(iii) Always true, the null set is always a subset


(iv) Never true, all elements are in universal set


Practice questions 24.2 1. (ii) 15, (iii) 14, (iv) 26, (v) 20 2. (ii) 9, (iii) 15, (iv) 6


_ 24 = 25%


5. (ii) 95, (iii) 0


_ 100 = 0


_ 40 = 1


_ 2


3. (ii) 10, (iii) 14, (iv) 25% 4. (ii) 95, (iii) 25, (iv) 62.5%, (v) 165


_ 320 = 33


6. (ii) 25%, (iii) 15%, (iv) 30 people


Practice questions 24.3 3. (i) {3, 4, 5, 6, 7, 8, 9} (ii) {7, 8, 9, 10, 11, 12} (iii) [3, 4, 5, 6, 7, 8, 9, 10, 11, 12} (iv) {7, 8, 9} (v) {10, 11, 12, 13, 14} (vi) {3, 4, 5, 6, 13, 14} (vii) {10, 11, 12} (viii) {3, 4, 5, 6} (ix) {3, 4, 5, 6, 10, 11, 12, 13, 14} (x) ∅


4. (i) {2, 3, 4, 5, 7, 11} (ii) {2, 4, 6, 8, 10, 12, 14} (iii) {1, 4, 6, 8, 9, 10, 12, 14, 15} (iv) {1, 2, 3, 5, 7, 9, 11, 13, 15} (v) {1, 15} (vi) {3, 5, 7, 11, 13} (vii) {1, 2, 3, 5, 7, 9, 11, 13, 15} (viii) {1, 9, 15}


5. (i) People use WhatsUp or ShareChat (ii) People who use WhatsUp but not ShareChat


(iii) People who have a mobile phone and do not use WhatsUp


(iv) People who have a mobile phone and do not use ShareChat


(v) People who have a mobile phone and do not use ShareChat or WhatsUp


6. (i) 31, (ii) 12, (iii) 18, (iv) 11, (v) 8


7. (ii) 55, (iii) 30, (iv) 15 8. (ii) 9, (iii) 34, (iv) 35


9. (ii) {2, 6, 10, 14, 18, 22} (iii) {4, 8, 16, 20, 2, 10, 14, 22} (iv) {4, 8, 16, 20} (v) {2, 10, 14, 22} (vi) 3


_ 80 = 44%


10.(ii) 23, (iii) 21, (iv) 50 11.(ii) 6 , (iii) 21


_ 29


12.A(iii), B5(v), C(i), D(ii), E(iv)


_ 35


Revision questions 24A Core skills


1. (ii) 60 (iii) 40 (iv) 20 (v) 90% (vi) Any valid mathematical answer, e.g. give each student in the college a number and randomly select the numbers to be surveyed


586 Linking Thinking 1


_ 107


(vi) People who have a mobile phone and do not use ShareChat and WhatsUp


_ 31


_ 64


2. (ii) 40, (iii) 10, (iv) 50, (v) 50


3. 30 videos 4. (i) 50, (ii) 24


5. 35 6. (i) 2


7. (ii) 300 (iii) 800 (iv) 600 (v) The number of people who listen to the news but don’t listen to music


__ 6 = 1


__ 3, (ii) 2


__ 3, (iii) 2, (iv) 100%


9. Set A = {1,2,3} and set B ={4, 5}


24B Taking it further 1. (i) Categorical data, (iii) 10, (iv) 80, (v) 20, (vi) 30


3. (i)


(a) {1, 2, 3, 4, 5, 6, 7, 8, 9} (b) Null set (c) {1, 3, 5, 7, 9} (d) #=5


4. (i) x = 10, (ii) 18, (iii) 44, (iv) 6 5. Numerous valid answers 6. Numerous valid answers, e.g. A = 3, B = 2, C = 8, D = 10


7. Numerous valid answers, e.g. A = length 9, width 3; B = length 8, width 4; C = length 9, width 5; D = length 3, width 4


8. Numerous valid answers, e.g. A = 0·45, B = 0·4, C = 0·35, D = 0·15


9. (ii) Numerous valid answers, e.g. {30, 45, 60}


10.(ii) 5 (iii) 37


11.(i) False, (ii) True, (iii) False, (iv) True, (v) True, (vi) False (any valid mathematical justification for questions accepted)


_ 50


Unit 25 Linking Thinking revision material


Questions 1. (a)


(i) 3 200 min (ii) 1200 min (iii) 290 min (iv) 16


2. (a)


(b) (i) 126 (ii) 116 815 (iii) €6 136.20 (i) 107


m2 (ii) 2·2 × 104 m


(iii) The rules can be applied to the product of two values, but cannot be applied to the sum of two values


(b) (i) Opposite angles in a parallelogram are equal in measure


3. (a)


(ii) 21˚ (iii) 50˚ (i)


10.(a)


(a) Cost = 28 + 0·45x (b) Cost = 40 + 0·20x


(ii) Plan A: 28, 34·75, 41·5, 48·25, 55, 61·75, 68·5, 75·25 Plan B: 40, 43, 46, 49, 52, 55, 58, 61


(iv) 49 min (v) 48 min (vi) Algebraic method


(c) 11.(a) 6. (a)


_ 50 = 12


_ 25, (iii) 14


_ 100 = 1


_ 25, (iv) 2


_ 25


_ 2


(b) (i) €74·40 (ii) €90·02


(c) 4. (a)


(i) Categorical nominal; numerical discrete


(iii) Phone


(i) Diameter (ii) Radius (iii) Chord (iv) Arc


(b) (i) 5 cm (ii) 31·4 cm (iii) 78·5 cm2 (iv) 61%


(c) 90˚; an angle standing on a diameter of a circle is 90˚


5. (a)


(i) 960 m2 (ii) €79·96 (iii) 13·82 m; 15·21 m2 (iv) 1 419·03 m2 (v) 70 952 (vi) €53 214


(b) (i) 150 m (ii) 30 m


(i) 12:00 (ii) 687 km/hr


(b) $2 850 (c) 55% (d) 23˚


7. (a) 12 km (b) Ann’s distance (km): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Rachel’s distance (km): 0, 0·5, 1, 1·5, 2, 2·5, 3, 3·5, 4, 4·5, 5, 5·5, 6


(d) Ann: 1 (e) 1


speeds


__ 3, 1


(f) Ann: t__ 8. (a)


__ 6; the slopes are equal to the


__ 3 km/min; Rachel: 1


(g) Ann: 30 km; Rachel: 15 km 3 km; Rachel: t__ 6 km


(i) 2(3x + 2) + 2(2x + 5) = 64; 5 (ii) 17 cm, 15 cm (iii) 255 cm2


(b) (i) One thousand and twenty-four (ii) 210 (iii) 1·024 × 103 (iv) One million, forty-eight thousand, five hundred and seventy-six


(v) 220 (vi) 1·05 × 106


(c) 9. (a)


(i) 1 571 cm3 (iii) 83%


(d) (i) 9 (i)


l = 4w (ii) C


(b) (i) 1 × 105 (ii) 1 × 1011


(c)


(i) Numerical discrete and categorical nominal


(iii) 73 (iv) 170


(d) 64


(i) 2, –3 (ii) 4, 3 (iii) 2 × 2 × 2 × 2; –3 × –3 × –3 (iv) 16, –27


(b) (i) €298 (iii) 40·5 min


(ii) Hot tub (large)


(i) 250 m2 (ii) 2·5W (iii) W = 10 m, L = 25 m


__ 6 km/min


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