1MA1 Practice papers Set 6: Paper 3H (Regular) mark scheme – Version 1.0
Question	Working	Answer	Mark	Notes
1	4	M1 for a correct method to find of 40; eg. 40 ÷ 5 × 2 (= 16) or for a correct method to find of 40; eg. 40 ÷ 8 × 5 (= 25) M1 for a correct method to find of 40 and of 40 M1 (dep on M1) for 80 ‒ "16" – "25" (= 39) or = A1 oe OR M1 for 1 – (= ) and 1 – (= ) M1 for a correct method to find of 40; eg. 40 ÷ 5 × 3 (= 24) or for a correct method to find of 40; eg. 40 ÷ 8 × 3 (= 15) M1 (dep on M1) for "24" + "15" (= 39) A1 oe
2	w = 2P + 3	2	M1 for a clear intention to multiply both sides by 2 or add to both sides as a first step A1 for w = 2P + 3 oe
3	25 ÷ 50 = 0.5 h = 30 min 25 ÷ 60 = 0.416h = 25 min	5	3	M1 for 25 ÷ 50 or or 30 (min) or 0.5(h) or 25 ÷ 60 or or 25 (min) or 0.41(6)(h) M1(dep) ‘0.5’ –‘0.41(6)’or ‘30’ – ‘25’ A1 cao OR M1 for 60 ÷ 25 (= 2.4) and 60 ÷ “2.4” or 50 ÷ 25 (= 2) and 60 ÷ “2” M1(dep) for ‘30’ – ‘25’ A1 cao
4	12x + 9y = –21 12x – 16y = 104 25y = −125 y = −5 4x + 3 × −5 = –7 OR 16x + 12y = –28 9x – 12y = 78 25x = 50 x = 2 4 × 2 + 3y = –7	x = 2 y = –5	4	M1 for correct process to eliminate either x or y (condone one arithmetic error) A1 for either x = 2 or y = –5 M1 (dep on 1st M1) for correct substitution of their found value or (indep) for correct process to eliminate the other variable (condone one arithmetic error) A1 cao for both x = 2 and y = –5 SC: B1 for x = 2 or y = –5 if M0 scored
5	(a)	4867.20	3	M1 for 4500 1.04 or for 4500 + 0.04 4500 or for 4680 or 180 or 360 or 4860 M1 (dep) ‘4680’ 1.04 or for ‘4680’ + 0.04 ‘4680’ A1 for 4867.2(0) cao (If correct answer seen then ignore any extra years) Alternative method M2 for or 4500 1.043 A1 for 4867.2(0) cao [SC: 367.2(0) seen B2]
(b)	2580 2773.5 2981.5125 3205.12… 3445.51…	5	2	M1 for an attempt to evaluate for at least one value of n (not equal to 1) or 3445.51 ÷ 1.075n (n ≥ 2) or (=1.4356...) and evaluated, A1 for 5 cao
6	2 10 cos 70 OR BC2 = 102 + 102 – 2 10 10 cos 40 BC =	6.84	4	M1 for 180 – 270 M1 for = M1 for BC = A1 for 6.84(0…) OR M1 for 180 – 270 M1 for 102 + 102 – 21010cos(180 – 270) M1 for A1 for 6.84(0…) M1 for perpendicular from A to BC, may be implied by correct working M1 for 10cos70 or 10sin20 or correct attempt to use sin or cos M1 for 2 ‘10cos70’ A1 for 6.84(0...)
7	(i)	or (x + 6)(x − 1) or (x − 1)(3x − 4) or	3	M1 correct algebraic expression for any relevant area
M1 for correct equation with at least one pair of brackets expanded correctly
shown	A1 for completion to given equation
(ii)	(2x ±15)(x ± 8) (= 0) or or	3	M1 Start to solve quadratic condone one sign error in substitution if quadratic formula used; allow −12 or 12 or 1 in place of (−1)2 M1 ft from an incorrect 3 term quadratic equation
(2x +15)(x − 8) (=0) or or or −7.5 and 8 given as solutions	8	A1 dep ft method from an incorrect 3 term quadratic equation Award all 3 marks if first M1 awarded and 8 alone given as final answer
8	(a)	x ≥ −1	1	B1 cao
(b)	−4,−3,−2	2	B2 for all 3 values and no extras (ignore repeats) (B1 for 2 correct values and no extras or all 3 correct values and −5)
(c)	y < 4	2	M1 for clear intention to add 2 onto each side of an inequality (or equation) or clear intention to divide all terms by 5 as a first step or (y =) 4 A1 cao
9	eg.	5	M1 (probabilities from selecting 2, 2, 2) allow or
eg.	M1 (probabilities from selecting 1, 2, 3) allow
M1 (probabilities for all combinations of 1, 2, 3) allow
M1 complete correct method
A1 oe eg. , 0.298, 0.297619…
10	20 = 2, 2, 5 140 = 2, 2, 5, 7 420 = 2, 2, 3, 5, 7	60	2	M1 for identifying the prime factors for 2 of the 3 numbers 20,140,420 (can be implied by a factor tree, repeated division or Venn diagram) or For a complete Venn diagram for x and 140 with 20 in the intersection or x = 20 × 3 or 20 ×7 × y = 420 or or At least the 1st 3 multiples of 20 or 140x = 420 × 20 oe A1 (Allow 2×2×3×5)
11	380	3	M1 for 1 – 0.15 (= 0.85) or 100 – 15 ( = 85) M1 for 323 ÷ 0.85 oe or 323 ÷ 85 × 100 oe A1 cao
12	T 4 6 6 D L 4 2 3 2 5	M1 for 5 in the middle and 1 from 4(D ∩ L ∩ T) or 2(L ∩ T ∩ D') or 6(D ∩ T ∩ L') M1 for any 4 correct entries A1 for all correct including 2 outside the circles inside the rectangle
5/9	B1 ft from incorrect diagram
13	(a)	1	1	B1
(b)	y = (x – 6) / 2 2y = – 6 2y + 6 =	2 + 6	2	M1 or for a correct flowchart including inverse A1
14	5	B1 Recognition of angle LRM as required angle either drawn on diagram or from working
(=10) or = ==23.32..) LR = =	M2 for a correct method to calculate PQ(ML) & MR or MR & LR or PQ(ML) & LR (NB: LR requires use of RQ = ) Or M1 for a correct method to calculate one of the sides PQ or MR or LR
or or	M1 (Dep on M2) Use of a correct trig ratio to find angle MRL
25.4	A1 25.38 – 25.5

1MA1 Practice papers Set 6: Paper 3H (Regular) mark scheme – Version 1.0
Question	Working	Answer	Mark	Notes
15	21 or 22	5	M1 for 160r2 = 90 or M1 for (r=) oe M1 (dep M2) for 160 × oe A1 for 21.3… A1 for 21 or 22 or M1 for 160 × r2 = 90 or M1 for 160 × × = 90 M1 (dep M2) for 160 × 0.757 A1 for 21.3… A1 for 21 or 22
16	AC2 = 11.82 + 7.42 – 2 × 11.8 × 7.4 × cos132 AC = 17.63… ½ ×8.2 × “17.63… (= 72.28..) + ½ × 11.8 × 7.4 × sin132 (= 32.445..)	105	6	M1 for AC2 = 11.82 + 7.42 – 2 × 11.8 × 7.4 × cos132 M1 for correct order of operations or 310.85… A1 for AC = 17.63… M1 for Area of ABC = ½ ×8.2 × “17.63…” or Area of ADC = ½ × 11.8 × 7.4 × sin132 M1 for “½ ×8.2 × “17.63…”” + “½ × 11.8 × 7.4 × sin132” A1 for an answer in the range 104.7 – 105
17	or or oe	4	M1 Correct rearrangement for or correct expression for or
oe or oe	M1 Correct expressions for t or t² or for at² or 2at in terms of x and a
oe	M1 for correct substitution of t and t² into expression for y
A1 Fully correct answer in required form

1MA1 Practice papers Set 6: Paper 3H (Regular) mark scheme – Version 1.0
Question	Working	Answer	Mark	Notes
18	Area (1 < l < 6) = (0.12 × 1) + (0.32 × 1) + (0.38 × 1) + (0.52 × 1) + (0.16 × 1) = 1.50 Total Area= (0.12 × 2) + (0.32 × 1) + (0.38 × 1) + (0.52 × 1) + (0.16 × 2) = 1.78 Proportion =	0.84 or	4	M1 for attempt to use frequency density × width e.g. 0.12 × 2 or 0.24 M1 for (0.12 × 2) + (0.32 × 1) + (0.38 × 1) + (0.52 × 1) + (0.16 × 2) or 1.78 seen M1 for ((0.12 × 1) + (0.32 × 1) + (0.38 × 1) + (0.52 × 1) + (0.16 × 1))/”1.78” A1 for answer which rounds to 0.84 or 84% or or equivalent vulgar fraction OR M1 for attempt to use area e.g. sight of any one of 4.8, 6.4, 7.6, 10.4 or 6.4 (cm²) oe M1 for 4.8 + 6.4 + 7.6 + 10.4 + 6.4 or 35.6 (cm2) oe seen M1 for (2.4 + 6.4 + 7.6 + 10.4 + 3.2) “35.6” oe A1 for answer which rounds to 0.843 or 84.3%% or or equivalent vulgar fraction
19	congruency proved	3	M1 for correct statement with correct reason M1 for a second correct statement with correct reason C1 for complete proof justifying congruency, eg SAS or AAS Eg DAE = BCF (opposite angles of parallelogram are equal) AE = FC (E and F are midpoints of lines of equal length) AD = BC (opposite sides of parallelogram are equal) AED ≡ CFB (SAS)
explains why DE = FB	1	C1 for relevant statement using congruency Eg DE and FB are corresponding sides of congruent triangles

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	5MM2	2H	1411	Q07	Fractions	4	1.98	3.50	2.97	2.44	1.18	0.76	0.10
2	5MM2	2F	1506	Q20	Rearranging equations	2	0.14	0.51	0.15	0.03
3	1MA0	2F	1211	Q23	Compound measures	3	0.59	1.35	0.70	0.35
4	5MM2	2H	1211	Q18	Simultaneous equations	4	2.07	4.00	3.41	2.37	1.38	0.17	0.00
5	1380	2H	0906	Q19	Compound interest	5	3.41	4.93	4.59	3.68	2.25	0.94	0.35
6	5MM2	2H	1111	Q17	Trigonometry	4	1.62	3.93	3.28	1.63	0.55	0.45	0.00
7	4MA0	3H	1606	Q17	Solving quadratic equations	6	3.21	5.22	3.03	1.13	0.32	0.13	0.02
8	5MM2	2H	1406	Q10	Solve inequalities	5	3.77	4.81	4.52	3.98	3.18	2.25	0.82
9	4MA0	3H	1606	Q21	Probability	5	1.70	2.88	1.45	0.57	0.14	0.04	0.02
10	4MA0	4H	1606	Q10	LCM and HCF	2	1.26	1.78	1.20	0.76	0.40	0.23	0.16
11	5MM2	2H	1306	Q12	Reverse percentages	3	1.90	2.98	2.76	2.18	1.06	0.35	0.14
12	4MA0	4H	1606	Q21	Venn diagrams	4	2.04	3.15	1.80	0.94	0.4	0.15	0.05
13	4MA0	2H	1305	Q17	Functions	5	3.03	4.26	3.09	1.78	0.95	0.45	0.18
14	4MA0(R)	4H	1606	Q17	Trigonometry	5	2.33	4.36	2.96	1.36	0.47	0.14	0.02
15	5AM2	2H	1311	Q25	Proportional change	5	1.33	4.58	2.62	1.07	0.28	0.00	0.00
16	5MM2	2H	1106	Q24	Sine and cosine rule	6	1.30	5.46	3.05	0.73	0.23	0.02	0.00
17	4MA0(R)	4H	1606	Q21	Rearranging equations	4	1.00	2.72	0.66	0.11	0.01	0.01	0.00
18	5AM1	1H	1111	Q22	Histograms and grouped data	4	0.72	1.67	0.86	0.50	0.09	0.14	0.00
19	5MM2	2H	1311	Q26	Geometric proof	4	0.26	1.41	0.42	0.11	0.03	0.00	0.00
80