Educate.ie & SEC MATHEMATICS SOLUTIONS

Transcription

1 Educate.ie & SEC MATHEMATICS SOLUTIONS Leaving Certificate Foundation Level Educate.ie Sample Papers Sample Paper 1 Solutions... Sample Paper Solutions...7 Sample Paper 3 Solutions...13 Sample Paper 4 Solutions...19 Sample Paper 5 Solutions...4 Sample Paper 6 Solutions...31 Sample Paper 7 Solutions...37 Sample Paper 8 Solutions...43 SEC Papers SEC Sample Paper 015 Solutions SEC 014 Solutions SEC 013 Solutions SEC 01 Solutions SEC 011 Solutions... 69

2 Educate.ie Sample Paper 1 1. (a) 4 4 = = 56 1_ 7 3 = 3 7 = 3 (b) 3 = (c) = (a) = (b) = (c) (i) 13% of price = % = Price excluding VAT = 90 10% of 90 = (a) (i) 0 7 m = 348 Decreases by ( ) = m A 1 = = 0 1 m r = 0 35 m A A = πr = π(0 35) = 0 19 m Mathematics Leaving Certificate

3 (iii) A Sample 1 A = A 1 + A = 0 4 m (b) V = A 3 8 = = 1 5 m 3 4. (a) (i) h = 8 5 = 40 mm = 4 cm r = 3 5 = 15 mm = 1 5 cm (b) V = πr h = π(1 5) 4 = 9π cm 3 (c) A = πrh + πr = π π 1 5 = 16 5π cm 5. (a) 3(x 5) (3x ) = 6x 15 6x + 4 = 11 (b) 9x 11 = 4x x = 5 x = 5 (c) x 7 9 x 16 x 8 The numbers are 1,, 3, 4, 5, 6, 7, 8 6. (a) p = 0 4 = ( ) (b) (i) p(4) = = 0 1 p = 0 1 (c) p = = 0 4 Foundation Level, Educate.ie Sample 1 3

4 7. (a) Colour Red Black White Silver Model 16 GB 3 GB 64 GB 16 GB 3 GB 64 GB 16 GB 3 GB 64 GB 16 GB 3 GB 64 GB (b) (i) 1 (iii) White and 3 GB Silver and 64 GB 4 3 = 1 (c) (i) p = 1 1 p = 4 1 = 1 3 (iii) p = 6 1 = 1 8. (a) (i) 9 0 (b) (i) Range = 30 8 = Median = 19 (iii) The percentage that scored less than the median = = 48% 9 (c) (i) No affect New median = = Mathematics Leaving Certificate

5 9. (a) (i) l = 10 m w = 8 m Sample 1 A = 10 8 = 80 m (iii) Area of bathroom = = 10 4 m (b) (i) Rebuilding cost = Kitchen fittings = Built-in wardrobes = 5000 Wooden floor = 3700 Miscellaneous = Total = = (iii) = 374 (c) (i) V = = m 3 Volume of cement = (a) Number of hexagons (n) = m 3 Volume of water = (b) (i) P = n 4 + = m 3 Length of perimeter (P) = (4n + ) cm n = 6 P = (4 6 + ) = 6 cm Foundation Level, Educate.ie Sample 1 5

6 (c) n = 0 P = (4 0 + ) (d) 14 = 4n = 4n n = hexagons (e) (i) n + 1 = 8 cm n + (n + 1) = n + 1 (iii) (n + 1) = 4n (a) (i) Total = = tonnes Percentage household waste = 100 = 55% (b) (i) 40% 3% (c) Same percentage recycled as the EU average 16% more landfill than the EU average and 16% less incineration (d) (i) 53% of = = tonnes 40% of = = tonnes (e) (i) tonnes Percentage = = 47% Recovered (f) 17 trees from 1 tonne = trees 6 Mathematics Leaving Certificate

7 1. (a) (i) 3 5 = 15 Educate.ie Sample Paper Sample Yes, because 95 5 < 3 5 (b) (i) Because = is approximately = 6077 (c) (iii) He multiplied = = Plants He forgot the zero in (a) (i) 3 m V = = 450 m 3 (b) A = 5 9 = 5 m 5 5 (c) Average speed = = 1 7 km/h 3. (a) (i) = (b) Expected value = (1 06) 3 = Foundation Level, Educate.ie Sample 7

8 4. (a) (i) x + 5, x + 10 x + x x + 10 = 4 3x = 9 x = 3 (b) (i) ( ) = h = 189 h = h = 10 hours 5. (a) (i) x y = 5 4 = 49 (x y)(x + y) = (5 4)(5 + 4) = 1 49 = 49 (b) = (78 77)( ) = 1 (155) = 155 (c) (i) A prime number is a natural number greater than 1 that can be divided only by itself and 1 without any remainder., 3, 5, 7, 11, 13, 17, 19, 3, 9 6. (a) O(0, 0) A(5, 1) B(5, 16) (b) (i) OA = = 13 AB = 4 (c) OA: = t 1 t 1 = AB: 700 = 85 4 t t = OAB: T = t 1 + t = 064 T hrs 4 mins 8 Mathematics Leaving Certificate

9 7. (a) E F O A D B C H Sample G (b) k = = 3 (c) (i) AD = 3 cm = 1 cm 3 FG = 3 3 = 9 cm 8. (a) (i) 1 4 (iii) 8 (b) (i) Week 4 Area ABCD = 1 (3 + 1)1 5 = 3 cm Area EFGH = 1 (3 + 9) 4 5 = 7 cm Area EFGH = 9 Area ABCD Week 4 (c) (i) Total = = 65 Percentage of babies which were girls = = 5 3% 65 Foundation Level, Educate.ie Sample 9

10 (d) B B G BBB BBG B G B BGB G BGG B B GBB G G B GBG GGB G G GGG 9. (a) = Since 1000 l = 1 m l = 1000 m3 = m 3 (b) 93 m 3 = l = l Number of litres per day = = 54 8 l (c) (1) Gross number of m 3 used = 168 m 3 Water allowance = 93 m 3 Net number of m 3 used = 75 m 3 () Net number of m 3 used at 4 88 per m 3 = 366 Total charge = 366 (d) (1) Gross volume used in m 3 = = 16 Water allowance in m 3 = 93 Net volume used in m 3 = 33 () 33 m 3 at 4 88 per m 3 = Total charge = (e) Saving per year = Number of years to pay for the installation = = 3 = 1 1 years 10. (a) (i) 10 Total number of females = Mathematics Leaving Certificate

11 (b) 10 9 Number of males Number of females Litter size Sample 3 1 A B C D E F G H I J (c) l 13 8 m 59 (d) sin 59 = 13 8 l l = l 16 m 13 8 sin 59 = m m A sin A = A = 67 (e) Number of cats = 70 Number of females in litter I = 5 p = 5 70 = (a) (i) Range = = Foundation Level, Educate.ie Sample 11

12 11. (a) (i) Range = = Mean = = 8 7 (iii) 7 5, 8, 8 5, 9, 9, 9, 9, 9, 9 5 Median = 9 (b) (i) Range = = 5 Mean = 76 9 = 8 44 (iii) 4 5, 8, 8 5, 9, 9, 9, 9, 9 5, 9 5 (c) (i) Paula Median = 9 Paula s mean = = Brenda s mean = 6 7 = Brenda won it. (d) It excludes biased judging. (e) (i) 7, 8, 8 5, 8 5, 9, 9, 9 5 Score = ( ) 1 = 31 6, 6.5, 7, 8, 8, 8 5, 8 5 Score = ( ) 4 8 = (iii) Total raw score from the three scoring judges = = 8 5 Average score from each scoring judge = = 9 5 (f) v = 19 6 h h = 10 v = = 196 v = 196 = 14 m/s 1 Mathematics Leaving Certificate

13 Educate.ie Sample Paper 3 1. (a) (i) = (iii) Close to = Sample 3 (b) (i) 780 = Order of magnitude 3 Order of magnitude 0 = Order of magnitude 3 Order of magnitude = 975 She divided by (iii) 975. (a) (i) Error = ( ) kg = 7 kg % Error = = 3 15% 86 4 Weight = % of her weight = 64 kg % = 100 kg = 6 06 kg (b) Weight after 3 weeks = 10 (0 98) 3 = kg 96 kg 3. (a) V = π r h Foundation Level, Educate.ie Sample 3 13

14 = π = cm 3 (b) 350 millilitres = 350 cm = π 3 5 h 350 h = 3 5 = 9 1 cm π 4. (a) (i) 8% = = (iii) = (iv) = 40 4 (b) After year 1 Value = = After year 3 Value = (0 93) = (a) 4 (3x ) = 16 1x 8 = 16 1x = 4 x = (b) (i) x x + x = 3x (iii) 3x = 18 x = 6 (iv) 6, 1 (v) < Number of goals < 6 3, 4, 5 14 Mathematics Leaving Certificate

15 6. (a) p = 6 5 = 1 (b) p = 13 5 = 1 4 (c) p = 1 5 = 3 13 (d) p = 4 5 = 1 13 (e) p = 5 = 1 6 (f) p = 1 5 (g) p = 8 5 = 13 (h) p = 16 5 = (a) (i) 6 Sample 3 10 (iii) = (b) = (c) = (a) (i) A m B C ACB = = 90 (iii) Sin 44 = BC BC = sin 44 = 15 8 m Cos 44 = AC AC = cos 44 = m Foundation Level, Educate.ie Sample 3 15

16 (b) (i) E C D h A 7 cm B (b) 3 9 = 7 h h = 4 7 cm 9. (a) (i) 6 stages paid in cash cost 15 per journey per day = 1 50 per week 6 stages using a Leap card costs 1 90 per journey per day = 19 per week (iii) Saving per week = (1 5 19) = 50 % Saving = = 11 6% 1 5 (b) (i) 3 stages paid in cash cost 0 80 per journey per day = 8 per week 3 stages using a Leap card cost 0 7 per journey per day = 7 per week (iii) 3 stages paid in cash cost 0 80 per journey. He makes only 4 journeys per week = 3 0 (c) (i) x journeys at 80 per journey = 8x x journeys at 45 = 45x 16 Mathematics Leaving Certificate

17 (iii) Savings = 8x 45x = 0 35x 0 35x = 8 x = x = 8 (d) (i) Dublin airport to City Centre is 14 stages. Cost = 80 11:36 + 0:40 = 11:76 = 1:06 (e) (i) Speed = Distance = 19 = 11 4 mph Time 5 3 Distance = = km Sample (a) Time = 5 3 h Speed = = km/h 5 3 E C 1 5 cm 10 cm 4 cm O (b) (i) AC = = 5 A 3 cm B 7.5 cm D k = = 5 Foundation Level, Educate.ie Sample 3 17

18 (iii) DE = 5 4 = 10 cm BD = 5 3 = 7 5 cm (c) (i) Area ΔABC = = 6 cm Area ΔBDE = = 37 5 cm Area ΔBDE Area ΔABC = k = 5 = 6 5 = 6 5 (d) (i) Sin CAB = 4 5 CAB = 53 BED = = 37 (e) (i) OD = x OB = x + 3 (f) ( x) = 5(x + 3) x = 5x = 1 5x cm = x 18 Mathematics Leaving Certificate

19 Educate.ie Sample Paper 4 1. (a) (b) (c) (d) = Press = (0 5) + 1 (1 5)3 = Press (0 5) = sin 7 = Press sin(7) = 0 95 (Make sure your calculator is in the degree mode.) = Press and then S D = 1 1 Sample 4. (a) Diagram 4 Diagram 5 (b) Diagram number Number of vertical lines (c) (i) = = 7 Diagram 7 (d) Number of vertical lines = (Diagram number ) (a) (i) Value = (1 03) 3 = Value = (1 03) 3 = (iii) Value = (1 038) 3 = (b) (i) Net interest = = Net interest = = (iii) Net interest = = Foundation Level, Educate.ie Sample 4 19

20 4. (a) p = 1 4 (b) Range = 9 1 = 8 Median of 1,, 6, = = 4 Median = 4 = 8 = Range (c) 9 x > 5 4 > x 5. (a) (i) (iv) x 0, 1,, 3 Large and white Large and brown Medium and white Medium and brown (v) 1 egg = 18 (vi) 30 eggs = 54 (vii) 90 eggs = 16 (viii) 35 eggs = 63 (ix) 45 eggs = 81 (b) (i) p(b) = = p(l or W) = = Mathematics Leaving Certificate

21 6. (a) Die A Die B (1,1) (1,) (1,3) (1,4) (1,5) (1,6) (,1) (,) (,3) (,4) (,5) (,6) 3 (3,1) (3,) (3,3) (3,4) (3,5) (3,6) 4 (4,1) (4,) (4,3) (4,4) (4,5) (4,6) 5 (5,1) (5,) (5,3) (5,4) (5,5) (5,6) 6 (6,1) (6,) (6,3) (6,4) (6,5) (6,6) Number of elements in S = 36 (b) (i) p = 6 36 = 1 6 E = {(3,6), (6,3), (4,5), (5,4)} p = 4 36 = 1 9 (iii) E = {(1,1), (1,3), (1,5), (,), (,4), (,6), (3,1), (3,3), (3,5), (4,), (4,4), (4,6), (5,1), (5,3), (5,5), (6,), (6,4), (6,6)} p = = 1 7. (a) AC = = 135 m Sample 4 (b) Pythagoras: 135 = = = 185 ABC = 90 (c) Area ΔADC = = m Area ΔABC = = 4374 Total area = m Foundation Level, Educate.ie Sample 4 1

22 8. (a) C 6 cm 8 cm A 10 cm B (b) 40 Because AB = AC + BC 10 = (c) (i) Perimeter = = 4 cm Area = = 4 cm 9. (a) Maximum height = = 76 m Minimum height = 50 6 = 4 m (b) (i) C = πr = π 6 (c) = 163 m A = πr = π 6 = 14 m Speed = Distance Time 13 = 163 t t = = 1 54s (d) (i) Watts is three million seven hundred thousand Watts Watts = Watts (iii) 3 MW = W 3 MW = W Mathematics Leaving Certificate

23 (e) 000 mw = W 1 3 million households = households Average power per household = = 1538 W per household (f) (i) 1 5 kw 0 8 hr = 1 kwh = 1 u Cost = = 0 04 kw 3hrs = 6 kwh = 6 u Cost = = (a) (i) Score = (0 ) + (9 3) + 19 = 86 Score = = 170 (iii) 3 Treble 0s = 3 60 = 180 Sample 4 (b) (i) p(b) = = = p(d5) = = (iii) p(t) = = = (c) (i) d = = 4 m tan A = A = 0 7 (d) (i) 141 Dart 7 Treble Dart 8 Treble Dart 9 Double Total Foundation Level, Educate.ie Sample 4 3

24 Educate.ie Sample Paper 5 1. (a) (i) Maximum diameter = (11 + ) cm = 13 cm (b) (i) Minimum diameter = (11 ) cm = 9 cm = 90 = 45 Range = (45 ± 0 1) mm (1) ( ) m = 5 1 mm () ( ) m = 4 9 mm. (a) (3) (50 45) m = 5 mm A = 10% 50 5 cm 4 cm B 3 cm C AB = = 5 cm (b) V = A h = = 60 cm 3 (c) A = = = 13 cm 3. (a) (i) 5(x 3) + 7(x + 1) 4 Mathematics Leaving Certificate

25 = 10x x + 7 = 4x (x + 1) = 3 + 4x + = 4x + 5 (Multiplication before addition) (b) (i) V 1 = 10 t t = 0 V 1 = 10 0 = 10 m 3 V = 3t + t = 0 V = = m 3 (iii) V 1 = V 10 t = 3t + 8 = 4t 4. (a) t = mins And so V 1 = V = 10 = 8 m 3 Number of groups Total number of throws Total number of sixes Relative frequency of sixes Sample Foundation Level, Educate.ie Sample 5 5

26 (b) y Relative frequency x Total number of throws (c) Yes For a fair die p = 1 = whereas for our die p(6) = (a) Sum = 7 5 = 35 (b) (i) Sum = 6 5 = x = 30 x = 4 (c) (i) Median = 5 Mean = 5 (iii) x + 8 = 5 x = 8 6. (a) 1 B B B B B B B G 3 B B G G 4 B G G G 5 G G G G 6 Mathematics Leaving Certificate

27 (b) (i) p(r) = 0 50 = 5 p(b or G) = = 3 5 (iii) p(nb) = = 7 10 (c) (i) = (a) (i) = y 7 C (a) (i) 6 5 Axis of symmetry [CD] 4 A B 3 1 (a) D Sample x (b) A(3, 4), B(8, 4), C(5 5, 7), D(5 5, 1) (c) (i) Isosceles because AC = BC One, [CD] Foundation Level, Educate.ie Sample 5 7

28 8. (a) 4 cm O (b) (i) A = π(r) = π(4) = 50 cm 9. (a) P = πr = π 4 = 5 cm (iii) Average speed = Distance Time = 0.5 = 0.05 m/s 5 3 Tables together 4 Tables together (b) Number of tables (x) Number of seats ( y) Mathematics Leaving Certificate

29 (c) Number of seats (y) Number of tables (x) (d) A straight line. The number of seats increases at twice the rate as the number of tables put together increases. (e) y = (x + 1) (f) (i) x = 9 y = (9 + 1) = 0 y = 8 8 = x + 6 = x x = (a) (i) km 18 minutes (b) (i) 0 75 km Sample km (c) (i) d = 1 km t = 8 mins Speed = Distance = 1 = 7 5 km/h Time 15 d = 1 km t = 10 mins = 1 6 h v = d t = 1 = 6 km/h 1 6 (iii) d = km t = 18 mins = 0 3 h v = d t = 0 3 = 6 km/h 3 (iv) He was tired having run 1 km. (d) 4 mins and 13 mins Foundation Level, Educate.ie Sample 5 9

30 (e) (i) t 8d = 0 t = 5 5 8d = 0 8d = 5 t + 10d = 18 d = 0 65 km t = d = 18 10d = 3 d = 0 3 km 11. (a) (i) Number = = 600 Number = = 500 (iii) 1100 (b) (i) Percentage pass rate on first attempt = = 40 9% 1100 Percentage after 3 attempts or less = ( 1100 ) = 11 = 93 6% (iii) p = = = 0 78 (c) (i) = 40% 500 p = = 5 45 = 9 5 (d) (i) 50% 50% of 1100 = 550 (iii) 180 = = = = (e) = = 4 5 (f) = = = 990 Total number of lessons taken = Mathematics Leaving Certificate

31 Educate.ie Sample Paper 6 1. (a) (i) Estimate = = 64 = 8 = Calculator value = = = 4 0 (b) (i) Average = = 80. (a) 43, = 3 3 (iii) 30 = 74 4 (iv) Error = = 5 6 % Error = = 7% 80 Multiply each term by 3 to get the next term. (b), 4 Add to each term to get the next term. (c) 10, 70 Multiply the number of the term by all the natural numbers less than or equal to it. 10 = = Sample 6 3. (a) (i) l = = 9 m b = = 55 m P = (9 + 55) = 94 m A = 9 55 = 5060 m (b) (i) d = ( ) 8 = 5 m πr A = = π ( ) = m Foundation Level, Educate.ie Sample 6 31

32 4. (a) Cross tax = = 6300 (b) Net tax = (c) (i) Net yearly Income = ( ) = Net monthly income = 5. (a) (i) p(d) = 0 1 p(nd) = = 0 88 (iii) Number = = 8800 (b) (i) p(<3) = = = = p = = 500 = (iii) = (iv) p = = (a) (i) 007 NI D B NI D Mathematics Leaving Certificate

33 Increase = Percentage increase = (b) = 1% 6100 (c) (i) 006: Population change = = (a) Yes 01: Population change = = The outcome of one event has no influence on the outcome of the other event. (b) Outcomes of tossing a coin Outcomes of rolling a die (c) (i) p(h) = 1 1 H T 1 (1H) (1T) (H) (T) 3 (3H) (3T) 4 (4H) (4T) 5 (5H) (5T) 6 (6H) (6T) Sample 6 E = {(H), (4H), (6H)} p = 3 1 = (a) t(s) h(m) Foundation Level, Educate.ie Sample 6 33

34 (b) Height h (m) Time t (s) (c) Slope = (d) h = t = 5 10 (e) 10 = t 5t = 90 t = 36 s = 5 m/s rate of change of height (f) Average speed = Slope = 5 m/s 9. (a) (b) Arrangement number Number of tiles (c) (i) A = = 5 65 m Area of one tile = = 0 09 m Number of tiles = = Mathematics Leaving Certificate

35 (d) (i) 85 = boxes = 8 08 m (e) Cost of tiles = = Cost of tiler = = Cost of adhesives etc = Total (a) (i) barrels barrels (b) (i) Decrease = = Percentage decrease = 100 = 5% The economy goes into recession. (c) (i) $65 $95 (iii) $ = $ (d) Mean = 10 = $55 (e) 100% = $95 113% = $ Sample 6 (f) Number of kwh = = kwh 11. (a) AB = = 450 m (b) (i) Sin ABX = = 3 5 DCX α 5 3 Alternate angles 4 (c) (i) sin DCX = DX 115 = 3 5 DX = 675 m CX = = 900 m Foundation Level, Educate.ie Sample 6 35

36 (d) Time = AD 60 = hours 1 minute (e) A X C D Distance = ( ) m = 95 m = 95 km (f) A X: Time = = 0 7 minutes 60 X C: Time = = 0 9 minutes 60 C D: Time = = minutes 80 Shortest time = 014 minutes 36 Mathematics Leaving Certificate

37 Educate.ie Sample Paper 7 1. (a) Number of parallel lines Number of pieces of circumference (b) (i) Number of pieces = = 15 Number of parallel lines 31 1 = 15 (c) Number of pieces = n + 1. (a) w = 4 5 cm b = 3 cm h = 5 cm (b) V = = cm 3 (c) A = ( ) = 64 5 cm 3. (a) Labour = 30 = 0 3 Call out = 45 Labour + call out = 65 Labour + call out + VAT = = Parts + VAT = = 76 6 Total = Sample 7 (b) Actual = ( ) = 31 5 Estimate = ( ) = 31 Error = 0 5 % Error = = 0 8% 31 5 Foundation Level, Educate.ie Sample 7 37

38 4. (a) t (Hours) C ( C ) (b) t (Hours) T ( C) (c) y C ( C) t (Hours) x (d) (i) 11 hours 10 hours (e) (f) 8 hours C = 80 5t T = 0 + 5t 5. (a) = (b) Value = (0.96) 3 = (c) (i) ( ) = (iii) ( ) = Mathematics Leaving Certificate

39 6. (a) (i) p(b) = 6 0 = 3 10 = 0 3 p(r or B) = 10 0 = 1 = 0 5 (iii) p(not white) = 15 0 = 3 4 = 0 75 (b) (i) 4 19 (iii) p = (a) (i) Percentage that scored below par = = 60% 5 Range = = 8 (iii) 70 (iv) 70 (b) 79 7 = = (a) (b) G F D C Sample 7 A B E (c) Area AEFG = = 100 cm Area between the two squares = (100 5) cm = 75 cm Foundation Level, Educate.ie Sample 7 39

40 9. (a) (b) 6 hours 5 hours (c) They took a break for an hour at a service station. (d) (i) Average speed = 50 = 15 km/h Average speed = 300 = 100 km/h 3 (iii) Average speed = = 91 3 km/h (e) Yes, from O to A. As average speed 15 km/h > speed limit of 10 km/h (f) (i) From the graph 1 hour 40 minutes From the graph 75 km 10. (a) = (b) (i) 5 1 = Total interest due = = (iii) Total sum to be repaid = (iv) Monthly repayment = = (c) (i) Total interest = 1 73 = (d) Saving = (iii) Monthly repayment = On 1st September 014 value of car = = On 1st September 017 value of car = (0 8) 3 = = Mathematics Leaving Certificate

41 11. (a) (i) = = 801 (iii) = 1045 (iv) Add up female column to give = 611 (v) Add up male column to give 659 (vi) Add up the total column to give 5713 (b) (i) (iii) = 5 5% = 7 4% = (c) (i) 011: = : = PTR = 5808 = (iii) PTR = 5374 = 14 3 Sample 7 Foundation Level, Educate.ie Sample 7 41

42 (d) y PTR Year 01 x (e) D : = C : = B : = A = = 73 4 Mathematics Leaving Certificate

43 Educate.ie Sample Paper 8 1. (a) (i) Likely p = 8 10 = 4 5 Impossible p = 0 (iii) Certain p = 1 (iv) Evens p = 1. (a) 3(4x 1) + (x 3) = 1x x 6 = 10x 3 so x = 5 10x 3 = 10( 5) 3 = 47 (b) 9x 4 = 3x + 0 9x 3x = x = 4 x = 4 (c) 5x 4 1 5x 5 x 5 The natural numbers are 1,, 3, 4, 5 3. (a) = = 1 53 (b) (i) m m = 6 million four hundred thousand metres (iii) = 6400 km (c) Speed = Distance = πr Time t π 6 10 = = km/h Sample 8 Foundation Level, Educate.ie Sample 8 43

44 4. (a) Key 6 3 represents 63 mm (b) (i) Mean = ( ) = 63 mm Median = = 61 5 mm (c) Percentage of months = 4 1 = 33 3% 5. (a) = = = = 799 (b) = (1000 5) 5 = = (1000 6) 6 = = (1000 7) 7 = = (1000 8) 8 = 799 (c) (i) (1000 x) x = 1000 x 1 x = 999x = = (a) (i) Red Colour 15 6 = 90 Red Colour 14 6 = 84 (b) (i) 1 st nd 3 rd = Mathematics Leaving Certificate

45 7. (a) (i) A 1 st nd 3 rd = 60 Scale factor k = 8 3 = 5 (b) (i) EF = 4 5 = 6 cm Area = 8 6 = 48 cm (c) (i) AC = = 4 cm AF = k AC = 5 4 = 10 cm CF = (10 4) = 6 cm 8. (a) r = 3 cm (b) V = πr h = 4 πr 3 = 4 π(3) = 36π cm 3 (c) A = 4πr = 4π(3) = 36π cm 9. (a) (i) A whole positive number which is divisible only by itself and 1, 3, 5, 7, 11, 13, 17, 19 (b) Value of prime Number of primes Total 168 Sample 8 Foundation Level, Educate.ie Sample 8 45

46 (c) y Number of primes x Value of prime (d) They would end in, 4, 5, 6, 8 which would be divisible by in the case of, 4, 6, 8 and 5 in the case of 5. (e) 101, 131, 151, 181, 191, 313, 353, 373, 383, 77, 757, 787, 797, 919, 99 (f) p = = 56 = (a) (i) Number = 50 Number = 5 (iii) Range = 50 5 = Mathematics Leaving Certificate

47 (b) (i) Number = = 130 Number = = 195 (iii) Number of houses and apartments rented in October = 45 Percentage = = 3% 195 (c) (d) The bar chart shows the number of rentals is steadily increasing over the number of houses sold from August to November. 50 apartments in November Rent = = % of rent = = (a) R = 16 = x 9 x = 5 minutes (b) (i) Total time = = 56 minutes = 4 hours, 16 minutes y = 56 y + 34 = 56 y = y = 11 minutes (c) 9, 10, 10, 11, 11, 13, 15, 16, 17, 18, 18, 0, 0, 1,, 5 Median = = 16 1 minutes (d) (i) Percentage of flights delayed by less than 0 minutes 11 = 100 = 68 75% 16 No, it is only 68 75%. 0 minutes 13 = = 81 5% Yes Sample 8 Foundation Level, Educate.ie Sample 8 47

48 (e) (i) Total = = 480 Number = 400 (iii) % delayed less than 0 minutes = = 83 1 % 3 (f) (i) Yes A bigger sample means a better result. Look at the data for Dublin London flights for a full year. 48 Mathematics Leaving Certificate

49 015 SEC Sample Paper 1. (a) (i) = = 94 4 (b) (c) He has 1 4 left. 1 4 of 4 = Speed = Distance Time Time = Distance Speed 165 = 75 = hours = hours 1 minutes. (a) (i) 33% of 10 = = New price = Original price Reduction = = (b) 13% of price = % of price = % of price = 160 (c) 6 3 = = 81 = 16 = 9 3. (a) 6% = = 0 06 (b) Value = 5000 (1 06) 3 = SEC Sample 015 Foundation Level, SEC Sample

50 4. Answer Number of students Percentage Angle for pie chart Get a job 6 1% 43 Go to a third-level college 5 50% 180 Do a Post-Leaving Cert course 7 14% 50 (PLC) Other 4 8% 9 Don t know 8 16% 58 Total % 360 Don t know Get a job 1% Other Do a PLC course Go to a third level college 5. (a) (Monday, Tuesday) (Tuesday, Wednesday) (Saturday, Sunday) (b) First person Second person 7 7 = 49 (c) (i) P(w,w) = P 7 = 49 (SA, SU) (SU, SA) (SA, SA) (SU, SU) P = Mathematics Leaving Certificate

51 (iii) First at the weekend and then second on a weekday 5 = 10 or First on a weekday and second at the weekend = 10 5 or Both at the weekend = 4 P = = (a) Area = Area of square Area of 1 4 of a circle = π 8 = cm (b) Volume V = Cross sectional area Length = = 1741 cm 3 7. (a) Distance (km) Fare (cent) (b) Fare in cent Distance in kilometres SEC Sample 015 Foundation Level, SEC Sample

52 (c) (i) F = DD = 1000 cent 1000 = DD 103D D = 693 D = 6 73 km F = = cent = O A B C D E F (a) Mountain A Mountain B Time Liam s Temperature ( C) Mairead s Temperature ( C) Mathematics Leaving Certificate

53 (b) Rate = = C/h = Slope (c) (d) The same temperature is 1 C. 7 hours Temperature ( C) Time (Hours) (e) (y = mx + c) T = t + 7 T = Temperature in C after t hours SEC Sample 015 Foundation Level, SEC Sample

54 11. (a) (i) B A O Image Original pattern OA = 5 cm OB = 7 5 cm k = OA OB = 1 3 (iii) A = 7 k = = 3 cm (b) 6 cm α 11 cm 6 tan a = 11 a = 9 (c) 7 cm d 7 cm d = = cm 1 cm 54 Mathematics Leaving Certificate

55 SET A 014 SEC Paper 1 1. (a) (i) (iii) 73 (b) (a) (i) (b) a 3 (c) (i) 16, , 1 3. (a) (i), 15, 5 6 (iii) 5 6 (b) (i) % 4. (a) 79 5 m (b) (i) 15 m 91 m 3 5. (a) (i) 1 and 1 and (iii) 3 and 5 (b) (i) (a) 0 (b) 11a + 5 (c) 1 4, (a) 6 (b) {1,, 3} (c) (i) x + 7 3x (iii) (a) 9 (b) (i) h(x) SEC Papers , Paper 1 & g(x) (iii) (iv) 1 and 4 Foundation Level, SEC Papers , Paper 1 & 55

56 9. (a) (i) (iii) Height of rectangle No. of small squares in the rectangle No. of squares Height 4 5 (b) (i) h + h because 1 + (1) = 3 + () = (3) = (4) = (5) = 5 56 Mathematics Leaving Certificate

57 (iii), 4, 6, 8, 10 (iv) Yes Pattern n 10. (a) (i) 17 km 58 km (b) Derry and Cork (c) Stages of her journey Statement 1 D C 3 E 4 A 5 B (d) (i) 5 hours 15 minutes 63 km/h (e) 4 hours (f) (a) Outcome SET A 014 SEC Paper Probability The number is odd. 1 4 SEC Papers , Paper 1 & The number is even. 3 4 The number is The number is less than 8. 1 (b) (i) (a) (i) (b) (i) (iii) Black B, 1 B, B, 3 B, 4 B, 5 B, 6 White W, 1 W, W, 3 W, 4 W, 5 W, 6 Grey G, 1 G, G, 3 G, 4 G, 5 G, 6 Silver S, 1 S, S, 3 S, 4 S, 5 S, 6 Foundation Level, SEC Papers , Paper 1 & 57

58 3. (a) 1 4 (iii) 1 1 (iv) 0 7, 9 Key 5 = 5 1 1, 9 3 5, 7, 8, 9, 9 4,,, 5, 7, 8 5 0,,, (b) 40 5, 4 (c) (a) m = 4 5 (b) 4x + 5y + 8 = 0 (c) 4x + 5y = (a) y A(4, 6) B(1, ) C(7, ) x 1 (b) Midpoint [BC] = (4, ) (c) (i) (a) Social networking (b) 45 (c) 3 hours (d) 1 8 hours 7. (a) 17 5 cm (b) 96 5 cm (c) cm (d) cm (e) 5:1 58 Mathematics Leaving Certificate

59 8A. (a), (c) A O D (b) 1 8B. (a) 10 cm (b) 5 cm (c) (i) ΔOAB and ΔOAC AOB = 74 OBA = (a) (i) August 9 C (iii) 9 8 C (b) (i) 30 (iii) 103 Table Number of children per caravan Number of caravans SEC Papers , Paper 1 & Foundation Level, SEC Papers , Paper 1 & 59

60 (iv) (a) (i) 3 9 m 0 5 m (iii) 0 3 m (iv) 5 5 m (v) 660 (b) (i) 3 75 m CAB = 40 SET B 013 SEC Paper 1 1. (a) 6 4 (b) 7 (c) 1. (a) (i) Number sin 30 π 0.5 sin 30 3 π Mathematics Leaving Certificate

61 (b) (i) 384,000 km km/h 3. (a) (i) 100 m = Length m = Breadth, Perimeter = m (b) (i) 63 0 m cm 4. (a) 1,000 (b) 4, (a) w = 4 cm, d = 3 cm (b) 1600 mm (c) 4000 mm 6. (a) 841 (b) 9 (c), 5 7. (a) x 4 (b) 10 (c) x {1,, 3, 4, 5} 8. (a) (i) x x y 0 y x x y x (iii) (, 1) (b) (, 1) SEC Papers , Paper 1 & 9. (a) (i) E 107 E (iii) 3 hours 55 minutes (iv) on Sunday morning (b) (i) (iii) (a) Number of posts x Number of rails y Foundation Level, SEC Papers , Paper 1 & 61

62 (b) y = 3(x 1) (c) 9 (d) 177 (e) y = 3x 3 (f) (i) 7 77 (g) y (h) x 1. (a) (i) 1, 0, 0 5 (b) (i) 5 SET B 013 SEC Paper Even number, Number > 6, Number between 1 and 6 inclusive 1 6 (iii). (a) (i) 55% 16% (b) A+: 0 05 AB: 0 03 A or B: 0 4 Rhesus Negative: 0 84 Not O: (c) (i) (iii) (a) Melon, fish of the day, ice cream (b) 60 (c) 4. (a) 37 (b) 87 (c) 36 (d) 43 1, 1 4 1, 1 30 (e) 31, 3, 36, 36, 36, 39, 43, 46, 50, 50, 55, (a) B( 3, 6) C(1, ) 6 Mathematics Leaving Certificate

63 (b) (i) B y M A (1, 5) (c) C x 6. (a) 7. (a) y P(1, 6) l 1 Q(4, ) (b) 4 3 (c) Yes, because their slopes multiply to 1. C x y z z' x SEC Papers , Paper 1 & x' y' (b) (i) 5 cm 3 cm (c) 3 cm Foundation Level, SEC Papers , Paper 1 & 63

64 8A. (a), (b) R Q' P Q R' (c) 39 8B. (a) 9 cm (b) 10 (c) AB DC (d) True, the diagonals of a parallelogram bisect each other. D C A B D' C' 9. (a) Sunday (b) 64 Mathematics Leaving Certificate

65 (c) Daily spend in (d) 16 (e) 1 Mon Tues Wed Thurs Fri Sat Sun 10. (a) (i) m (b) (i) m (c) m SET C 01 SEC Paper 1 1. (a) 34, 39 5 (b) 34, 486 (c) 34, 55. (a) (i) (b) % (a) 3 cm (b) 550 cm 3 (c) kg 4. (a) x {1,, 3, 4, 5} (b) (5, 1) 5. (a) 1, 8 (b) 1 65, (a) 9 (b) 10 5 (c) 1 6, 4 1 (d) 0 35 x 85 (e) 0 9, 3 6 SEC Papers , Paper 1 & 7. (a) (i) 5 00 hours, 9 00 hours, 7 75 hours 8 5 hours, 39 hours, hours (iii) (iv) (b) (i) Time (hours) Number of thousands of bacteria Foundation Level, SEC Papers , Paper 1 & 65

66 Number of bacteria, in thousands Time in hours (iii) 5600 hours (iv) 14:34 8. (a), (b) y Received in dollars x Paid in euro 66 Mathematics Leaving Certificate

67 (c) $91 (d) 67 (e) 1 3, (5, 0) (f) up by $13 (g) 1 = $1 3, 5 (h) Frank (i) Olga and Deirdre SET C 01 SEC Paper 1. (a) E, B, A, C, B, A (b) Mean = 680, Median = 800, Difference = 10. (a) 6 (b) 1 6 (c) 1 3 (d) (a) (b) 30, 54 (c) Thursday of the second week 4. (a) A( 1, 6), B( 3, ), C(4, 5) (b) Midpoint of [BC] = ( 1, 3 ) (c) 4 (d) Yes (b) Yes (c) 6A. (a) (b) 10 (c) PQR = 10 S R SEC Papers , Paper 1 & P Q 6B. (a) 90 (b) 15 (c) ΔOAB, ΔOBC (d) 74 (e) (a) (i) Hours spent studying Number of students Foundation Level, SEC Papers , Paper 1 & 67

68 (iii) = 1 student Number of students Hours spent studying (iv) 5 (b) (i) 4 1 4, 1 1, (a) (i) 4 x 8 84 cm 56 cm (iii) 8 cm (b) (i) 74 cm 11 (c) 3 m 68 Mathematics Leaving Certificate

69 1. (a) Rational Irrational π 3 14 SET D 011 SEC Paper 1 (b) 0 1 (c) (i) 93,000,000, billion. (a) 0 08 (b) (a) cm 3 (b) 8 74 cm 4. (a) 4 (b) (a) 11, 1 (b) 4 11, (a) Year Value ( ) (a) (c) (i) 40 3 years (b) (iii) 00 (b) (i) Price per clock ( ) Number sold SEC Papers , Paper 1 & Number sold Price per clock ( ) Foundation Level, SEC Papers , Paper 1 & 69

70 (c) 130 (d) (e) Charlie. It is the only equation which gives n = 300 when x = 15. (f) Charlie s formula expanded out. 8. (b) (i) (iii) 7, (iv) 0 5 x 3 SET D 011 SEC Paper 1. (a) Tossing an unbiased coin once: head, tail (b) Tossing a biased coin: head, tail. (a) (3, 1) (, ) (4, 7) (b) 100 (d) (a) 8 8 mm (b) 7 mm (c) Two peaks 4. (a) y 6 C 4 A x 4 B 6 (b) Slope AB: Slope AC: 1 (c) Slope AB Slope AC = 1 70 Mathematics Leaving Certificate

71 5. (a) A (1, 0), B (0, 5) (b) y 5 B P(5, 3) 6A. (b) B. (a) (i) (b) s = 36, t = 7 7. (a) 00 A 1 x SEC Papers , Paper 1 & (b) birth-weight/kg Foundation Level, SEC Papers , Paper 1 & 71

72 (c) 3 3 kg (d) Above average (e) 9 (f) (g) (a) (i) O 3 cm 1 5 cm (iii) 8 4 cm (iv) (b) (i) 4 1 cm Mathematics Leaving Certificate