ZIMSEC A Level Pure Mathematics Paper 1 June 2014

Question 101

[1 marks]indices / exponential equations

Solve the equation

\dfrac{27^{4x}}{3^4} = 9^{(x-1)}

for

x

A $x=\dfrac15$
B $x=-\dfrac15$
C $x=\dfrac{3}{10}$
D $x=-\dfrac12$

Question 102

[1 marks]indices / exponential equations

Express

27^{4x}

3

raised to what power, in terms of

x

Answer this when you sit the paper.

Question 103

[1 marks]indices / exponential equations

Express

9^{x-1}

3

raised to what power, in terms of

x

Answer this when you sit the paper.

Question 201

[1 marks]binomial expansion

Find the coefficient of

x^2

in the expansion of

\left(x-\dfrac{2}{5x}\right)^6

A $-\dfrac{12}{5}$
B $\dfrac{12}{5}$
C $\dfrac{6}{5}$
D $\dfrac{24}{5}$

Question 202

[1 marks]binomial expansion

In the expansion of

\left(x-\dfrac{2}{5x}\right)^6

, the general term is

\binom{6}{r}x^{6-r}\left(-\dfrac{2}{5x}\right)^r=\binom{6}{r}(-1)^r\dfrac{2^r}{5^r}x^{6-2r}

. What value of

r

gives the term in

x^2

A $r=1$
B $r=4$
C $r=3$
D $r=2$

Question 203

[1 marks]binomial expansion

Evaluate

\binom{6}{2}

, the binomial coefficient used in finding the

x^2

term of

\left(x-\frac{2}{5x}\right)^6

Answer this when you sit the paper.

Question 301

[1 marks]small changes / differentiation

Given that

y=\dfrac{1}{\sqrt{2x-1}}

, find the exact value of

\dfrac{dy}{dx}

x=5

A $-\dfrac{1}{54}$
B $-\dfrac13$
C $-\dfrac{1}{27}$
D $\dfrac{1}{27}$

Question 302

[1 marks]small changes / differentiation

Given that

y=\dfrac{1}{\sqrt{2x-1}}

, find the approximate percentage change in

y

when

x=5

is decreased by 5%.

A1.39% increase
B2.78% increase
C2.78% decrease
D5.56% increase

Question 303

[1 marks]small changes / differentiation

Find

\delta x

, the change in

x

, when

x=5

is decreased by

5\%

Answer this when you sit the paper.

Question 304

[1 marks]small changes / differentiation

State the value of

y=\dfrac{1}{\sqrt{2x-1}}

x=5

Answer this when you sit the paper.

Question 401

[1 marks]composite functions

The functions

f

and

g

are defined for

x\in\mathbb{R}

f:x\to x^2+4x+1

and

g:x\to ax+b

. Given that

fg(2)=-2

and

gf(0)=-3

, find the values of

a

and

b

A $a=2,\ b=-5$
B $a=4,\ b=-7$
C $a=-2,\ b=-1$
D $a=-5,\ b=2$

Question 402

[1 marks]composite functions

Evaluate

f(0)

for

f(x)=x^2+4x+1

(used to find

gf(0)

Answer this when you sit the paper.

Question 403

[2 marks]composite functions

Given

a+b=-3

(from

gf(0)=-3

), using

fg(2)=-2

leads to

(2a+b)^2+4(2a+b)+3=0

, which factorises as

(2a+b+1)(2a+b+3)=0

. State the two possible values of

2a+b

Answer this when you sit the paper.

Question 404

[1 marks]composite functions

Using

a+b=-3

and

2a+b=-1

(the valid branch), find

a

Answer this when you sit the paper.

Question 501

[1 marks]polynomial remainder theorem / inequalities

The polynomials

P(x)=x^3-x^2+4x

and

Q(x)=x^3+6x-10

leave the same remainder when divided by

x-a

. Find the possible values of

a

A $a=-2\pm2\sqrt{11}$
B $a=-1\pm\sqrt{11}$
C $a=-1\pm\sqrt{14}$
D $a=1\pm\sqrt{11}$

Question 502

[1 marks]polynomial remainder theorem / inequalities

The polynomials

P(x)=x^3-x^2+4x

and

Q(x)=x^3+6x-10

leave the same remainder when divided by

x-a

, where

a=-1\pm\sqrt{11}

. Solve the inequality

P(x)>Q(x)

A $-1-\sqrt{11}<x<1+\sqrt{11}$
B $-1-\sqrt{11}<x<-1+\sqrt{11}$
C $x<-1-\sqrt{11}$ or $x>-1+\sqrt{11}$
D $1-\sqrt{11}<x<1+\sqrt{11}$

Question 503

[2 marks]polynomial remainder theorem / inequalities

Setting

P(a)=Q(a)

for

P(x)=x^3-x^2+4x

and

Q(x)=x^3+6x-10

leads to

a^2+2a-10=0

. State the discriminant

b^2-4ac

used in the quadratic formula.

Answer this when you sit the paper.

Question 504

[1 marks]polynomial remainder theorem / inequalities

P(x)-Q(x)

simplifies to

-x^2-2x+10

, so

P(x)>Q(x)

becomes

x^2+2x-10<0

. Evaluate

x^2+2x-10

x=0

(to confirm

0

lies in the solution interval).

Answer this when you sit the paper.

Question 601

[1 marks]optimisation / differentiation

An open rectangular tin (no lid) has a square base of side

x

cm and holds 500 cm

^3

of liquid when full. Which expression gives the total area,

A

^2

, of sheet metal used?

A $A=2x^2+\dfrac{2000}{x}$
B $A=x^2+\dfrac{1000}{x}$
C $A=x^2+\dfrac{500}{x}$
D $A=x^2+\dfrac{2000}{x}$

Question 602

[1 marks]optimisation / differentiation

An open rectangular tin (no lid) has a square base of side

x

cm and holds 500 cm

^3

of liquid when full, so its sheet-metal area is

A=x^2+\dfrac{2000}{x}

^2

. Find the minimum value of

A

A $300\ \text{cm}^2$
B $400\ \text{cm}^2$
C $150\ \text{cm}^2$
D $200\ \text{cm}^2$

Question 603

[2 marks]optimisation / differentiation

For the open tin with square base of side

x

, find

h

(the height) in terms of

x

, given

x^2h=500

Answer this when you sit the paper.

Question 604

[2 marks]optimisation / differentiation

Setting

\dfrac{dA}{dx}=2x-\dfrac{2000}{x^2}=0

, solve

x^3=1000

for

x

Answer this when you sit the paper.

Question 701

[1 marks]trigonometry / areas

In triangle

ABC

AB=5

cm,

BC=7

cm and

CA=8

cm. Find angle

BAC

A $\dfrac{\pi}{3}$
B $\dfrac{\pi}{4}$
C $\dfrac{2\pi}{3}$
D $\dfrac{\pi}{6}$

Question 702

[1 marks]trigonometry / areas

In triangle

ABC

AB=5

cm,

BC=7

cm,

CA=8

cm and angle

BAC=\dfrac{\pi}{3}

. Find

\sin B

A $\dfrac{5\sqrt3}{14}$
B $\dfrac{4}{7}$
C $\dfrac{4\sqrt3}{7}$
D $\dfrac{5\sqrt3}{16}$

Question 703

[1 marks]trigonometry / areas

Triangle

ABC

has

AB=5

cm,

BC=7

cm,

CA=8

cm and angle

BAC=\dfrac{\pi}{3}

, with

\sin B=\dfrac{4\sqrt3}{7}

. A circular arc, centred at

A

, is drawn touching line

BC

R

, so its radius is

AR=AB\sin B

. Find the exact area of the region between the triangle and the sector swept out by the arc between the two sides from

A

A $10\sqrt3-\dfrac{25\pi}{6}$
B $10\sqrt3-\dfrac{200\pi}{49}$
C $10\sqrt3+\dfrac{200\pi}{49}$
D $10\sqrt3$

Question 704

[2 marks]trigonometry / areas

Find the exact area of triangle

ABC

, given

AB=5

cm,

CA=8

cm and angle

BAC=\frac{\pi}{3}

Answer this when you sit the paper.

Question 705

[2 marks]trigonometry / areas

Find the exact radius

r=AR

of the arc, given

AR=AB\sin B

with

AB=5

and

\sin B=\frac{4\sqrt3}{7}

Answer this when you sit the paper.

Question 801

[1 marks]numerical methods / Newton-Raphson

For the equation

x-3+3\tan x=0

(with

x

in radians), let

h(x)=x-3+3\tan x

. Evaluate

h(0.6)

correct to 2 decimal places.

A $-2.37$
B $-1.72$
C $-0.35$
D $0.35$

Question 802

[1 marks]numerical methods / Newton-Raphson

Taking

x_0=0.6

as the first approximation to the root of

x-3+3\tan x=0

(with

x

in radians), apply the Newton-Raphson method to find the root correct to 3 decimal places.

A $0.6$
B $0.652$
C $0.662$
D $0.664$

Question 803

[2 marks]numerical methods / Newton-Raphson

Evaluate

h(0.7)=0.7-3+3\tan(0.7)

, correct to 2 decimal places (used to confirm the root lies between 0.6 and 0.7).

Answer this when you sit the paper.

Question 804

[2 marks]numerical methods / Newton-Raphson

Given

h'(x)=1+3\sec^2x

, evaluate

h'(0.6)

, correct to 3 significant figures (used in the Newton-Raphson formula).

Answer this when you sit the paper.

Question 805

[2 marks]numerical methods / Newton-Raphson

Using

x_0=0,6

h(0,6)=-0,3476

and

h'(0,6)=5,404

, find the first Newton-Raphson iterate

x_1=x_0-\dfrac{h(x_0)}{h'(x_0)}

, correct to 4 decimal places.

Answer this when you sit the paper.

Question 901

[1 marks]differential equations / separation of variables

A rumour spreads through a school so that the proportion

x

who have heard it satisfies

\dfrac{dx}{dt}=kx(1-x)

, where initially (at

t=0

) a proportion

c

of the population had heard it. Which expression correctly gives

x

in terms of

t

A $x=\dfrac{c}{c+(1-c)e^{kt}}$
B $x=\dfrac{ce^{-kt}}{c+(1-c)e^{-kt}}$
C $x=\dfrac{1-c}{(1-c)+ce^{-kt}}$
D $x=\dfrac{c}{c+(1-c)e^{-kt}}$

Question 902

[2 marks]differential equations / separation of variables

Express

\dfrac{1}{x(1-x)}

in partial fractions, in the form

\dfrac{1}{x}+\dfrac{1}{A-x}

. State

A

Answer this when you sit the paper.

Question 903

[2 marks]differential equations / separation of variables

Integrating gives

\ln x-\ln(1-x)=kt+C

, i.e.

\dfrac{x}{1-x}=Ae^{kt}

. Using

x=c

t=0

, find

A

in terms of

c

Answer this when you sit the paper.

Question 904

[3 marks]differential equations / separation of variables

From

\dfrac{x}{1-x}=\dfrac{c}{1-c}e^{kt}

, cross-multiplying and collecting

x

terms gives

x[(1-c)+ce^{kt}] =

[blank]. State the blank (the right-hand side).

Answer this when you sit the paper.

Question 1001

[1 marks]coordinate geometry / circles

The line

l_1

has equation

x+3y-33=0

. The line

l_2

is parallel to

l_1

and passes through

P(3,0)

. Find the equation of

l_2

A $x+3y+3=0$
B $x+3y-33=0$
C $x+3y-3=0$
D $3x-y-9=0$

Question 1002

[1 marks]coordinate geometry / circles

The line

l_1

has equation

x+3y-33=0

. Find the product of the gradient of

l_1

and the gradient of the line joining

P(3,0)

Q(6,9)

A $3$
B $1$
C $-1$
D $-\dfrac19$

Question 1003

[1 marks]coordinate geometry / circles

The line

l_1

has equation

x+3y-33=0

, and

l_2

(parallel to

l_1

) passes through

P(3,0)

. Given that

R(9,-2)

lies on

l_2

and

Q(6,9)

lies on

l_1

, find the equation of the circle passing through

P

Q

and

R

A $(x-7.5)^2+(y-3.5)^2=68.5$
B $(x-3.5)^2+(y-7.5)^2=32.5$
C $(x-7.5)^2+(y-3.5)^2=32.5$
D $(x+7.5)^2+(y+3.5)^2=32.5$

Question 1004

[2 marks]coordinate geometry / circles

Find the gradient of line

l_1: x+3y-33=0

Answer this when you sit the paper.

Question 1005

[1 marks]coordinate geometry / circles

Find the gradient of the line joining

P(3,0)

Q(6,9)

Answer this when you sit the paper.

Question 1006

[2 marks]coordinate geometry / circles

Find the midpoint of

PQ

, where

P(3,0)

and

Q(6,9)

Answer this when you sit the paper.

Question 1101

[1 marks]vectors

Points

P

Q

R

have position vectors

\mathbf{i}-2\mathbf{j}+\mathbf{k}

3\mathbf{i}-\mathbf{j}-\mathbf{k}

and

7\mathbf{i}+\mathbf{j}-5\mathbf{k}

respectively. Find the angle between

\overrightarrow{OQ}

and

\overrightarrow{PR}

, correct to 1 decimal place.

A $44.7°$
B $38.9°$
C $45.3°$
D $72.5°$

Question 1102

[1 marks]vectors

Points

P

and

Q

have position vectors

\mathbf{i}-2\mathbf{j}+\mathbf{k}

and

3\mathbf{i}-\mathbf{j}-\mathbf{k}

, and

R

has position vector

7\mathbf{i}+\mathbf{j}-5\mathbf{k}

. Find the value of

k

such that

\overrightarrow{PR}=k\overrightarrow{PQ}

, hence showing

P

Q

R

are collinear.

A $k=3$
B $k=\dfrac13$
C $k=2$
D $k=-3$

Question 1103

[1 marks]vectors

Point

P

has position vector

\mathbf{i}-2\mathbf{j}+\mathbf{k}

. Given that the vector

\lambda\mathbf{i}+3\mathbf{j}-4\mathbf{k}

is perpendicular to

\overrightarrow{OP}

, find the value of

\lambda

A $\lambda=-2$
B $\lambda=10$
C $\lambda=2$
D $\lambda=4$

Question 1104

[2 marks]vectors

Find vector

\overrightarrow{PR}=\overrightarrow{OR}-\overrightarrow{OP}

, for

P=(1,-2,1)

and

R=(7,1,-5)

Answer this when you sit the paper.

Question 1105

[2 marks]vectors

Find

|\overrightarrow{OQ}|

, correct to 3 significant figures, for

\overrightarrow{OQ}=3\mathbf{i}-\mathbf{j}-\mathbf{k}

Answer this when you sit the paper.

Question 1106

[2 marks]vectors

Find

|\overrightarrow{PR}|

, for

\overrightarrow{PR}=6\mathbf{i}+3\mathbf{j}-6\mathbf{k}

Answer this when you sit the paper.

Question 1201

[1 marks]sequences and series

The numbers

p

, 10,

q

are three consecutive terms of an arithmetic progression, and

p

, 6,

q

are three consecutive terms of a geometric progression. Which pair of equations correctly expresses these two conditions?

A $p-q=20,\ pq=36$
B $p+q=20,\ pq=6$
C $p+q=10,\ pq=36$
D $p+q=20,\ pq=36$

Question 1202

[1 marks]sequences and series

The numbers

p

, 10,

q

are consecutive terms of an arithmetic progression, and

p

, 6,

q

are consecutive terms of a geometric progression, so

p+q=20

and

pq=36

, giving

p^2-20p+36=0

. Find the values of

p

q

and the common ratio

r

for which the geometric progression converges.

A $p=18,\ q=2,\ r=\tfrac13$
B $p=2,\ q=18,\ r=3$
C $p=18,\ q=2,\ r=3$
D $p=2,\ q=18,\ r=\tfrac13$

Question 1203

[1 marks]sequences and series

A woman measures her child's height at birth and then at monthly intervals. The height increases by 5% each month. Find how many measurements (including the one at birth) she will have made by the time the child's height is first at least double its height at birth.

A $14$
B $15$
C $16$
D $17$

Question 1204

[2 marks]sequences and series

From

p+q=20

and

pq=36

, substituting

q=20-p

gives

p^2-20p+36=0

. State the discriminant

400-144

Answer this when you sit the paper.

Question 1205

[2 marks]sequences and series

Solve

p^2-20p+36=0

using

\sqrt{256}=16

. State the two roots for

p

, in ascending order.

Answer this when you sit the paper.

Question 1206

[2 marks]sequences and series

For the child's height increasing

5\%

per month, find

n

from

(1.05)^n=2

using logarithms, correct to 1 decimal place (before rounding up to the next whole measurement).

Answer this when you sit the paper.

Question 1301

[1 marks]complex numbers

Given that

a=2+i

and

b=1+3i

, find

ab

A $-1+7i$
B $-1-7i$
C $-7+i$
D $5+7i$

Question 1302

[1 marks]complex numbers

Given that

a=2+i

and

b=1+3i

, find

\dfrac{a}{b}

A $-\tfrac12+\tfrac12i$
B $\tfrac12+\tfrac12i$
C $\tfrac54-\tfrac54i$
D $\tfrac12-\tfrac12i$

Question 1303

[1 marks]complex numbers

Given that

a=2+i

and

b=1+3i

, so that

ab=-1+7i

, find the modulus and argument of

ab

Amodulus $5\sqrt2$ , argument $\approx81.9°$
Bmodulus $2\sqrt2$ , argument $\approx98.1°$
Cmodulus $5\sqrt2$ , argument $\approx-81.9°$
Dmodulus $5\sqrt2$ , argument $\approx98.1°$

Question 1304

[1 marks]complex numbers

Given that

a=2+i

and

b=1+3i

, so that

\dfrac{a}{b}=\tfrac12-\tfrac12i

, find the modulus and argument of

\dfrac{a}{b}

Amodulus $\tfrac12$ , argument $-45°$
Bmodulus $\tfrac{\sqrt2}{2}$ , argument $135°$
Cmodulus $\tfrac{\sqrt2}{2}$ , argument $-45°$
Dmodulus $\tfrac{\sqrt2}{2}$ , argument $45°$

Question 1305

[2 marks]complex numbers

Given

a=2+i

and

b=1+3i

, evaluate

i(1+3i)

in the form

c+di

(part of expanding

ab

Answer this when you sit the paper.

Question 1306

[2 marks]complex numbers

Rationalising

\dfrac{a}{b}=\dfrac{2+i}{1+3i}

by multiplying by the conjugate

1-3i

, find the resulting denominator

(1+3i)(1-3i)

Answer this when you sit the paper.

Question 1307

[2 marks]complex numbers

Given

a=2+i

b=1+3i

, so

ab=-1+7i

, in which quadrant of the Argand diagram does

ab

lie?

AThird quadrant
BFourth quadrant
CFirst quadrant
DSecond quadrant

Question 1401

[1 marks]Maclaurin series

Given that

f(x)=e^{3x}\sin x

f'(x)=e^{3x}\cos x+3e^{3x}\sin x

f''(x)=e^{3x}(8\sin x+6\cos x)

and

f'''(x)=e^{3x}(18\sin x+26\cos x)

, write down the Maclaurin series of

f(x)

up to and including the term in

x^3

A $x+3x^2+\dfrac{13}{3}x^3$
B $x+3x^2+\dfrac{26}{3}x^3$
C $x+3x^2-\dfrac{13}{3}x^3$
D $x+6x^2+26x^3$

Question 1402

[1 marks]Maclaurin series

Given that

f(x)=e^{3x}\sin x

, evaluate

f(0.5)

correct to 4 decimal places.

A $0.0391$
B $1.6446$
C $2.1486$
D $2.1490$

Question 1403

[1 marks]Maclaurin series

Given that

f(x)=e^{3x}\sin x

, with exact value

f(0.5)\approx2.1486

and Maclaurin approximation

f(x)\approx x+3x^2+\dfrac{13}{3}x^3

, state the absolute error in using the Maclaurin series to estimate

f(0.5)

A $0.3570$
B $0.3573$
C $0.5417$
D $1.7917$

Question 1404

[2 marks]Maclaurin series

Given

f''(x)=e^{3x}(8\sin x+6\cos x)

, evaluate

f''(0)

Answer this when you sit the paper.

Question 1405

[2 marks]Maclaurin series

Given

f'''(x)=e^{3x}(18\sin x+26\cos x)

, evaluate

f'''(0)

Answer this when you sit the paper.

Question 1406

[3 marks]Maclaurin series

Using the Maclaurin series

f(x)\approx x+3x^2+\frac{13}{3}x^3

, evaluate the series estimate at

x=0.5

(before comparing to the exact value).

Answer this when you sit the paper.

Question 1501

[1 marks]integration / area and volume

A curve has equation

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

. The point

A(0,2)

and point

B(1,4)

both lie on the curve, and the line

AB

has equation

y=2x+2

. Find the area of the finite region bounded by the curve and the line

AB

A $\dfrac12$
B $\dfrac14$
C $-\dfrac14$
D $\dfrac{13}{4}$

Question 1502

[1 marks]integration / area and volume

A curve has equation

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

, and the line

AB

from

A(0,2)

B(1,4)

has equation

y=2x+2

. Find the volume of the solid formed when the finite region bounded by the curve and the line

AB

is rotated completely about the

x

-axis, correct to 2 decimal places.

A $0.24$
B $1.61$
C $5.06$
D $34.38$

Question 1503

[2 marks]integration / area and volume

The curve

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

and line

AB

y=2x+2

intersect where

f(x)-(2x+2)=-x^3+x=0

. Factorise

-x^3+x

completely.

Answer this when you sit the paper.

Question 1504

[2 marks]integration / area and volume

State the

y

-coordinate of point

B

on the curve

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

, where

x=1

Answer this when you sit the paper.

Question 1505

[2 marks]integration / area and volume

Find the gradient of line

AB

, from

A(0,2)

B(1,4)

Answer this when you sit the paper.

Question 1506

[3 marks]integration / area and volume

Expanding

(-x^3+3x+2)^2 = x^6-6x^4-4x^3+9x^2+12x+4

, state the coefficient of

x^4

(part of the volume integrand).

Answer this when you sit the paper.

Question 1601

[1 marks]trigonometry

In quadrilateral

RPQS

PQ=8

cm,

RS=12

cm, angle

QPR=60°

, angle

QSR=90°

, diagonal

QR=13

cm, and angle

PRQ=\theta

. Find

\sin\theta

and

\cos\theta

A $\sin\theta=\tfrac{4}{13},\ \cos\theta=\tfrac{3\sqrt{17}}{13}$
B $\sin\theta=\tfrac{4\sqrt3}{13},\ \cos\theta=-\tfrac{11}{13}$
C $\sin\theta=\tfrac{13\sqrt3}{16},\ \cos\theta=\tfrac{11}{13}$
D $\sin\theta=\tfrac{4\sqrt3}{13},\ \cos\theta=\tfrac{11}{13}$

Question 1602

[1 marks]trigonometry

In quadrilateral

RPQS

with

PQ=8

cm,

RS=12

cm,

QR=13

cm, angle

QPR=60°

and angle

QSR=90°

, it is given that

\sin\theta=\tfrac{4\sqrt3}{13}

\cos\theta=\tfrac{11}{13}

(where

\theta=\angle PRQ

), and

\cos(\angle QRS)=\tfrac{12}{13}

\sin(\angle QRS)=\tfrac{5}{13}

. Find

\cos(\angle PRS)

, where

\angle PRS=\theta+\angle QRS

A $\dfrac{4(5\sqrt3-33)}{169}$
B $\dfrac{4(33-5\sqrt3)}{169}$
C $\dfrac{4(33+5\sqrt3)}{169}$
D $\dfrac{132-20\sqrt3}{13}$

Question 1603

[1 marks]trigonometry

The graph of

y=\sin x

is drawn for

0\le x\le3\pi

. Point

A

has coordinates

(\alpha,\sin\alpha)

, where

0<\alpha<\dfrac{\pi}{2}

. A horizontal line through

A

cuts the graph again at points

B

C

and

D

(in order of increasing

x

). Write down the coordinates of

B

C

and

D

A $B=(\pi-\alpha,\sin\alpha),\ C=(2\pi+\alpha,\sin\alpha),\ D=(3\pi-\alpha,\sin\alpha)$
B $B=(\pi+\alpha,\sin\alpha),\ C=(2\pi-\alpha,\sin\alpha),\ D=(3\pi+\alpha,\sin\alpha)$
C $B=(\pi-\alpha,\sin\alpha),\ C=(2\pi-\alpha,\sin\alpha),\ D=(3\pi-\alpha,\sin\alpha)$
D $B=(2\pi+\alpha,\sin\alpha),\ C=(\pi-\alpha,\sin\alpha),\ D=(3\pi-\alpha,\sin\alpha)$

Question 1604

[1 marks]trigonometry

Solve the equation

e^{\sin x}=2

for

0\le x\le3\pi

, giving your answers correct to 2 decimal places.

A $x\approx2.38,\ 7.05$
B $x\approx0.77,\ 2.38$
C $x\approx0.77,\ 2.38,\ 7.05,\ 8.66$
D $x\approx0.76,\ 2.38,\ 7.04,\ 8.66$

Question 1605

[2 marks]trigonometry

In right triangle

QRS

(right angle at

S

QR=13

cm and

RS=12

cm. Find

QS

Answer this when you sit the paper.

Question 1606

[1 marks]trigonometry

State

\sin(\angle QRS)

, given

QS=5

cm and

QR=13

cm.

Answer this when you sit the paper.

Question 1607

[1 marks]trigonometry

State

\cos(\angle QRS)

, given

RS=12

cm and

QR=13

cm.

Answer this when you sit the paper.

Question 1608

[2 marks]trigonometry

For

0\le x\le3\pi

, write down the solution of

\sin x>\sin\alpha

(in terms of

\alpha

) for the first interval only, between

A

and

B

Answer this when you sit the paper.

Question 1609

[2 marks]trigonometry

Using

\cos\theta=\frac{11}{13}

and

\cos(\angle QRS)=\frac{12}{13}

, evaluate

\cos\theta\cos(\angle QRS)

(the first term of

\cos(\angle PRS)

Answer this when you sit the paper.

Question 1610

[2 marks]trigonometry

Using

\sin\theta=\frac{4\sqrt3}{13}

and

\sin(\angle QRS)=\frac{5}{13}

, evaluate

\sin\theta\sin(\angle QRS)

(the second term of

\cos(\angle PRS)

Answer this when you sit the paper.

Pure Mathematics Paper 1 June 2014

Sit this paper online

The questions

Question 101

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Question 201

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Question 401

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Question 601

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Question 701

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Question 703

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Question 705

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Question 804

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Question 901

Question 902

Question 903

Question 904

Question 1001

Question 1002

Question 1003

Question 1004

Question 1005

Question 1006

Question 1101

Question 1102

Question 1103

Question 1104

Question 1105

Question 1106

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

Question 1206

Question 1301

Question 1302

Question 1303

Question 1304

Question 1305

Question 1306

Question 1307

Question 1401

Question 1402

Question 1403

Question 1404

Question 1405

Question 1406

Question 1501

Question 1502

Question 1503

Question 1504

Question 1505

Question 1506

Question 1601

Question 1602

Question 1603

Question 1604