1MA1 Practice papers Set 6: Paper 1H (Regular) mark scheme – Version 1.0
Question	Working	Answer	Mark	Notes
1	2	M1 for correct intersecting arcs A1 for correct angle bisector
2	P: T: B = 1: 3: 6 54÷10 × 6 OR e.g. T = 3P B = 2T So, B = 2(3P) = 6P P+T+B=P+3P+6P=10P P = 54÷10 = £5.40 B = 6 × £5.40	32.40	3	M1 for 1 : 3 : 6 or any three numbers in the ratio 1:3:6 in any order M1 for 54 ÷ (1 + 3 + 6) × 6 A1 for 32.4(0) Alternative: M1 for 1: 3: 6 oe or P + 3P + 6P (=10P) oe, e.g. T/3 + T + 2T (=10T/3) or e.g. B/6 + B/2 + B (=10B/6) or 5.4(0) or 16.2(0) seen M1 for 54 ÷ 10 × 6 or [54 ] × 2 or 54 oe A1 for 32.4(0) OR M1 for a partial decomposition of £54 in ratio 1:3:6, e.g. (£)5 +( £)15 + (£)30 (=(£)50) M1 for a decomposition of the remaining amount in ratio 1:3:6, e.g. 40(p) + 120(p) + 240 (=400(p)) A1 for 32.4(0)
3	x –2 –1 0 1 2 3 4 5 y 6 5 4 3 2 1 0 –1	graph	3	(Table of values) M1 for at least 2 correct attempts to find points by substituting values of x M1 ft for plotting at least 2 of their points (any points plotted from their table must be correct) A1 for correct line between x = –2 and x = 5 or (No table of values) M2 for at least 2 correct points (and no incorrect points) plotted or line segment of x + y = 4 drawn (ignore any additional incorrect segments) (M1 for at least 3 correct points plotted with no more than 2 incorrect) A1 for correct line between x = –2 and x = 5 or (Use of y = mx + c) M2 for at least 2 correct points (and no incorrect points) plotted (M1 for y = 4 – x or line drawn with gradient of -1 or line drawn with a y intercept of 4 and a negative gradient) A1 for correct line between x = –2 and x = 5
4	Proof	4	M1 for setting up a correct equation in x, eg. 3x – 2 = x + 1 M1 (dep) for a fully correct method to solve their equation or for x = 1.5 M1 (dep) for ("1.5" + 1) × 4 or (3 × "1.5" – 2) × 4 or (3 × "1.5" – 2) × 2 + ("1.5"+ 1) × 2 C1 (dep on M3) for completing the proof resulting in a perimeter of 10 OR M1 for setting up a correct equation in x, eg. 2(3x – 2) + 2(x + 1) = 10 M1 (dep) for a fully correct method to solve their equation or for x = 1.5 M1 (dep) for "1.5" + 1 and 3 × "1.5" – 2 C1 (dep on M3) for completing the proof resulting in a justification that the shape is a square
5	9	4	M1 for method to find area of one rectangle, eg 15 × 8 (=120) or 15 × 11 (=165) M1 (dep) for subtracting from/by given area, eg (138 – “120”) (=18) or “165” – 138 (=27) M1 for final step from complete method shown, eg 15 − "18"÷ 3 or “27” ÷ 3 A1 cao OR M1 for a correct expression for the area of one rectangle, eg (8 + 3) × (15 − x) or 8 × x M1 (dep) for a correct equation eg (8 + 3) × (15 − x) + 8 × x = 138 M1 for correct method to isolate x, eg 3x = 27 A1 cao
6	= =320 seconds	320	3	M1 for 40 × 1000 or 125 ÷ 1000 or 40000 or 0.125 M1 for or ’ A1 cao OR M1 for 1000 ÷ 125 M1 for ‘8’ × 40 A1 cao
7	(a)	+	M1 for both fractions expressed with a suitable common denominator (multiple of 20) and at least one of the two fractions correct A1 for oe or M1 for 0.4 + 0.25 A1 for 0.65 or M1 for table structure, all cells correct A1 for 13/20 oe
(b)	×	M1 for a correct method to convert to improper fractions or M1 (dep) for A1 for or or 7.5 (SC: B2 for 7.5)
8	(a)	2	M1 for A1 for oe
(b)	60 ÷ 5 = 12 12 × 2 = Alternative: Total sum = 60 2 = 120 Lillian = of 120 = 120 2 ÷ 10	24	3	M1 for 60 ÷ 5 M1 for “12” × 2 A1 for 24 cao Alternative: M1 for 60 2 = 120 seen M1 for 120 2 ÷ 10 A1 cao SC: B2 for 24, 36 and 60 SC: B1 for 36 on answer line
9	(a)	11 + 3 = 6y + 4y 14 = 10y	1.4	2	M1 for collecting the y terms or the numbers on one side of equation, eg 11 = 6y – 3 + 4y or 11 – 4y +3 = 6y A1 for 1.4 or oe
(b)	(x – 8)(x + 5) OR	8, –5	3	M2 for (x – 8)(x + 5) (M1 for (x ± 8)(x ± 5) A1 cao 8 and –5 OR M1 for correct substitution in formula of a = 1, b = ± 3 and c = ± 40 M1 for reduction to A1 cao 8 and –5
10	( × ) + ( × ) = +	4	B1 for or oe seen as the 2nd probability M1 for ( × ) or ( × ) oe M1 for ( × ) + ( × ) o.e. A1 for oe Tree diagram method B1 for or oe seen as the 2nd probability M1 for (‘’ × ‘’) or (‘’ × ‘’) oe M1 for (‘’ × ‘’) + (‘’ × ‘’) oe A1 for oe Alternative scheme for replacement B0 for or seen as the 2nd probability M1 for ( × ) or ( × ) oe M1 for ( × ) + ( × ) oe A0 for Special Cases SC: Award B2 for or oe or oe SC: Award B1 for or
11	Or 90 –	2	M1 for 180 – x seen (eg 180 – x ÷ 2) A1 correct expression
12	(a)	3	1	B1 for 3 (accept ±3, but not –3 alone)
(b)	1	B1 for (= 0.5)
(c)	4	1	B1 cao
(d)	6	3	M1 for using 8 = 23 M1 for deriving a correct equation in m A1 cao
13	Boys Girls Median: 115 112 Range: 41 33 IQR: 17 9	Comparison of data	4	B1 for correct median for girls or boys B1 for any correct range or IQR C1 for a correct comparison of the medians C1 ft for a correct comparison of the ranges or IQRs For the award of both C marks at least one of the comparisons made must be in the context of the question and all figures used for comparisons correct. OR B2 for an accurately drawn boxplot ( superimposed) C1 for a correct comparison of the medians C1 for a correct comparison of the ranges or IQRs For the award of both C marks at least one of the comparisons made must be in the context of the question
14	(a)	820 000	1	B1 cao
(b)	3.76 × 10–4	1	B1 cao
(c)	5 × 108	2	M1 for 2.3 ÷ 4.6 × 1012 – 3 oe or 500 000 000 or 0.5 × 109 A1 cao (accept 5.0 × 108
15	4	M1 for M1 (indep) for = – c + b or = – b + 3c M1 for – c + b + (– b + 3c) A1 for OR M1 for M1 (indep) for = 2c or = – 3c + b M1 for 2c + (– 3c + b) A1 for
16	(a)	1 – 0.3	0.7	1	B1 0.7 oe
(b)	0.3 + 0.5	0.8	1	B1 0.8 oe
(c)	0.2 × 0.4 = 0.08 0.08 ≠ 0.06	Not independent with reason	2	M1 for 0.2 × 0.4 (= 0.08) C1 for 0.08 and stating events not independent
17	3	M1 for factorizing the numerator correctly M1 for factorizing the denominator correctly A1 for
18	ACB = 90o angle in a semi circle CBD = 180 – ACB co-interior angles add to 180° CBD = 90° DCB = CDB = (180o – 90o) ÷ 2 base angles of an isosceles triangles	45	4	B1 ACB = 90 (could be on the diagram) or 45 seen in a correct position on the diagram B1 answer of 45 B1 angle in a semicircle = 90 B1 base angles isosceles triangle are equal or alternate angles are equal
19	E, B, F, C, D, A	3	B3 all correct (B2 4,5 correct) (B1 2 or 3 correct)
20	1 + 2	2	M1 for 4 terms correct ignoring signs or 3 out of no more than 4 terms correct A1 cao
21	(a)	OR Pick any non-zero value of a and show that LHS ≠ RHS OR Solves to get a = 0 and indicates a contradiction	Correctly shown	2	M1 for or a2 + a + a + 1 (Expansion must be correct but may not be simplified) A1 for statement that a2 + 2a + 1 (eg. they are different) OR M1 for correct substitution of any integer into both expressions eg. (2 + 1)2 and 22 + 1 A1 for correct evaluation of both expressions and statement that they are not equal (eg. they are different) OR M1 or a2 + a + a + 1 A1 Solves to get a = 0 and indicates a contradiction
(b)	But So	AG	3	M1 use of Pythagoras in either triangle – one of a2 + b2 = c2 or (a + 1)2 + ( b+ 1)2 = (c + 1)2 A1 and A1
(c)	LHS is odd, RHS is even	Explanation	1	B1 eg. LHS is odd, RHS is even or one side is odd and the other side is even oe

National performance data from Results Plus

Original source of questions	Mean score of students achieving grade:
Qn	Spec	Paper	Session YYMM	Qn	Topic	Max score	ALL	A*	A	B	C	D	E
1	2540	1F	0811	Q25	Constructions	2	0.15	0.36	0.12	0.05
2	1380	1F	1106	Q27	Ratio	3	0.27	0.75	0.29	0.10
3	1380	1F	1011	Q21	Graphs of linear equations	3	0.59	1.45	0.48	0.12
4	5MM1	1H	1411	Q09	Solve linear equations	4	2.07	3.57	2.93	2.47	1.52	0.77	0.20
5	1MA0	1H	1411	Q07	Perimeter and area	4	1.38	3.85	3.56	2.93	1.51	0.68	0.29
6	1380	1H	906	Q10	Compound measures	3	2.20	2.86	2.57	2.20	1.88	1.49	0.99
7	5MM1	1H	1311	Q13	Fractions	5	2.87	4.72	4.20	3.32	2.20	0.93	0.12
8	1387	3I	0711	Q13	Ratio	5	2.48	4.30	3.07	1.65	0.78
9	5MM1	1H	1211	Q15	Solve quadratic equations	5	2.32	4.94	4.63	3.62	1.47	0.47	0.00
10	5MM1	1H	1206	Q20	Selection with or without replacement	4	1.68	3.65	2.88	1.74	0.51	0.17	0.00
11	5MM1	1H	1111	Q11	Angles	2	0.80	1.50	1.73	0.98	0.18	0.00	0.00
12	5MM1	1H	1411	Q17	Index laws	6	2.32	5.70	3.87	2.33	1.30	0.52	0.10
13	1MA0	1H	1611	Q18	Box plots	4	Data to be added January 2017
14	1MA0	1H	1303	Q16	Standard form	4	1.18	3.27	2.48	1.68	0.91	0.35	0.09
15	5MM1	1H	1411	Q23	Vectors	4	1.10	3.85	2.12	1.03	0.17	0.03	0.00
16	5MM1	1H	1211	Q23	Venn diagrams	4	1.03	1.82	1.33	0.87	0.57	0.40	0.00
17	5MM1	1H	1411	Q22	Simplify algebraic fractions	3	0.70	2.96	1.68	0.37	0.02	0.00	0.00
18	1380	1H	1111	Q19	Circle theorems	4	0.93	3.21	2.33	1.39	0.55	0.18	0.11
19	1380	1H	1203	Q20	Graphs of trigonometric functions	3	0.67	2.14	1.26	0.70	0.38	0.23	0.19
20	1MA0	1H	1411	Q21	Surds	2	0.28	1.85	1.58	0.83	0.16	0.03	0.01
21	1380	1H	1203	Q24	Algebraic proof	6	0.54	2.55	1.27	0.56	0.16	0.03	0.02
TOTAL	80