(ax+b\right)\left(cx+d\right)^2}=$

a)

$\frac{A}{\left(ax+b\right)}+\frac{B}{\left(cx+d\right)}$

b)

$\frac{A}{\left(ax+b\right)}+\frac{\left(Bx+C\right)}{\left(cx^2+dx+e\right)}$

c)

$\frac{A}{\left(x+2\right)}+\frac{B}{\left(cx+d\right)}+\frac{C}{\left(cx+d\right)^2}$

d)

$\frac{A}{\left(ax+b\right)}+\frac{\left(Bx+C\right)}{\left(cx^2+dx+e\right)}+\frac{\left(Dx+E\right)}{\left(cx^2+dx+e\right)^2}$

42.

$\frac{P\left(x\right)}{\left(ax+b\right)\left(cx^2+dx+e\right)}=$

a)

$\frac{A}{\left(ax+b\right)}+\frac{B}{\left(cx+d\right)}$

b)

$\frac{A}{\left(ax+b\right)}+\frac{\left(Bx+C\right)}{\left(cx^2+dx+e\right)}$

c)

$\frac{A}{\left(x+2\right)}+\frac{B}{\left(cx+d\right)}+\frac{C}{\left(cx+d\right)^2}$

d)

$\frac{A}{\left(ax+b\right)}+\frac{\left(Bx+C\right)}{\left(cx^2+dx\ +e\right)}+\frac{\left(Dx+E\right)}{\left(cx^2+dx+e\right)}$

43.

$\frac{P\left(x\right)}{\left(ax+b\right)\left(cx^2+dx+e\right)}=$

a)

$\frac{A}{ax+b}+\frac{B}{cx+d}$

b)

$\frac{A}{x+2}+\frac{B}{cx+d}+\frac{C}{\left(cx+d\right)^2}$

c)

$\frac{A}{ax+b}+\frac{\left(Bx+C\right)}{cx^2+dx+e}+\frac{\left(Dx+E\right)}{\left(cx^2+dx+e\right)^2}$

d)

$\frac{A}{ax+b}+\frac{\left(Bx+C\right)}{cx^2+dx+e}$

44.

$\int_x^y\ x^n=$

a)

$\frac{1}{x}+C$

b)

$\frac{x^{n+1}}{n+1}+C$

c)

$\frac{x^{n-1}}{n-1}+C$

45.

$\int_x^y\left(ax+b\right)^n=$

a)

$\frac{\left(ax+b\right)^{n+1}}{n+1}+C$

b)

$\frac{1}{a}\left[\frac{\left(ax+b\right)^{n+1}}{n+1}\right]+C$

46.

$\int_x^y\ \frac{1}{x}=$

a)

$\ln x\ +C$

b)

$x\ln x+C$

47.

$\int_x^y\ \frac{1}{ax+b}=$

a)

$\frac{1}{a}\ \ln\ \left(ax+b\right)+C$

b)

$\frac{1}{ax+b}\ \ln\left(ax+b\right)+C$

c)

$\frac{1}{ax}\ln\left(ax+b\right)+C$

48.

$\int_x^{y\ }\ e^{ax+b}=$

a)

$\frac{1}{ax}e^{ax+b}+C$

b)

$\frac{1}{a}e^{ax+b}+C$

49.

$\int_x^y\ \sin\left(ax+b\right)=$

a)

$\cos\left(ax+b\right)+C$

b)

$\frac{1}{a}\left(\cos\left(ax+b\right)\right)$

c)

$-\frac{1}{a}\cos\left(ax+b\right)+C$

50.

$\int_x^y\ \cos\left(ax+b\right)=$

a)

$\frac{1}{ax}\sin\left(ax+b\right)+C$

b)

$\frac{1}{a}\sin\left(ax+b\right)\ +C$

c)

$-\frac{1}{a}\sin\left(ax+b\right)+C$

51.

$\int_x^y\ \tan x=$

a)

$-\ln\left(\cos x\right)+C$

b)

$\ln\left(\cos x\right)+C$

c)

$\ln\left(\sec x\right)+C$

d)

$-\ln\left(\sec x\right)+$

CAPE Pure Math Unit 2 Module 1 Revision

Total questions: 51

Worksheet time: 29mins

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