ZIMSEC A Level Pure Mathematics Paper 1 November 2016

Question 101

[1 marks]complex numbers

The complex number

u = \dfrac{1}{-2+i}

. Find

|u|

A $\dfrac{1}{5}$
B $\dfrac{2}{5}$
C $\sqrt{5}$
D $\dfrac{\sqrt{5}}{5}$

Question 102

[1 marks]complex numbers

The complex number

u = \dfrac{1}{-2+i}

. Find

\arg u

correct to the nearest

0.1°

A $153.4°$
B $-153.4°$
C $-26.6°$
D $26.6°$

Question 103

[2 marks]complex numbers

Express

u=\dfrac1{-2+i}

in the form

x+iy

Answer this when you sit the paper.

Question 201

[1 marks]binomial expansion

Find the series expansion of

(9+2x)^{-3/2}

up to and including the term in

x^2

A $\tfrac{1}{27} - \tfrac{x}{81} + \tfrac{5}{1458}x^2$
B $\tfrac{1}{27} - \tfrac{x}{9} + \tfrac{5}{162}x^2$
C $\tfrac{1}{3} - \tfrac{x}{81} + \tfrac{5}{1458}x^2$
D $\tfrac{1}{27} + \tfrac{x}{81} + \tfrac{5}{1458}x^2$

Question 202

[1 marks]binomial expansion

Factoring

(9+2x)^{-3/2}=9^{-3/2}\left(1+\dfrac{2x}9\right)^{-3/2}

, state

9^{-3/2}

as a fraction.

Answer this when you sit the paper.

Question 203

[2 marks]binomial expansion

In the binomial expansion

(1+u)^n\approx1+nu+\ldots

with

n=-\dfrac32

u=\dfrac{2x}9

(used for

\left(1+\frac{2x}9\right)^{-3/2}

, before multiplying by

9^{-3/2}

), state the coefficient of

x

Answer this when you sit the paper.

Question 301

[1 marks]circles / tangency / discriminant

The line

y = 2mx + c

is a tangent to the circle

x^2 + y^2 = 4

. Which condition must

m

and

c

satisfy?

A $16m^2 - c^2 - 4 = 0$
B $16m^2 - c^2 + 4 = 0$
C $4m^2 - c^2 + 4 = 0$
D $16m^2 + c^2 - 4 = 0$

Question 302

[1 marks]circles / tangency / discriminant

Substituting

y=2mx+c

into

x^2+y^2=4

gives

(1+4m^2)x^2+4mcx+(c^2-4)=0

. State the coefficient of

x

in this quadratic, in terms of

m

and

c

Answer this when you sit the paper.

Question 303

[2 marks]circles / tangency / discriminant

For the tangency condition

(4mc)^2-4(1+4m^2)(c^2-4)=0

(from substituting

y=2mx+c

into

x^2+y^2=4

and setting the discriminant to zero), state

(4mc)^2

in simplified form.

Answer this when you sit the paper.

Question 401

[1 marks]modulus functions / inequalities

Given

f(x) = 2 - |x+3|

, solve the inequality

|f(x)| > 1

A $x < -6$ or $x > 0$ only
B $x < -6$ or $-4 < x < -2$ or $x > 0$
C $-6 < x < 0$
D $-4 < x < -2$ only

Question 402

[2 marks]modulus functions / inequalities

For

f(x)=2-|x+3|

, state the coordinates of its vertex (maximum point), as 'x,y'.

Answer this when you sit the paper.

Question 403

[1 marks]modulus functions / inequalities

For

f(x)=2-|x+3|

, state the two values of

x

where

f(x)=0

(where

y=|f(x)|

touches the

x

-axis), as 'a, b' in ascending order.

Answer this when you sit the paper.

Question 501

[1 marks]linearising relationships / graphs

Variables

x

and

y

satisfy

y = \dfrac{P}{\sqrt{x}}

. Which graph is a straight line, and what does its gradient give?

A $y$ against $\sqrt{x}$ : gradient $P$
B $\ln y$ against $\ln x$ : gradient $P$
C $y$ against $x$ : gradient $P$
D $y$ against $\dfrac{1}{\sqrt{x}}$ : gradient $P$

Question 502

[2 marks]linearising relationships / graphs

For the data

y=\dfrac P{\sqrt x}

plotted against

\dfrac1{\sqrt x}

, evaluate

\dfrac1{\sqrt x}

x=20

, correct to 4 decimal places.

Answer this when you sit the paper.

Question 503

[2 marks]linearising relationships / graphs

For the same data, evaluate

\dfrac1{\sqrt x}

x=75

, correct to 4 decimal places.

Answer this when you sit the paper.

Question 601

[1 marks]related rates

An aeroplane flies horizontally at height 5 500 m; its angle of elevation from an observer

x

m from the point directly beneath it is

\theta

. Which expression gives

\dfrac{d\theta}{dx}

A $\dfrac{5500}{x^2\sec^2\theta}$
B $-\dfrac{5500}{x^2}$
C $-\dfrac{5500}{x^2\sec^2\theta}$
D $-\dfrac{x^2\sec^2\theta}{5500}$

Question 602

[1 marks]related rates

An aeroplane flies at a constant height of 5 500 m at

550\,000

m/hr. When the angle of elevation from the observer is

25°

, the horizontal distance

x

from the observer to the point below the plane is

A $\dfrac{5500}{\tan 25°}$ m
B $5500\tan 25°$ m
C $\dfrac{5500}{\sin 25°}$ m
D $5500\cos 25°$ m

Question 603

[2 marks]related rates

For the aeroplane problem, evaluate

\sec^225°

, correct to 4 decimal places (needed in

\dfrac{d\theta}{dx}=-\dfrac{5500}{x^2\sec^2\theta}

\theta=25°

Answer this when you sit the paper.

Question 604

[1 marks]related rates

For the aeroplane flying at

550\,000

m/hr, state

\dfrac{dx}{dt}

in m/hr (the rate at which the horizontal distance

x

to the point below the plane changes, since

x

decreases as the plane approaches).

Answer this when you sit the paper.

Question 701

[1 marks]partial fractions / integration

Express

\dfrac{x-3}{x^2-1}

in partial fractions.

A $-\dfrac{2}{x+1} + \dfrac{1}{x-1}$
B $\dfrac{2}{x+1} - \dfrac{1}{x-1}$
C $\dfrac{1}{x+1} - \dfrac{2}{x-1}$
D $\dfrac{2}{x+1} + \dfrac{1}{x-1}$

Question 702

[1 marks]partial fractions / integration

Find

\displaystyle\int_2^3 \dfrac{x-3}{x^2-1}\,dx

, giving your answer as a single logarithm.

A $\ln\tfrac{9}{8}$
B $\ln\tfrac{16}{9}$
C $\ln\tfrac{8}{9}$
D $2\ln\tfrac{4}{3}$

Question 703

[2 marks]partial fractions / integration

Using

\dfrac{x-3}{x^2-1}=\dfrac2{x+1}-\dfrac1{x-1}

, evaluate

[2\ln(x+1)-\ln(x-1)]

x=3

, in the form

2\ln4-\ln p

. State

p

Answer this when you sit the paper.

Question 704

[2 marks]partial fractions / integration

Using

\dfrac{x-3}{x^2-1}=\dfrac2{x+1}-\dfrac1{x-1}

, evaluate

[2\ln(x+1)-\ln(x-1)]

x=2

, in the form

2\ln3-\ln q

. State

q

Answer this when you sit the paper.

Question 801

[1 marks]compound angle identities

The equation

\cos(45° + \theta) = 2\sin(45° - \theta)

reduces to which simple equation?

A $\tan\theta = 1$
B $\tan\theta = 2$
C $\tan\theta = \tfrac{1}{2}$
D $\tan\theta = -1$

Question 802

[1 marks]compound angle identities

Solve

\cos(45° + \theta) = 2\sin(45° - \theta)

for

0° \le \theta \le 360°

A $\theta = 45°$ only
B $\theta = 135°$ or $\theta = 315°$
C $\theta = 45°$ or $\theta = 225°$
D $\theta = 45°$ or $\theta = 135°$

Question 803

[2 marks]compound angle identities

Expanding

2\sin(45°-\theta)=2\sin45°\cos\theta-2\cos45°\sin\theta

(used to reduce

\cos(45°+\theta)=2\sin(45°-\theta)

), evaluate

2\sin45°

exactly.

Answer this when you sit the paper.

Question 804

[2 marks]compound angle identities

Expanding

\cos(45°+\theta)=\cos45°\cos\theta-\sin45°\sin\theta

, evaluate

\cos45°

exactly.

Answer this when you sit the paper.

Question 901

[1 marks]geometric and arithmetic series

A country's population is 27 million now and is projected to be 38 million in 36 years. Which equation determines the annual growth factor

r

under a geometric model?

A $38 = 27r^{36}$
B $38 = 27 + 36r$
C $27 = 38r^{36}$
D $38 = 27r^{1/36}$

Question 902

[1 marks]geometric and arithmetic series

Find the sum

S = \displaystyle\sum_{n=1}^{15}\left(2n + \tfrac{1}{2}\right)

A $127.5$
B $240$
C $247.5$
D $255$

Question 903

[2 marks]geometric and arithmetic series

A country's population grows from 27 million to 38 million in 36 years, following

38=27r^{36}

. Evaluate

r

, correct to 4 decimal places.

Answer this when you sit the paper.

Question 904

[1 marks]geometric and arithmetic series

Given

r\approx1.0095

for the population growth, state the annual growth rate as a percentage, correct to 2 decimal places.

Answer this when you sit the paper.

Question 905

[1 marks]geometric and arithmetic series

For

S=\displaystyle\sum_{n=1}^{15}\left(2n+\dfrac12\right)

, state the first term (at

n=1

Answer this when you sit the paper.

Question 1001

[1 marks]circle geometry / radian measure

Points

P

Q

R

lie on a circle of centre

O

radius

r

, and

S

is on

OQ

produced with

QS = r

and

PS = RS

. If angle

POS = \theta

radians, the shaded area

PQRS

A $r^2\sin\theta - \tfrac{1}{2}r^2\theta$
B $2r^2\sin\theta + r^2\theta$
C $2r^2\sin\theta - r^2\theta$
D $r^2\theta - 2r^2\sin\theta$

Question 1002

[1 marks]circle geometry / radian measure

In a circle of radius

r

centre

O

S

lies on

OQ

produced with

OS = 2r

and angle

POS = \theta

. Find

PS

A $r\sqrt{5 + 4\cos\theta}$
B $r\left(5 - 4\cos\theta\right)$
C $2r\sin\theta$
D $r\sqrt{5 - 4\cos\theta}$

Question 1003

[3 marks]circle geometry / radian measure

In the circle centre

O

radius

r

with points

P,Q,R,T

on it and angle

POS=\theta

(

S

OQ

produced),

P

and

R

are symmetric about line

OS

, so the reflex arc

PTR

(not through

Q

) subtends angle

2\pi-2\theta

O

. State the arc length of

PTR

, in terms of

r

and

\theta

Answer this when you sit the paper.

Question 1004

[2 marks]circle geometry / radian measure

For the circle problem,

PS=r\sqrt{5-4\cos\theta}

. Evaluate

\sqrt{5-4\cos\theta}

when

\theta=\dfrac{\pi}3

, correct to 3 decimal places.

Answer this when you sit the paper.

Question 1005

[2 marks]circle geometry / radian measure

The shaded area is

PQRS=2r^2\sin\theta-r^2\theta

. Evaluate this area when

\theta=\dfrac{\pi}3

and

r=2

, correct to 3 decimal places.

Answer this when you sit the paper.

Question 1101

[1 marks]factor and remainder theorems

For

f(x) = 2x^3 + ax^2 - bx + 12

(x-1)

is a factor of

f(x)

and

f'(x)

leaves remainder

-5

when divided by

(x-1)

. Find

a

and

b

A $a = 3$ , $b = 17$
B $a = 3$ , $b = -11$
C $a = -3$ , $b = -17$
D $a = 17$ , $b = 3$

Question 1102

[1 marks]factor and remainder theorems

Solve the equation

2x^3 + 3x^2 - 17x + 12 = 0

A $x = 1,\ x = -4,\ x = \tfrac{3}{2}$
B $x = -1,\ x = 4,\ x = \tfrac{3}{2}$
C $x = 1,\ x = -4,\ x = -\tfrac{3}{2}$
D $x = 1,\ x = 4,\ x = -\tfrac{3}{2}$

Question 1103

[2 marks]factor and remainder theorems

For

f(x)=2x^3+ax^2-bx+12

, the factor theorem (

f(1)=0

, since

(x-1)

is a factor) gives an equation relating

a

and

b

, in the form

a-b=k

. State

k

Answer this when you sit the paper.

Question 1104

[2 marks]factor and remainder theorems

For

f'(x)=6x^2+2ax-b

, the remainder theorem (

f'(1)=-5

) gives an equation, in the form

2a-b=k

. State

k

Answer this when you sit the paper.

Question 1105

[3 marks]factor and remainder theorems

With

a=3

b=17

f(x)=2x^3+3x^2-17x+12=(x-1)(2x^2+px+q)

. State

p

and

q

as 'p, q'.

Answer this when you sit the paper.

Question 1201

[1 marks]vectors

Given

\overrightarrow{OB} = -\mathbf{i} + \mathbf{j} - \mathbf{k}

, find the unit vector in the direction of

\overrightarrow{OB}

A $-\mathbf{i} + \mathbf{j} - \mathbf{k}$
B $\tfrac{1}{\sqrt{3}}(-\mathbf{i} + \mathbf{j} - \mathbf{k})$
C $\tfrac{1}{3}(-\mathbf{i} + \mathbf{j} - \mathbf{k})$
D $\tfrac{1}{\sqrt{3}}(\mathbf{i} - \mathbf{j} + \mathbf{k})$

Question 1202

[1 marks]vectors

Given

\overrightarrow{OA} = 3\mathbf{i} + 4\mathbf{j} + (2-b)\mathbf{k}

and

\overrightarrow{OB} = -\mathbf{i} + \mathbf{j} - \mathbf{k}

, find

b

such that

B\hat{O}A = 90°

A $b = 2$
B $b = 1$
C $b = -1$
D $b = 3$

Question 1203

[1 marks]vectors

With

\overrightarrow{AB} = -4\mathbf{i} - 3\mathbf{j} + (b-3)\mathbf{k}

, find the value of

b

for which

|\overrightarrow{AB}|^2

is a minimum.

A $b = 0$
B $b = 1$
C $b = 3$
D $b = 6$

Question 1204

[2 marks]vectors

With

\overrightarrow{OA}=3\mathbf i+4\mathbf j+(2-b)\mathbf k

and

\overrightarrow{OB}=-\mathbf i+\mathbf j-\mathbf k

, state

\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}

as 'x,y,z', in terms of

b

Answer this when you sit the paper.

Question 1205

[2 marks]vectors

With

\overrightarrow{AB}=-4\mathbf i-3\mathbf j+(b-3)\mathbf k

, write down an expression for

|\overrightarrow{AB}|^2

, in terms of

b

Answer this when you sit the paper.

Question 1206

[1 marks]vectors

Given

|\overrightarrow{AB}|^2=25+(b-3)^2

, state its minimum value (occurring at

b=3

Answer this when you sit the paper.

Question 1207

[2 marks]vectors

Evaluate

\overrightarrow{OA}\cdot\overrightarrow{OB}

in terms of

b

(using

\overrightarrow{OA}=3\mathbf i+4\mathbf j+(2-b)\mathbf k

\overrightarrow{OB}=-\mathbf i+\mathbf j-\mathbf k

), before setting it to zero to find

b

Answer this when you sit the paper.

Question 1301

[1 marks]differential equations / exponential decay

A wet substance loses moisture at a rate proportional to its moisture content

M

. Solve the resulting differential equation given that

M = m_0

when

t = 0

A $M = m_0\ln(kt)$
B $M = \dfrac{m_0}{kt}$
C $M = m_0 + kt$
D $M = m_0e^{kt}$

Question 1302

[1 marks]differential equations / exponential decay

A substance loses half of its moisture in the first hour, so that

M = m_0 e^{-t\ln 2}

. Find the time it takes to lose

95\%

of its moisture.

A $4.3$ hours
B $5.0$ hours
C $19.0$ hours
D $3.0$ hours

Question 1303

[2 marks]differential equations / exponential decay

Separating variables in

\dfrac{dM}{dt}=kM

and integrating gives

\ln M=kt+c

. Using

M=m_0

when

t=0

, state

c

in terms of

m_0

Answer this when you sit the paper.

Question 1304

[2 marks]differential equations / exponential decay

Given

M=m_0e^{kt}

and that half the moisture is lost in the first hour (

M=0.5m_0

t=1

), evaluate

e^k

Answer this when you sit the paper.

Question 1305

[2 marks]differential equations / exponential decay

Using

e^k=0.5

, evaluate

k

, correct to 4 decimal places.

Answer this when you sit the paper.

Question 1306

[2 marks]differential equations / exponential decay

To lose 95% of moisture, 5% remains, i.e.

M=0.05m_0

. State the resulting equation in the form

e^{kt}=p

. State

p

Answer this when you sit the paper.

Question 1307

[2 marks]differential equations / exponential decay

Using

k\approx-0.6931

and

e^{kt}=0.05

, evaluate

kt

(i.e.

\ln0.05

), correct to 4 decimal places.

Answer this when you sit the paper.

Question 1401

[1 marks]Newton-Raphson method

Let

f(x) = \tan x - 4x

. Which calculation shows that the positive root of

\tan x = 4x

lies between

x = 1

and

x = 1.5

A $f(1) = 1.557$ and $f(1.5) = 14.10$
B $f(1) = 2.443$ and $f(1.5) = -8.10$
C $f(1) = -2.443$ and $f(1.5) = 8.10$
D $f(1) = -2.443$ and $f(1.5) = -8.10$

Question 1402

[1 marks]Newton-Raphson method

Applying the Newton-Raphson method to

f(x) = \tan x - 4x

gives which iterative formula?

A $x_{n+1} = \dfrac{x_n\tan^2 x_n - \tan x_n + x_n}{\tan^2 x_n + 3}$
B $x_{n+1} = \dfrac{\tan x_n - 4x_n}{\tan^2 x_n - 3}$
C $x_{n+1} = \dfrac{x_n\tan^2 x_n - \tan x_n + x_n}{\tan^2 x_n - 3}$
D $x_{n+1} = \dfrac{x_n\tan^2 x_n + \tan x_n - x_n}{\tan^2 x_n - 3}$

Question 1403

[1 marks]Newton-Raphson method

Starting with

x_1 = 1.4

, use the Newton-Raphson iteration for

\tan x = 4x

to estimate the root correct to 4 decimal places.

A $1.3932$
B $1.3935$
C $1.4000$
D $1.5000$

Question 1404

[2 marks]Newton-Raphson method

x=0.1

radians, evaluate

\tan x

, correct to 4 decimal places (used to compare

y=\tan x

and

y=4x

near the origin).

Answer this when you sit the paper.

Question 1405

[1 marks]Newton-Raphson method

Comparing

\tan(0.1)\approx0.1003

with

4(0.1)=0.4

, which is true just after

x=0

A $\tan x=4x$
B $\tan x$ is undefined
C $\tan x<4x$
D $\tan x>4x$

Question 1406

[2 marks]Newton-Raphson method

x\to\dfrac{\pi}2^-

\tan x\to\infty

while

4x\to4\times\dfrac{\pi}2=2\pi

(a finite value). State

2\pi

, correct to 4 decimal places.

Answer this when you sit the paper.

Question 1407

[2 marks]Newton-Raphson method

For

f(x)=\tan x-4x

, evaluate

f(1)

, correct to 3 decimal places.

Answer this when you sit the paper.

Question 1408

[2 marks]Newton-Raphson method

For

f(x)=\tan x-4x

, evaluate

f(1.5)

, correct to 2 decimal places.

Answer this when you sit the paper.

Question 1501

[1 marks]functions / composite and inverse functions

Given

f(x) = 2x - 3

and

g(x) = 3x^2 + 2x - 2

, express

gf(x)

in its simplest form.

A $12x^2 - 32x + 25$
B $6x^2 + 4x - 7$
C $12x^2 + 32x + 19$
D $12x^2 - 32x + 19$

Question 1502

[1 marks]functions / composite and inverse functions

Find the minimum value of

gf(x) = 12x^2 - 32x + 19

A $-\tfrac{4}{3}$
B $-\tfrac{7}{3}$
C $\tfrac{4}{3}$
D $19$

Question 1503

[1 marks]functions / composite and inverse functions

The function

g(x) = 3x^2 + 2x - 2

is defined for

x \ge k

. State the minimum value of

k

for which

g

has an inverse, and give

g^{-1}(x)

A $k = \tfrac{1}{3}$ ; $g^{-1}(x) = \tfrac{1}{3}\sqrt{3x+7} + \tfrac{1}{3}$
B $k = -\tfrac{1}{3}$ ; $g^{-1}(x) = \tfrac{1}{3}\sqrt{3x+7} - \tfrac{1}{3}$
C $k = -\tfrac{7}{3}$ ; $g^{-1}(x) = \sqrt{3x+7} - \tfrac{1}{3}$
D $k = -\tfrac{1}{3}$ ; $g^{-1}(x) = \tfrac{1}{3}\sqrt{3x-7} - \tfrac{1}{3}$

Question 1504

[2 marks]functions / composite and inverse functions

For

f(x)=2x-3

, state

f^{-1}(x)

Answer this when you sit the paper.

Question 1505

[2 marks]functions / composite and inverse functions

For

f(x)=2x-3

and

f^{-1}(x)=(x+3)/2

, state the point where the graphs of

y=f(x)

and

y=f^{-1}(x)

intersect (on the line

y=x

), as 'x,y'.

Answer this when you sit the paper.

Question 1506

[2 marks]functions / composite and inverse functions

For

gf(x)=12x^2-32x+19

, state the value of

x

at which the minimum occurs.

Answer this when you sit the paper.

Question 1507

[2 marks]functions / composite and inverse functions

Completing the square,

g(x)=3x^2+2x-2=3\left(x+\dfrac13\right)^2+d

for some constant

d

. State

d

Answer this when you sit the paper.

Question 1508

[1 marks]functions / composite and inverse functions

Hence state the

x

-coordinate of the vertex of

g(x)=3x^2+2x-2

(the minimum value of

k

for which

g

has an inverse on

x\ge k

Answer this when you sit the paper.

Question 1601

[1 marks]exponential functions / areas and volumes

The curve

y = e^{2x} - e^{3x}

has a maximum point

P

. Find the

x

-coordinate of

P

A $0$
B $\ln\tfrac{1}{6}$
C $\ln\tfrac{3}{2}$
D $\ln\tfrac{2}{3}$

Question 1602

[1 marks]exponential functions / areas and volumes

Calculate the area of the region bounded by

y = e^{2x} - e^{3x}

, the

x

-axis, from

x = \ln\tfrac{2}{3}

x = 0

A $\tfrac{7}{81}$ square units
B $\tfrac{1}{6}$ square units
C $\tfrac{10}{81}$ square units
D $\tfrac{7}{162}$ square units

Question 1603

[1 marks]exponential functions / areas and volumes

The region bounded by

y = e^{2x} - e^{3x}

and the

x

-axis between

x = \ln\tfrac{2}{3}

and

x = 0

is rotated completely about the

x

-axis. Find the volume, correct to 3 significant figures.

A $0.0167$ cubic units
B $0.0432$ cubic units
C $0.167$ cubic units
D $0.00533$ cubic units

Question 1604

[2 marks]exponential functions / areas and volumes

For

y=e^{2x}-e^{3x}

, state

\dfrac{dy}{dx}

Answer this when you sit the paper.

Question 1605

[2 marks]exponential functions / areas and volumes

Setting

\dfrac{dy}{dx}=2e^{2x}-3e^{3x}=0

and dividing throughout by

e^{2x}

, state the resulting equation in the form

2=ce^x

. State

c

Answer this when you sit the paper.

Question 1606

[2 marks]exponential functions / areas and volumes

Evaluate

\left[\dfrac{e^{2x}}2-\dfrac{e^{3x}}3\right]

x=0

(one part of the area calculation for region R).

Answer this when you sit the paper.

Question 1607

[2 marks]exponential functions / areas and volumes

Evaluate

\left[\dfrac{e^{2x}}2-\dfrac{e^{3x}}3\right]

x=\ln\dfrac23

, as a single fraction.

Answer this when you sit the paper.

Question 1608

[1 marks]exponential functions / areas and volumes

Expanding

(e^{2x}-e^{3x})^2

(needed for the volume integral) gives

e^{4x}-2e^{5x}+e^{6x}

. State the coefficient of

e^{5x}

in this expansion.

Answer this when you sit the paper.

Pure Mathematics Paper 1 November 2016

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 301

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Question 1001

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Question 1601

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Question 1605