Mathematics - .NET Framework

L.17/20

Pre-Leaving Certificate Examination, 2016

Mathematics

Higher Level

Marking Scheme

Paper 1 Paper 2

Pg. 2 Pg. 36

Page 1 of 68

DEB

exams

Pre-Leaving Certificate Examination, 2016

Mathematics

Higher Level ? Paper 1 Marking Scheme (300 marks)

Structure of the Marking Scheme

Students' responses are marked according to different scales, depending on the types of response anticipated. Scales labelled A divide students' responses into two categories (correct and incorrect).

Scales labelled B divide responses into three categories (correct, partially correct, and incorrect), and so on. These scales and the marks that they generate are summarised in the following table:

Scale label

A

No. of categories

2

5 mark scale

10 mark scale

15 mark scale

B 3 0, 2, 5

C 4 0, 2, 4, 5 0, 4, 7, 10

D 5

0, 4, 6, 8, 10 0, 6, 10, 13, 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)

DEB 2014 LC-H Scale label

No of categories

5 mark scale 10 mark scale 15 mark scale 20 mark scale

A

B

C

D

2

3

4

5

0, 2, 5 0, 2, , 5 0, 2, 3,

0, 5, 10 0, 3, 7, 10 0, 2, 5,

0, 7, 15 0, 5, 10,15 0, 4, 7, 1

D-scales (five categories)

response of no substantial merit (no credit) response with some merit (low partial credit) response about half-right (middle partial credit) almost correct response (high partial credit) correct response (full credit)

In certain cases, typically involving incorrect rounding, omission of units, a misreading that does not oversimplify the work or an arithmetical error that does not oversimplify the work, 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.

The * for units to be applied only if the student's answer is fully correct. The * to be applied once only within each section (a), (b), (c), etc. of all questions. The * penalty is not applied to currency solutions.

Unless otherwise specified, accept correct answer with or without work shown.

Accept students' work in one part of a question for use in subsequent parts of the question, unless this oversimplifies the work involved.

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Summary of Marks ? 2016 LC Maths (Higher Level, Paper 1)

Q.1 (a) (i) 10C* (0, 4, 7, 10)

(ii) 5C (0, 2, 4, 5)

(b)

10D (0, 4, 6, 8, 10)

25

Q.2 (a)

5C (0, 2, 4, 5)

(b) (i) 10C (0, 4, 7, 10)

(ii) 5B (0, 2, 5)

(c)

5B (0, 2, 5)

25

Q.3 (a) (b)

10D (0, 4, 6, 8, 10) (i) 5C (0, 2, 4, 5) (ii) 5C (0, 2, 4, 5) (iii) 5C (0, 2, 4, 5)

25

Q.4 (a) (b)

(i) 5C (0, 2, 4, 5) (ii) 5C (0, 2, 4, 5) (iii) 5C (0, 2, 4, 5)

10D (0, 4, 6, 8, 10)

25

Q.5 (a) (b) (c) (d)

5B (0, 2, 5) 10C (0, 4, 7, 10) 5C (0, 2, 4, 5) 5C (0, 2, 4, 5)

25

Q.6 (a)

5C (0, 2, 4, 5)

(b)

10D (0, 4, 6, 8, 10)

(c) (i) (ii)

10D (0, 4, 6, 8, 10)

25

Q.7 (a) (b)

(i) 5B* (0, 2, 5) (ii) 10C (0, 4, 7, 10) (iii) 5B (0, 2, 5)

(iv) 10D* (0, 4, 6, 8, 10) (i) 15D (0, 6, 10, 13, 15) (ii) 5B (0, 2, 5)

50

Q.8 (a) (b)

(c)

5B (0, 2, 5) (i) 5B* (0, 2, 5) (ii) 10C* (0, 4, 7, 10) (i) 10D* (0, 4, 6, 8, 10) (ii) 10C* (0, 4, 7, 10)

(iii) 5C (0, 2, 4, 5) (iv) 5B (0, 2, 5)

50

Q.9 (a)

(b) (c)

(i) 5B (0, 2, 5) (ii) 5B* (0, 2, 5) (iii) 5B (0, 2, 5) (iv) 10C (0, 4, 7, 10) (i) 10D (0, 4, 6, 8, 10) (ii) 5C (0, 2, 4, 5)

10D* (0, 4, 6, 8, 10)

50

Assumptions about these marking schemes on the basis of past SEC marking schemes should be avoided. While the underlying assessment principles remain the same, the exact details of the marking of a particular type of question may vary from a similar question asked by the SEC in previous years in accordance with the contribution of that question to the overall examination in the current year. In setting these marking schemes, we have strived to determine how best to ensure the fair and accurate assessment of students' work and to ensure consistency in the standard of assessment from year to year. Therefore, aspects of the structure, detail and application of the marking schemes for these examinations are subject to change from past SEC marking schemes and from one year to the next without notice.

General Instructions

There are two sections in this examination paper.

Section A Section B

Concepts and Skills Contexts and Applications

150 marks 150 marks

Answer all questions.

Marks will be lost if all necessary work is not clearly shown.

Answers should include the appropriate units of measurement, where relevant.

Answers should be given in simplest form, where relevant.

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6 questions 3 questions

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DEB

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Pre-Leaving Certificate Examination, 2016

Mathematics

Higher Level ? Paper 1 Marking Scheme (300 marks)

Section A

Concepts and Skills

Answer all six questions from this section.

Question 1

1(a) Fifty stones are placed in a straight line on level horizontal ground, at equal intervals of 5 m. A bucket is located on the same line 10 m away from the first stone. Tom, who can lift only one stone at a time, wishes to put all of them in the bucket. He starts from the bucket.

150 marks

(25 marks)

Bucket

10 m

5m 5m

(i) Calculate the total distance, in km, that Tom travels to put all the stones in the bucket.

(10C*)

Stone:

1

Distance: 20

Sn

a d For n = 50 S50

2

3 ... 50

30

40 ...

=

n 2

[2a

+

(n

?

1)d

]

= 20

= 10

=

50 2

[2(20)

+

49(10)]

= 25[40 + 490]

= 25[530]

= 13,250 m

= 13?25 km

... arithmetic series

Scale 10C* (0, 4, 7, 10)

Low partial credit: (4 marks) High partial credit: (7 marks)

? Any relevant first step, e.g. writes down `example of arithmetic series' or relevant correct formula for Tn or Sn of arithmetic series.

? Finds a = 20 and d = 10. ? Some correct substitution into relevant

formula for S50.

? Substitutes correctly into formula for S50, but fails to evaluate or evaluates incorrectly.

? Finds S50, but fails to give final answer in the desired form (km).

* Deduct 1 mark off correct answer only for the omission of or incorrect use of units (`km') - apply only once in each section (a), (b), (c), etc. of question.

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Question 1 (cont'd.)

1(a) (cont'd.)

(ii) More stones are added and placed at the same intervals along the line. Find the number of extra stones added if the total distance that Tom travels to put all of the stones in the bucket is 27 km.

More stones added and placed at the same interval

Sn

= 27 km

= 27,000 m

Sn

a d

=

n [2a + (n ? 1)d ]

2

= 20

= 10

For n stones in total

Sn

=

n 2

[2(20)

+

(n

?

1)10]

= 27,000

n 2

[40

+

10n

?

10]

=

27,000

n [10n + 30] 2

= 27,000

5n2 + 15n

= 27,000

n2 + 3n ? 5,400 =

0

(n ? 72)(n + 75) =

0

n ? 72

=

0

n + 75

=

n

= 72

n

=

Number of extra stones added = 72 ? 50 = 22

(5C)

0 ?75 (not possible)

Scale 5C (0, 2, 4, 5)

Low partial credit: (2 marks) High partial credit: (4 marks)

? Any relevant first step, e.g. Sn formula correctly substituted (in terms of n).

? Substitutes correctly into formula for Sn and finds equation in terms in n.

? Solves correctly to find value of n, but fails to finish or finishes incorrectly.

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