Higher Terminal June 07

8/6/2019 Higher Terminal June 07

1/28

GENERAL CERTIFICATE OF SECONDARY EDUCATION 2343AMATHEMATICS C (GRADUATED ASSESSMENT)HIGHER TERMINAL PAPER SECTION A Afternoon

MONDAY 4 JUNE 2007 Time: 1 hour

Candidates answer on the question paper.

Additional materials: Geometrical instruments

Tracing paper (optional)

This document consists of 15 printed pages and 1 blank page.

SP (KN) T30977/3 OCR 2007 [100/1142/0] OCR is an exempt Charity [Turn over

INSTRUCTIONS TO CANDIDATES

Write your name, Centre Number and Candidate Number in the boxes above. Answer all the questions. Use blue or black ink. Pencil may be used for graphs and diagrams only. Read each question carefully and make sure you know what you have to do before starting your answer. In many questions marks will be given for a correct method even if the answer is incorrect. Do not write in the bar code. Do not write outside the box bordering each page. WRITE YOUR ANSWER TO EACH QUESTION IN THE SPACE PROVIDED. ANSWERS WRITTEN

ELSEWHERE WILL NOT BE MARKED.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question.

The total number of marks for this Section is 50.

WARNING

You are not allowed to use acalculator in Section A of this paper.

For Examiners Use

Section A

Section B

Total

H*

C

U

P

/

T

3

0

9

7

7

*


2/28

2

OCR 2007

Formulae Sheet

length

Volume of prism = (area of cross-section) length

hl

r

r

cross-

section

=

13Volume of cone =

Curved surface area of cone

r2h

r2

rl

12

A

b a

c

C

B

43

Volume of sphere =

Surface area of sphere =

r34

In any triangleABC

a

sinA=

b

sinB=

c

sin C

a2 = b2 + c2 2bccosAArea of triangle = ab sin C

The Quadratic Equation

b (b2 4ac)2a

x =

Sine rule

Cosine rule

The solutions ofax2 + bx + c = 0,where a 0, are given by

PLEASE DO NOT WRITE ON THIS PAGE


3/28

3

[Turn over OCR 2007

1

0 1 3 4 5

1

1

2

3

4

5

2345

2

3

4

5

y

x

A

B

21

(a) Describe fully the single tranformation that maps triangle A onto triangle B.

............................................................................................................................................................

....................................................................................................................................................... [2]

(b) Reflect triangle A in the liney =x.

Label the image C. [2]

2 Work out.

334

+ 225

.......................................... [3]

4

3


4/28

4

OCR 2007

3 The times, tminutes, that 120 runners took to complete a marathon were recorded.

The results are summarised in this table.

Time

(tminutes)120 < t140 140 < t160 160 < t180 180 < t200 200 < t220 220 < t240

Frequency 4 36 42 29 7 2

(a) Draw a frequency polygon to represent this information.

120 140 160 180 200 220 240

Time (tminutes)

0

10

20

30

40

50

Frequency

[2]


5/28

5

[Turn over OCR 2007

(b) This box plot shows the distribution of the times for the men who completed the marathon.

MEN

120 140 160 180 200 220 240

Time (minutes)

Use this box plot to find

(i) the median time,

(b)(i) ................... minutes [1]

(ii) the interquartile range of the times.

(ii) ................... minutes [1]

(c) This box plot shows the distribution of the times for the womenwho completed the marathon.

WOMEN

120 140 160 180 200 220 240

Time (minutes)

Which group of runners, the men or the women, had the more consistent times?

Give a reason for your answer.

................................... because ..........................................................................................................

....................................................................................................................................................... [1]

5


6/28

6

OCR 2007

4 (a) Complete the table below fory =x2 2x 1.

x 2 1 0 1 2 3

y 7 1 2 1

[1]

(b) Draw the graph ofy =x2 2x 1.

4

3

2

1

2

1

4

3

6

7

5

0 1 2 3 x

y

12

8

[2]

(c) Use your graph to solve the equationx2 2x 1 = 0.

(c) ..................................... [2]

5


7/28

7

[Turn over OCR 2007

5 (a) Rearrange the formula v2 = u2 + 2as to make s the subject.

(a) ..................................... [2]

(b) Solve.

2x + 1

3=

x 35

(b) .................................... [4]

6


8/28

8

OCR 2007

6 (a) The exterior angle of a regular polygon is 45.

Work out the number of sides this polygon has.

(a) ..................................... [2]

(b)

QS

110

40

R

T

x

y

O

P

Not to scale

P, Q and R are points on a circle, centre O.

ST is the tangent to the circle at R.

Angle PQR = 110 and angle SRQ = 40.

(i) Work out anglex.

Give a reason for your answer.

x = ................... because ...........................................................................................................

............................................................................................................................................... [2]

(ii) Work out angley.

(b)(ii) ............................ [3]7


9/28

9

[Turn over OCR 2007

7 Solve, algebraically, these simultaneous equations.

2x + 3y = 7

5x 2y = 27

x= .........................................

y = .................................... [4]

4


10/28

10

OCR 2007

8 The histogram shows the distribution of the prices of houses advertised in a local newspaper.

00

10

20

30

40

50

60

2 31 4 5 6 7 8 9 10

Frequencydensity(numb

erofhousesper100000)

Price (100000)

Use the histogram to decide whether these statements are true or false, or whether there is not enoughinformation to decide.

(a) The cheapest house is priced at 100000.

Tick the correct box.

True FalseNot enoughinformation

Explain your answer.

............................................................................................................................................................

....................................................................................................................................................... [1]


11/28

11

[Turn over OCR 2007

(b) The number of houses represented in this histogram is 200.




............................................................................................................................................................

....................................................................................................................................................... [1]

(c) One quarter of the houses are priced at 400 000 or more.




............................................................................................................................................................

....................................................................................................................................................... [1]

(d) The median price of the houses is in the range 300 000 to 400 000.




............................................................................................................................................................

....................................................................................................................................................... [1]

4


12/28

12

OCR 2007

9 Solve, by factorising.

8x2 + 10x 3 = 0

.......................................... [4]

4


13/28

13

[Turn over OCR 2007

10 There are ten teams in a local football league.

The colour of their kit is shown in the table below.

Colour Number of teams

Red 4

Blue 2

Yellow 1

Green 3

For cup matches, teams from this league are chosen at random.

(a) Work out the probability that the first two teams chosen both wear red kit.

(a) ..................................... [2]

(b) Work out the probability that the first two teams chosen

both wear the same colour kit.

(b) .................................... [3]

5


14/28

14

OCR 2007

11 Sketch the graphy = 2 cos3x for values ofx from 0 to 360.

3

2

1

0

1

2

60 120 180 240 300 360 x

y

3

[3]

3


15/28

BLANK PAGE


15

OCR 2007


16/28

16

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every

reasonable effort has been made by the publisher (OCR) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the

publisher will be pleased to make amends at the earliest possible opportunity.

OCR is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES),

which is itself a department of the University of Cambridge.


OCR 2007


17/28

GENERAL CERTIFICATE OF SECONDARY EDUCATION 2343BMATHEMATICS C (GRADUATED ASSESSMENT)HIGHER TERMINAL PAPER SECTION B Afternoon

MONDAY 4 JUNE 2007 Time: 1 hour

Candidates answer on the question paper.Additional materials: Geometrical instruments

Scientific or graphical calculatorTracing paper (optional)

This document consists of 12 printed pages.

SP (KN) T30978/3 OCR 2007 [100/1142/0] OCR is an exempt Charity [Turn over

INSTRUCTIONS TO CANDIDATES

Write your name, Centre Number and Candidate Number in the boxes above. Answer all the questions. Use blue or black ink. Pencil may be used for graphs and diagrams only. Read each question carefully and make sure you know what you have to do before starting your answer. In many questions marks will be given for a correct method even if the answer is incorrect. Do not write in the bar code. Do not write outside the box bordering each page. WRITE YOUR ANSWER TO EACH QUESTION IN THE SPACE PROVIDED. ANSWERS WRITTEN

ELSEWHERE WILL NOT BE MARKED.

INFORMATION FOR CANDIDATES

You are expected to use a calculator in Section B of this paper.

The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this Section is 50. Section B starts with question 12. Use the button on your calculator or take to be 3142 unless the question says otherwise.

For Examiners Use

Section B

H*

C

U

P

/

T

3

0

9

7

8

*


18/28

2

OCR 2007

Formulae Sheet

length

Volume of prism = (area of cross-section) length

hl

r

r

cross-

section

=

13Volume of cone =

Curved surface area of cone

r2h

r2

rl

12

A

b a

c

C

B

43

Volume of sphere =

Surface area of sphere =

r34

In any triangleABC

a

sinA=

b

sinB=

c

sin C

a2 = b2 + c2 2bccosAArea of triangle = ab sin C

The Quadratic Equation

b (b2 4ac)2a

x =

Sine rule

Cosine rule

The solutions ofax2 + bx + c = 0,where a 0, are given by



19/28

3

[Turn over OCR 2007

12 This computer costs 840.

840

(a) Brian and Majid bought one of these computers.

They shared the 840 cost in the ratio 7 : 5.

How much did Brian pay?

(a) ................................... [2]

(b) In a sale the cost of the computer was reduced from840 to 777.

Calculate the percentage reduction.

(b) ................................% [3]

5


20/28

4

OCR 2007

13 All the lengths in this diagram are in metres.

x

x

x + 2

The diagram shows a cuboid.

(a) The volume of the cuboid is 13 m3.

Show thatx3 + 2x2 13 = 0.

............................................................................................................................................................

............................................................................................................................................................

....................................................................................................................................................... [2]

(b) The equationx3 + 2x2 13 = 0 has a solution between 1 and 2.

Use trial and improvement to find this solution correct to 1 decimal place.

You must show all your trials and their outcomes.

(b) .................................... [3]5


21/28

5

[Turn over OCR 2007

14 List all the integers, n, such that 3 < 3n 21.

.......................................... [3]

15 Decide if each statement in the table is true or false when n is a positive integer.

Give an example to justify each decision.

Statement True or false Example

1n


22/28

6

OCR 2007

16

PuddingRice

20%more

SPECIALOFFER

(a) A special offer can is advertised as 20% more rice pudding than the standard size.

The special offer can contains 494g of rice pudding.

Work out how much rice pudding the standard size can contained.

(a) .................................. g [3]

(b) The can is a cylinder.

The radius of the can is 4 cm and the height is 10 cm.

There is a label completely covering the curved surface of the can.

Work out the area of the label.

(b) .............................cm2

[3]

4cm

10cm

6


23/28

7

[Turn over OCR 2007

17

365

255m

A B

Not to scale

C

In the diagram,

AC = 255 m, angle ABC = 90 and angle BAC = 365.

Calculate BC.

Give your answer to an appropriate degree of accuracy.

......................................m [4]

4


24/28

8

OCR 2007

18 In the 2001 census the population of England was recorded as 49 000 000

and the population of Wales was recorded as 2 900 000.

(a) Work out the total population of England and Wales.Give your answer in standard form.

(a) ..................................... [1]

(b) In 2001 the population of England was 49 000 000 correct to 2 significant figures.

The area of England is 130 000 km2 correct to 2 significant figures.

Calculate the lower and upper bounds of the population density (people per km2).

Show your working clearly.

(b) lower bound ..................... people per km2

upper bound ..................... people per km2 [4]


25/28

9

[Turn over OCR 2007

(c) The total population of England and Wales was recorded in a census

every 10 years (a decade) from 1841 to 1901.

For these seven censuses the population, P million, fitted the formula

P = 159 1127t

where tis the number of decades after 1841.

(i) Use the formula to find the population of England and Wales

in 1841, when t= 0.

(c)(i) .....................million [1]

(ii) After 1901 the values given by the formula are generally too high.

Calculate the population given by the formula for the year 2001.

(ii) .....................million [3]

9


26/28

10

OCR 2007

19 (a) ABC is an isosceles triangle, where AB = AC.

D, E and F are the midpoints of AC, AB and CB respectively.

A

FBC

D E

Not to scale

Prove that the two shaded triangles CDF and BEF are congruent.

Give a reason for each step of your proof.

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

....................................................................................................................................................... [3]

(b) In triangle PQR, PR = 8 cm, RQ = 14 cm and angle PRQ = 40.

R Q

PNot to scale

40

8cm

14cm

Calculate the length PQ.

(b) .............................. cm [3]

6


27/28

11

OCR 2007

20 The graphs ofy = 6x2 2x 5 andy = 2x 1 intersect at points A and B.

(a) Show that thex-coordinates of A and B satisfy the equation 3x2 2x 2 = 0.

............................................................................................................................................................

............................................................................................................................................................

............................................................................................................................................................

....................................................................................................................................................... [2]

(b) Solve the equation 3x2 2x 2 = 0 to find the coordinates of A and B. Give the coordinates correct to 2 significant figures.

(b) (............... , ..............)

and (............... , ...............) [4]

TURN OVER FOR QUESTION 21

6


28/28

12

21 These two storage boxes are mathematically similar.

The volume of the large box is double the volume of the small box.

(a) Explain why the height of the large box is not double the height of the small box.

............................................................................................................................................................

............................................................................................................................................................

....................................................................................................................................................... [1]

(b) The height of the large box is 32 cm.

Calculate the height of the small box.

(b) .............................. cm [2]

3

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every

reasonable effort has been made by the publisher (OCR) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the

publisher will be pleased to make amends at the earliest possible opportunity.

OCR is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES),

which is itself a department of the University of Cambridge

Documents

Higher Terminal June 07