8. (i) 16 units2 (ii) 16 units (iii) Yes. Numerous valid answers, e.g. a rectangle with length of 2 and width of 8. Area = 16 units2


perimeter = 20 units. If it had a length of 1 and a width of 16, area would be 16 units2


but


perimeter would be 34 units. Area is the same, but perimeters are not.


(iv) 8 units × 2 units = 16 units2 16 units × 1 unit = 16 units2


(v)


(a) Largest perimeter = 34 units (b) Smallest perimeter = 16 units


(vi) False. It is possible to keep the same area and change the perimeter of a rectangle (see part (v) above).


Unit 2 Sets, number and chance


Practice questions 2.1 1. (i) {a, b, c, d, e} (ii)


{red, orange, yellow, green, blue, indigo, violet}


(iii) {a, p, l, e} (iv) {O, A} (v) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (vi) {September, October, November, December}


2. (i) Months of the year starting with ‘A’ (ii) Fingers on a hand (iii) Days of the week starting with ‘T’ (iv) First four planets of the solar system


3. 1 = C; 2 = A; 3 = B; 4 =E; 5 = D


4. (i) 2 ∈ℚ (ii) May ∉ {days of the week} (iii) #D = 8 (iv) {1, 2} ⊂ S (v) J = ∅ (vi) 2 ∉ {letters of the alphabet}


5. (i) A = B, the elements of A and B are the same


(ii) A ≠ B, the elements of A and B are not the same


(iii) A ≠ B, the elements of A and B are not the same


(iv) A ≠ B, the elements of A and B are not the same


6. All are sets except (ii) Justification: (i), (iii) and (iv) are a well- defined collection of objects with something in common but (ii) is not well-defined.


7. (i) B ⊄ A, (ii) C ⊂ A, (iii) B ⊄ C, (iv) C ⊂ C, (v)∅ ⊂ B, (vi) C ⊂ B


8. (i)


{1, 2, 3, 4, 5}; X = {x | x is one of the first 5 counting numbers}


(ii) {M, A, T, H, E, I, C, S}; X = {x | x is a letter in the word MATHEMATICS}


(iii) {2, 3, 4, 5, 6, 7}; set of numbers between 2 and 7 inclusive


9. (i) Always true (ii) Sometimes true (iii) Always true (iv) Never true


10. (i) True: 13 ∈ P, 9 ∈ P but 22 ∉ P (ii) True: 5 ∈ P, 7 ∈ P and 12 ∈ Q (iii) False: 3 ∈ P, 13 ∈ P but 10 ∈ Q (iv) True: 7 ∉ Q, 9 ∉ Q but 16 ∈ Q


, Practice questions 2.2.1


1. (i) {1, 2, 3, 6} (ii) {1, 3, 5, 15} (iii) {1, 3, 9, 27} (iv) {1, 2, 4, 5, 8, 10, 20, 40} (v) {1, 2, 4, 8, 16, 32, 64}


2. (i) {2, 4, 6, 8, 10 …} (ii) {3, 6, 9, 12, 15 …} (iii) {5, 10, 15, 20, 25 …} (iv) {6, 12, 18, 24, 30 …} (v) {8, 16, 24, 32, 40 …}


3. (i) {2, 3, 5, 7} (ii) {17, 19, 23} (iii) {101, 103, 107, 109}


4. (i) 2 × 3 × 3 (ii) 2 × 2 × 2 × 2 × 2 (iii) 2 × 2 × 2 × 5 (iv) 3 × 3 × 5 (v) 2 × 2 × 2 × 3 × 3 (vi) 2 × 2 × 2 × 2 × 3 × 3


5. (i) 2, (ii) 9, (iii) 6, (iv) 4, (v) 6, (vi) 4, (vii) 15, (viii) 2


6. (i) 20, (ii) 24, (iii) 18, (iv) 30, (v) 24, (vi) 12, (vii) 30, (viii) 24


7. (a)


(i) 60: 2× 2 × 3 × 5 (ii) 96: 2 × 2 × 2 × 2 × 2 × 3


(b) 12 (c) 480


8. 8 metres 9. 60th day 10. 3 pieces 11. (i) Even, e.g. LCM of 10 and 15 = 30 (ii) HCF is smaller number; LCM is larger number, e.g. 3 and 6: HCF = 3; LCM = 6


(iii) HCF = 1; LCM = product of the two numbers, e.g. 3 and 5: HCF = 1; LCM = 15


Practice questions 2.2.2 1. (i) False, e.g. −3 ∉ ℕ, not positive (ii) True, e.g. 3 ∈ ℚ, can be written as 3


(iii) False, e.g. −1 number


(v) True, e.g. 5 ∈ ℤ, ℕ ⊂ ℤ (vi) False, e.g. −3


__ 1


(vii) False, e.g. {1 __


not a whole number whole numbers


2, 1 __


__ 2 ∉ ℤ, not a whole


(iv) True, e.g. −3 ∈ ℚ, can be written as −3


__ 4 ∉ ℕ, negative and


3…} ⊄ ℤ, not


(viii) True, e.g. {1, 2, 3…} ⊂ ℤ, positive whole numbers


2. (i) {1, 2, 3, 4, 5} (ii) {11, 13, 17, 19} (iii) {–9, –7, –5, –3, –1, 1, 3, 5} (iv) {26, 28, 30, 32, 34} (v) {3, 6, 9, 12, 15, 18, 21, 24, 27} (vi) {1, 2, 4, 8, 16, 32}


3. (a)


(i) Positive whole numbers (ii) ℕ


(b) (i) Whole numbers, positive and negative


(ii) ℤ (c) 4. (i) 1


(i) Numbers that can be written as fractions


(ii) ℚ


5. (i) Sometimes true (ii) Sometimes true (iii) Always true (iv) Never true (v) Always true


__ 3, (ii) 1


__ 2, (iii) 1


__ 4, (iv) 1


__ 5


Practice questions 2.3


2. (i) A = {1, 2, 3, 5, 6, 9} (ii) B = {2, 3, 4, 5, 7, 8, 10} (iii) A∩B = {2, 3, 5} (iv) A∪B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (v) 핌 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}


3. (a)


(i) A = {a, b, e, h, q, t} (ii) B = { a, d, f, g, h, j} (iii) 핌 = {a, b, d, e, f, g, h, i, j, p, q, y, t}


(b) (i) 10 (ii) 2


7. (i) 12 people play both basketball and football


(ii) 52 people play basketball only (iii) 63 people play football only (iv) 8 people play neither basketball or football


(v) 115 (vi) 135


8. (i) 25, (ii) 7, (iii) 22, (iv) 47 9. (i) A: {1, 2, 3, 4, 6, 8, 12, 16, 24, 48} B: {1, 2, 4, 5, 10, 20}


(iii) The factors of both 48 and 20 (iv) 4


10. (i) (ii)


(a) 핌 (b) All of the elements


(a) H∪N (b) All of the elements in both H and N


__ 1


(iii) (a) H∩N (b) Elements in common between H and N


11. (a)


(i) P = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}


(ii) Q = {3, 6, 9, 12, 15, 18} (iii) P∪Q = {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}


(iv) P∩Q = {3, 9, 15}


(b) (i) 10 (ii) 6 (iii) 13 (iv) 3


12. (i) A = { 2, 3, 5, 7}, (ii) B = {2, 4, 6, 8}, (iv) A∪B = {2, 3, 4, 5, 6, 7, 8}, (v) 1, (vi) Yes, 2 ∈ A


Practice questions 2.4 1. (i) 1 (ii) 1 (iii) 1 (iv) 3 (v) 1


_ 2; 0·5;50%


_ 4; 0·25;25%


_ 4; 0·25;25%


_ 4; 0·75;75%


_ 6; 0·16˙ ; 162


_ 3%


566


Linking Thinking 1


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