PRE-LEAVING CERTIFICATE EXAMINATION, 2018 MARKING SCHEME

PRE-LEAVING CERTIFICATE EXAMINATION, 2018 MARKING SCHEME

MATHEMATICS

ORDINARY LEVEL

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Scale label No of categories

5 mark scale 10 mark scale 15 mark scale 20 mark scale 25 mark scale

A 2 0, 5 0, 10 0, 15 0, 20 0, 25

OVERVIEW OF MARKING SCHEME

B

C

D

3

4

5

0, 2, 5 0, 5, 10

0, 2, 4, 5 0, 3, 7, 10

0, 2, 5, 8, 10

0, 7, 15 0, 10, 20

0, 5, 10, 15 0, 7, 13, 20

0, 4, 7, 11, 15 0, 5, 10, 15, 20

0, 12, 25 0, 8, 17, 25 0, 6, 12, 19, 25

E 6

0, 5, 10, 15, 20, 25

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 body of 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)

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)

E-scales (six categories) response of no substantial merit (no credit) response with some merit (low partial credit) response almost half-right (lower middle partial credit) response more than half-right (upper middle partial credit) almost correct response (high partial credit) correct response (full credit)

Marking categories for all questions are shown throughout the solutions. In certain cases, typically involving 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 TO BE APPLIED

Section A

Question 1

(a)

10C*

(b) 10C

(c)

5C

Question 2 (a) (i) 5B

(ii) 5C (iii) 5C (b) 10C

Question 3

(a)

15C

(b) 10C

Question 4

(a)

5B

(b) 5B

(c)

5B

(d) 10D

Question 5 (a) (i) 5B

(ii) 10C (b) 10C

Question 6

(a)

10C

(b) (i) 5B

(ii) 5B*

(iii) 5B*

Section B

Question 7

(a)

10C

(b) 10C

(c)

10C

(d) 10B

(e) 10C

(f)

10C

Question 8 (a) (i) 10B*

(ii) 10C (iii) 10C* (iv) 10C* (b) 10C*

Question 9

(a)

5A

(b) 10C

(c)

5B

(d) 10C

(e) 10C

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PAPER 1

Q1 Model Solution ? 25 Marks (a) 2% ? 10036 = 200 72

4% ? 5980 = 239 20 7% ? 38984 = 2728 88

= 3168 80

(b) 28500 ? 20% = 5700 26500 ? 42% = 11130 11130 + 5700 - 2500 = 14330

(c) 14330 + 1930 + 3168 80 = 19428 80 55000 - 19428 80 = 35571 20 *Accept work based on previous answers

Marking Notes

Scale 10C* (0, 3, 7, 10)

High Partial Credit ? 3 percentages found correctly but not added

together ? 2 percentages found correctly, error in third

but continues to end

Low Partial Credit ? Calculates one value correctly

Scale 10C (0, 3, 7, 10)

High Partial Credit ? Gross tax correct but neglects tax credit ? 1 error in calculating gross tax and continues

to end correctly

Low Partial Credit ? Calculates 20% correctly and stops

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

High Partial Credit ? Finds total deductions correctly ? Error in total deductions but subtracts from

gross income correctly

Low Partial Credit ? Adds some deductions ? Subtracts some deductions from gross income

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Q2 Model Solution ? 25 Marks

(a) = 3 + 4 (i)

(a)

= (3 + 4 )

(ii)

= -4 + 3

*Accept work based on previous answers

(a) Rotation 90? anticlockwise (iii)

(b) (-2 + 5 )(2 - ) (2 + )(2 - )

-4 + 2 + 10 - 5 4+1

1 5

+

12 5

Marking Notes

Scale 5B (0, 2, 5)

Partial Credit ? Real or imaginary correct ? Writes 4 + 3i

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

High Partial Credit ? Multiplies correctly but plots incorrectly ? Multiplies incorrectly but plots resulting

complex number correctly

Low Partial Credit ? Any work of merit

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

High Partial Credit ? States rotation ? Connects to origin and indicates 90 degrees on

diagram

Low Partial Credit ? Connects to origin and stops

Scale 10C (0, 3, 7, 10)

High Partial Credit ? Answer not in correct form ? Error in multiplication but continues to end

Low Partial Credit ? Writes correct conjugate

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