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PRE-JUNIOR CERTIFICATE EXAMINATION, 2016

MARKING SCHEME

MATHEMATICS

ORDINARY LEVEL

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ORDINARY LEVEL

Structure of the marking scheme Candidate responses are marked according to different scales, depending on the types of response anticipated. Scales labelled A divide candidate responses into two categories (correct and incorrect). Scales labelled B divide responses into three categories (correct, partially correct, and incorrect), and so on. The scales and the marks that they generate are summarised in this table:

Scale label A B C

No of categories 2 3 4

5 mark scale 0, 5 0, 2, 5 0, 2, 3, 5

10 mark scale 0, 10 0, 5, 10 0, 4, 8, 10

15 mark scale 0, 7, 15 0, 4, 10, 15

A general descriptor of each point on each scale is given below. More specific directions in relation to interpreting the scales in the context of each question are given in the scheme, where necessary. Marking scales – level descriptors A-scales (two categories) ■ incorrect response (no credit) ■ correct response (full credit) B-scales (three categories) ■ response of no substantial merit (no credit) ■ partially correct response (partial credit) ■ correct response (full credit) C-scales (four categories) ■ response of no substantial merit (no credit) ■ response with some merit (low partial credit) ■ almost correct response (high partial credit) ■ correct response (full credit) In certain cases, typically involving incorrect rounding or omission of units, a mark that is one mark below the full-credit mark may also be awarded. Such cases are flagged with an asterisk. Thus, for example, scale 10C* indicates that 9 marks may be awarded.

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Summary of mark allocations and scales to be applied Paper 1

Question 1 (25) Question 2 (25) Question 3 (20) (a) (i) 5A (a) (i) 5C (a) 5B (ii) 5A (ii) 5B (b) 5B (iii) 5A (b) 5B (c) 5A (b) (i) 5A (c) 5B (d) 5B (ii) 5A (d) 5B

Question 4 (20) Question 5 (20) Question 6 (25) (a) 5B (a) 5A (a) 5B (b) 5B (b) 5A (b) (i) 5A (c) 5B (c) 5B (ii) 5B (d) 5B (d) 5B (iii) 5B (iv) 5B

Question 7 (25) Question 8 (15) Question 9 (20) (a) 5B (a) 5B (a) 10C (b) 5B (b) 10C (b) 5B (c) 5C (c) 5B (d) 5B (e) 5B

Question 10 (15) Question 11 (20) Question 12 (30) (a) 5B (a) 5B (a) 5A (b) 5B (b) 5B (b) 5A (c) 5C (c) 10C (c) 5A (d) 5A (e) 5B (f) 5B

Question 13 (20) Question 14 (20) (a) 10C (a) 10C (b) 5B (b) 5A (c) 5B (c) 5B

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PAPER 1

Question 1 (a) (i) Any even number Scale 5A

(ii) 87,532 Scale 5A (iii) 35,782 or variations Scale 5A

(b) (i) 825 −× Scale 5A (ii) 825 ×+ Scale 5A Question 2 (a) (i)

Item Actual Cost Estimate

(nearest 100 euro)

Flights 1,038 1000

Accommodation 1,251 1300

Car Hire 565 600

Food 820 800

Others 542 500

Total 4,216 4200

Scale 5C High partial credit: All numbers rounded correctly but fails to complete totals Low partial credit: At least two numbers rounded correctly

(ii) 1642004216 =− Scale 5B Partial credit: Meaningful attempt (b) 3109402 ×⋅ Scale 5B Partial credit: Meaningful attempt

(c) minutes 12 hours 4or hours 2.4700

2940 = Scale 5B

Partial credit: Writes down speed, distance, time formula and stops (d) 027521162 ⋅=× . and Alan should buy the game in Spain Scale 5B Partial credit: VAT correct but fails to add on and make conclusion

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Question 3 (a) 0504000 ⋅× Scale 5B 200€=

Partial credit: Some attempt to find percentage (b) 410200 ⋅× Scale 5B 82€=

Partial credit: Some attempt to find percentage (c)

4118€

822004000

=−+

Scale 5A

Accept the answer based on answers in (a) and (b) (d) 42.84902054118 −⋅+ Scale 5B 48.4239€=

Partial credit: Interest worked out correctly Question 4 (a) )2024(650 ×+ Scale 5B 1130€=

Partial credit: Meaningful attempt (b) )4024(250 ×+ Scale 5B 1210€=

Partial credit: Meaningful attempt (c) )4524( × Scale 5B 1080€=

Partial credit: Meaningful attempt (d) Any correct package Scale 5B Partial credit: Any package that references 24 months and is below

the smallest total above

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Question 5 (a) 54 Scale 5A (b) 53 Scale 5A (c) 52 Scale 5B

Partial credit: Denominator correct or numerical answer given (d) 32 )(2 is bigger Scale 5B

Partial credit: Correct evaluation of 32 )(2 or 32 22 × and stops No marks for correct choice without reason

Question 6 (a) No use of a common denominator Scale 5B Partial credit: References denominator (b) (i) Correct area shaded Scale 5A

(ii) Correct area shaded Scale 5B

Partial credit: 15

10

3

2 = and stops or 3

2written as some other equivalent fraction

(iii) Correct area shaded Scale 5B

Partial credit: 15

6

5

2 = and stops or 5

2written as some other equivalent fraction

(iv) 3

2,

15

7,

5

2 Order correct. Not necessary to show work Scale 5B

Accept answers based on incorrect equivalent fractions in parts above Partial credit: Writes answers correctly in decimal form, but order incorrect

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Question 7 (a) { }19 17, 13, 11, 7, 5, 3, 2, A = Scale 5B Partial credit: 5 elements correct (b) { }20 10, 5, 4, 2, 1, B = Scale 5B Partial credit: 4 elements correct (c) Venn Diagram Scale 5C U A B 3 1 2 7 4 5 11 10 13 17 20 19 16 High partial credit: 9 elements correct Low partial credit: 6 elements correct (d) { }5 2, BA =∩ Scale 5B Partial credit: One correct element (e) Location correct. Reason: 16 is not a prime and not a factor of 20 Scale 5B Partial credit: Location correct but reason not stated or not clear

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Question 8 (a) Next two patterns correct Scale 5B

Partial credit: Only one pattern correct (b)

Stage Perimeter First Difference Second Difference

1 6 0

2 10 4 0

3 14 4 0

4 18 4 0

5 22 4 0

Second differences not necessary for full marks Scale 10C

Pattern is linear

High partial credit: Table correct and some correct work on differences but does not identify that relationship is linear

Low partial credit: At least 2 more perimeters identified correctly or perimeters incorrect but difference calculated correctly

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Question 9 (a)

Instruction First Number Second Number Third Number

Number 9 10 11

Substract 3 form your answer

9 – 3 10 - 3 11 - 3

Multiply your answer by 2

2(6) 2(7) 2(8)

Outcome 12 14 16

Scale 10C High partial credit: Correct method but error in calculation Low partial credit: One horizontal line correct

(b) 63326 =+=÷ Scale 5B Partial credit: One of the two operations correctly reversed (c) ( )32 −p Scale 5B Partial credit: One of the two operations correct Question 10 (a) 204 −x 102 −x Scale 5B

)5(4 −= x )5(2 −= x

Partial credit: One correct factorisation

(b) 2)5(2

)5(4 =−−

xx

Scale 5B

Partial credit: Attempts to divide (c) spsdrprd 22 −+− Scale 5C

))(2(

)(2)(

pdsrpdspdr

−+=−+−=

High partial credit: )(2)(22 pdspdrspsdrprd −+−=−+− and stops

Low partial credit: )( pdr − correct and subsequent errors

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Question 11 (a) 24167 +=− xx Scale 5B

6

183

==

xx

Partial credit: Any single correct manipulation of the equation

(b) Subs values in and finds that 5−=x is the correct solution Scale 5B

correctFiona0101525

010)5(3)5( 2

=−−=−−+−

Partial credit: Any solution subbed into the equation and subsequent calculation

errors (c) 112 =+ yx Scale 10C

52

1126

6

122

12

⋅==+

===−

yy

xxyx

Accept answers based on trial and error

High partial credit: Solves for x (by algebra or trial and error) and stops or subsequent errors

Low partial credit: Attempts to cancel either variable

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Question 12 (a) D and E Scale 5A (b) 2 minutes Scale 5A (c) (i) 2 km Scale 5A

(ii) 2 km Scale 5A (d) 5m4000 ÷ Scale 5B

hourper km 84

minuteper m800

==

Partial credit: Speed, distance time formula stated correctly

(e) A to B 2 km in 4 mins Scale 5B

C to D 2 km in 5 mins E to F 4 km in 5 mins fastest or calculates slopes

Partial credit: Tries to use speed, distance time formula or tries to use slope formula

Question 13 (a) Axis calibrated correctly and points plotted correctly x-axis can be in hours 0,3,6,9…. or in nights 0,1,2,3……. Scale 10C

High partial credit: Axis labelled and calibrated correctly and two points correct Low partial credit: Axis labelled and calibrated correctly (b) cm 40)5)(8(80 =− Scale 5B Partial credit: Divides 24 by 8 and stops or multiplies 24 by 5 and stops (c) days 16580 =÷ Scale 5B Partial credit: Some attempt at division e.g. 3.....80 ÷

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Question 14 (a) Table and graph Scale 10C

x -2 -1 0 1 2 3 4

y 15 9 5 3 3 5 9

High partial credit: Table correct and two points plotted correctly Low partial credit: Table correct only

Errors in table and graph ‘correct’ (b) 5 m Scale 5A

(c) 1.30 p.m. Scale 5B

Partial credit: Writes down the height of the lowest tide