Practice questions 2.6
1. (i) Using graph, x = 1 and y = 7 (ii) Using graph, x = 2 and y = 5 (iii) Using graph, x = 1 y = 5 (iv) Using graph, x = 0.5 and y = 3.5
2. (i) Using graph, x = 1 and y = –2 (ii) Using graph, x = 1 and y = –2 (iii) Using graph, x = 1 and y = 1 (iv) Using graph, x = 2 and y = –1
3. (i) x = 8, y = 7 (ii) x = 46, y = 17 (iii) x = 14, y = 3 (iv) x = 15, y = 23
4. (i) x = 1, y = 5 (ii) x = 0, y = 5 (iii) x = 9, y = 12 (iv) x = 7, y = 3
5. (i) x = 7, y = 4 (ii) x = 24, y = −6 (iii) x = 9, y = 2 (iv) x = 15, y = 12
6. (i) x = 2, y = 4 (ii) x = −4, y = −6 (iii) x = 5, y = −2 (iv) x = 14, y = 3
7. x = 159, y = 202 8. (i) x + y = 23 x − y = 15
(ii) x = 19, y = 4
9. (i) x + y = 98 x − y = 20
(ii) x = 59, y = 39
10.(i) x + y = 74 x − y = 60
(ii) x = 67, y = 7
11.(i) 2a + 2c = 40 a + 5c = 52
(ii) Child’s ticket = €8 Adult ticket = €12
12.Child’s ticket = €28⋅15 Adult ticket = €60⋅10
13.l = 550⋅75m, b = 521⋅75m 14.x = 47, y = 36
Practice questions 2.7
1. (i) −30 (ii) 12 (iii) −3 (iv) 9
2. (i) 16 (ii) 28 (iii) −2 (iv) 4
3. (i) €12 (ii) €14 (iii) 11.6 km (iv) 2
4. (ii) €950 (iii) 18
5. (ii) €360 (iii) €516 (iv) 7 hours (v) 5 hours (vi) Ben (vii) Cathal
9. (i) 150 minutes or 2 hours 30 minutes
11.(i) 12.(a)
(ii) 3.25 kg (iii) (3, 7)
(b) (1, 1)
13.(i) 2 (ii) 1
(iii) −1
__ 5
14.(i) Slope = −2, y-intercept (0, 6) (ii) Slope = 5, y-intercept (0, −9) (iii) Slope = 5, y-intercept (0, 3
__ 4)
15.(i) Slope = −3, y-intercept (0, 6) (ii) Slope = 8
__ 9, y-intercept (0, 4)
(iii) Slope = 36, y-intercept (0, −21)
16.(ii) Glentiesphon (iii) (333, 2 000) (iv) Literphon would be cheaper
17.(ii) Slope = 23 (iii) y = 15 + 23 (iv) y = 5 + 24
__ 20
__ 20 x or 20y = 300 + 23x
__ 20 x or 20y = 100 + 24x
(v) $200 18.(ii) End of third month
Revision questions 2A Core skills
1. (i) 2x + 5y (ii) x − 23 (iii) −2x − 3y (iv) 2x − 2 (v) a + 4b (vi) 11x2
2. (i) x2 (ii) x2 (iii) x2
(iv) 2x2 (v) x2
(vi) 6x2 3. (i) (ii)
(iii) (iv)
(a) 3, 5, 7, 9, 11; (b) 1, 4, 7, 10, 13
(i) 10, 7, 4, 1, −2 (ii) 4, 3, 2, 1, 0
8. (i) (ii)
(a) 5, 9, 13, 17, 21 (b) Tn
= 4n + 5 (c) 101
(a) 12, 24, 36, 48, 60 (b) Tn
= 12n + 12 (c) 300
(iii) (a) 15, 30, 45, 60 (b) Tn
(c) 375
(iv) (a) 13, 26, 39, 52, 65 (b) Tn
= 13n + 13 (c) 325 (v)
(a) 11, 31, 51, 71 (b) Tn
(c) 491
(vi) (a) 9, 4, –1, –6 (b) Tn
(c) −111 9. (i) 3rd term = 18
(ii) 2nd term = 7 (iii) 2nd term = 22 (iv) 3rd term = 2.5 (v) 2nd term = −1 (vi) 2nd term = −13
10.(ii) Pattern is linear (iii) Tn
= n + 4 (iv) 53
11.(i) n = 3 (ii) a = 1 (iii) k = 6 (iv) x = −11 (v) x = 7
(vi) x = 3
12.(i) x = 13 (ii) x = 1
__ 7
13.(i) x = 2, y = 3 (ii) x = 6.5, y = −3.5 (iii) x = 19, y = 74
− 2x
+ 4x − 5 − 9
− x − 2 − 2
− 4
__________ (x − 8)(x + 3)
__________ (x − 4)(x + 4)
__________ (x − 3)(x + 3)
4. (i) 3a2 (ii)
5. (i)
__________ (x − 6)(x − 3)
7x − 12 2x + 18 −12
y2 (4y − 5a) (4x − 5)(3y − 7) (ii)
(iii) (4a − 5b)(u + 6v) (iv) (x + 3n)(7y − 1) (a + b)(x + y) (x + 3)(x − 2y)
(iii) (3y + 2)(y2
6. (i) x = y − 3 (ii) x = 2 − y (iii) 9C
6. (ii) 120 km, 2.5 hours 7. (i) 1 minutes 40 seconds (ii) 9 donuts
8. (i) 6 tonnes (ii) 61 cartons
370 Linking Thinking 2
____ 4
____ 5
___ 5 + 32 = F
_____ 1 − kn
(iv) x = √ − y2 (v) m = n2
_ w2
7. (iv) is the linear pattern − 2) (iv) (a + b)(b − c)
− 11x + 3 3x − 2
(iv) x = 1, y = 1
__ 2
14.(i) x = 8, y = 7 (ii) x = 46, y = 17 (iii) x = 0.5, y = 6 (iv) x = −7, y = −18.5
15.(i) 17 (ii) 33 (iii) −3 = a (iv) 12 = a
17.Distance = 90 × time 18 (i) True (ii) False (iii) False (iv) False
2B Taking it further
1. (i) €955 (ii) 23 images complete
2. (i) 336 = 132 + 12x (ii) 17
3. (i) 2(x + 3) = 20 (ii) 7
4. (i) 6x = 90 (ii) €15
5. (i) 216 = 8x (ii) €27
6. 5 = n 7. Slopes of both lines = 3 parallel
8. (i) h = V (ii) 11.2
___ πr2
9. 8.75(75 000) + 16 500 = €1 329 000
__ 5, they are
= −5n + 9 = 20n + 11 = 15n + 15
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