PRE-LEAVING CERTIFICATE EXAMINATION, 2018 MARKING SCHEME
PRE-LEAVING CERTIFICATE EXAMINATION, 2018 MARKING SCHEME
MATHEMATICS
ORDINARY LEVEL
Page 1 of 24
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.
Page 2 of 24
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
Page 3 of 24
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
Page 4 of 24
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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