Shubharambha OPT Mathematics 10 Final for CTP 2077

Exercise 2.1 (b) Rs. 2100

4. (a) 22mm

Exercise 2.3

3. (a) 4 (b) 5 (c) 6

4. (a) 5 (b) 7 (c) 4

5. (a) (i) 3 (ii) 3 (iii) 3 (iv) 3 (v) continuous at x = 1

(b) (i) 8 (ii) 8 (iii) 8 (iv) continuous at x = 2

7. (a) not continuous at x = 1 (b) continuous at x = 4

Exercise 3.1 (b) – 10 (c) – 32 (d) 1 (e) 0
(g) b2 – a2 (h) 1 (i) – 1 (d) 1 – a
1. (a) 4 (b) 7 – 12 m
(f) – 12 (c) (c) 15
(b) 2, 0
2. (a) – 3 – 1, 5 (d) 1
(e) – (x + 1) 2 1, – 6

4. (a) 2

(e) 3

5. (c) 2 –7 (d) 0, –7/3
6. (a) 9
–1,
(f)
7. (a) – 141 (b) 16 (c) 0 (d) 196 (e) 162
10. (a) – 2 – 7 , 15
150 (g) 0 (h) – 51 – 4 (d) 30 (e) 2
(d) x = 2, y = – 7
11. (a) 7 (b) 2 (c) (c)
3
13. (a) (b) x = – 2, y = 2

x = 4, y = 1 (e) x = 2, 0, y = 1, – 1
2 5

A singular matrix has no inverse. (c) x = 8 (d) y = 1, 6

–5 4 (b) 4 – 5 (c) 2 –1
77
9 –7 3 –4 –3 5
77

(d) 10 (e) – 8 5
2 3 –2
14. (a)
–2 1
15. (a) 33
16. (a)
44 – 31
(d) – 17 12

7 , 3 (b) –1, 2 (c) 18 – 1 (d) 3, 3 (e) – 3, 7
5 5 7, 7
(c) 3, 2
No solution (b) No solution (g) 6, 10

1 , 2 (e) 4, 5 (f) 1, 0
3 3

Infinity Optional Mathematics Book - 10 351

(h) 3, 2 (i) 8, –4 (j) 1183, 3 (k) – 1, 2 (l) 5, –1
13 2

(m) 2, 3 (n) 7 (o) 3 (p) 2, 3 (q) 1 , 1
(r) (s) 4, 3 3 2
17. (a)
1 , 1 (t) 2, 3
4 3

3, 2 (b) 1 , 2 (c) 3, 2 (d) – 1, 2 (e) 1, 0
3 3

Exercise 4.1

1. (a) θ = tan-1 ± m1 – m2 (b) m1 = m2, m1.m2 =–1
1+ m1m2

(c) – 3 (d) (3, 5), 2
8

2. (a) 23 (b) 78 (c) tanθ = ± a–b
1 + ab

3. (a) 36.87° (b) 60° (c) 60°

4. (a) tan-1 – 2 (b) 120° (c) tan-1 – 5
11 (b) 45°, 135° 12

5. (a) 60°, 120° (c) 60°, 120°

10. (a) 6 (b) –3 (c) 0

11. (a) 78 (b) – 251 (c) 172
4x – 3y – 32 = 0
12. (a) 2x + y – 14 = 0 (b) 5x + 3y – 16 = 0 (c) 3x + 5y + 19 = 0
13. (a) 5x + 4y + 25 = 0
14. (a) 5x + 8y – 40 = 0 (b) 7x + 5y – 41 = 0 (c) 7x + 6y – 1 = 0
(d)
(b) 5x + 4y + 12 = 0 (c) 6x + 5y – 18 = 0

15. (a) 2x + 3y – 12 = 0 (b) x – 3y – 5 = 0 (c) 4x + 3y – 11 = 0

(d) 7x + 6y – 20 = 0

16. (a) 2x – y – 1 = 0, x + 2y – 8 = 0

(b) y + 2 = 0, 3 x – y – (3( 3 + 2) = 0

(c) (2 – 3 ) x – y = 0, (2 + 3 ) x – y = 0

17. (a) 6x – 7y + 26 = 0 (b) 3x – y – 14 = 0 (c) x + 2y – 8 = 0 (d) x + 2y – 5 = 0

18. (a) 4x – y + 12 = 0 (b) x + y – 12 = 0
19. (a) 1, –1
20. (a) 6x – 3y – 4 = 0 (b) 1 , 1
3 3

(b) 15x – 3y – 22 = 0

21. (a) 12x + 3y – 4 = 0 (b) x – y + 1 = 0

Exercise 4.2

1. (a) θ = tan-1 ± 2 h2 – ab
a+b

352 Infinity Optional Mathematics Book - 10

2. (a) a + b = 0 (b) h2 = ab (c) 2x + 3y + 1 = 0, 4x – y = 0

3. (a) 3x2 + xy – 2y2 = 0 (b) 10x2 – 23xy – 42y2 = 0

(c) 6x2 + 7xy – 3y2 – 8x – 23y – 14 = 0 (d) abx2 + (a2 – b2) xy – aby2 = 0

(e) x2 + 2xy cosecθ + y2 = 0 (f) x2 + 2xysecθ + y2 = 0

4. (a) x + y = 0, 4x + y = 0 (b) x + y = 0, 3x + 2y = 0

(c) x + y = 0, 3x – 4y = 0 (d) x – y = 0, 3x – y = 0

5. (a) x + y + 1 = 0, x – y = 0 (b) x – y = 0, x + y – 3 = 0

(c) x – 2y = 0, 3x + y – 1 = 0 (d) x – 3y = 0, x – 3y – 1 = 0

(e) x – 4 = 0, y – 5 = 0 (f) ax + b = 0, bx + a = 0

6. (a) 59.04°, 120.96° (b) 45°, 135° (c) 90° – α
(d) α, 180° – α
(e) tan-1 ± 1
3
7
9. (a) 6 (b) –12 (c) 2 (d) – 3

10. (a) – 95 (b) 5 (c) 1, – 1 (d) 16
2

11. (a) 2x + y = 0, x + 3y = 0, 45° or 135°

(b) x + 2y = 0, x + 7y = 0, tan-1 ± 1
3

12. (a) x – 3y + 4 = 0, 2x – y + 3 = 0 (b) x – 3y + 4 = 0, 2x + y – 5 = 0

13. (a) x + y(secα + tanα) = 0, x + y(secα – tanα) = 0, θ = (± α)

(b) x – (cosecα + cotα)y = 0, x + (cosecα – cotα) y = 0, 90°

(c) x + y(tanθ + secθ) = 0, x + y(tanθ – secθ) = 0, 90°

(d) x – (cosecθ + cotθ) y = 0, x – (cosecθ – cotθ)y = 0, tan-1(± cotθ)

14. (a) x + 3y = 0, 3x – y = 0 (b) x – 2y = 0, 2x + y – 1 = 0

(c) 2x + 3y = 0, 2x + 3y = 0

15. (a) 3x2 + 2xy – y2 = 0 (b) 6x2 – 13xy + 6y2 = 0

(c) 5x2 + 7xy + 2y2 = 0 (d) 5x2 – 3xy – 2y2 = 0

16. (a) 5x2 – 8xy – 4y2 + 42x + 24y – 27 = 0

(b) 5x2 + 8xy + 3y2 – 44x – 34y + 95 = 0

17. (a) 7, 2x + y = 0, x + 3y = 0 (b) 0, 6

Exercise 4.3 (b) Circle (c) Ellipse (d) Hyperbola
(e) Circle (d) hyperbola
1. (a) Hyperbola (b) Ellipse (c) Parabola
(d) Parabola (b) Ellipse (c) Parabola
2. (a) Circle
4. (a) Circle

Exercise 4.4

1. (a) x2 + y2 = a2 (b) (x – p)2 + (y – q)2 = r2
(–g, –k), g2 + f2 – c
(c) (x – x1) (x – x2) + (y – y1) (y – y2) = 0 (d)

Infinity Optional Mathematics Book - 10 353

2. (a) x2 + y2 = 4 (b) 6 2 units
3. (a) 90° (b) x and y coordinates of the centre of circle.
4. (a) x2 + y2 = 36 (b) x2 + y2 – 6x – 16 = 0
(c) x2 + y2 – 8y = 0 (d) x2 + y2 – 4x + 2y – 4 = 0
(e) x2 + y2 + 8x – 2y + 1 = 0 (f) x2 + y2 – 4x – 6y – 12 = 0
(g) x2 + y2 – 2ax – 2ay = 0
5. (a) x2 + y2 – 25 = 0 (b) x2 + y2 – 8x + 2y – 24 = 0
(c) x2 + y2 – 8x – 4y = 0
6. (a) x2 + y2 – 8x – 4y + 16 = 0 (d) x2 + y2 – 4x – 6y – 12 = 0
(c) x2 + y2 – 10x – 10y + 25 = 0
7. (a) x2 + y2 – 7x + 8 = 0 (b) x2 + y2 + 4x – 10y + 25 = 0
(c) x2 + y2 – 10x – 4y + 9 = 0
8. (a) (0, 0), 6 units (d) 4x2 + 4y2 – 20x + 20y + 25 = 0
(c) (–2, 3), 5 2 units
(e) (–5, 0), 11 units (b) x2 + y2 + 10x + 4y + 21 = 0
9. (a) (2, 0), 3 units
(d) x2 + y2 – ax + ay = 0

(b) (2, 4), 3 units

(d) (a, b), c units

(f) (0, 3), 2 3 units

(b) (0, 10), 5 units

(c) (2, 3), 5 units (d) – 25, – 3 , 3 units
2

(e) (3, –4), 5 units (f) (4, 0), 13 units

10. (a) – 1, 3 , 17 units (b) (1, –3), 2 units
2 2
21, 3 53, 2
(c) – 2 , 5 units (d) – 3 , 2 units

11. (a) (0, –2) (b) (–4, 2)

12. (a) x2 + y2 – 6x + 2y + 6 = 0 (b) x2 + y2 – 2x + 6y – 40 = 0
(c) x2 + y2 – 2x + 6y – 90 = 0 (d) x2 + y2 – 8x – 6y = 0
13. (a) x2 + y2 – 2x – 6y – 7 = 0 (b) x2 + y2 – 6x – 4y + 8 = 0
14. (a) x2 + y2 – 8x + 12y – 49 = 0 (b) x2 + y2 – 4x + 6y – 12 = 0
15. (a) x2 + y2 – 6x – 8y – 15 = 0 (b) x2 + y2 + 3x + 12y + 2 = 0
16. (a) x2 + y2 – 4x – 6y – 12 = 0 (b) x2 + y2 + 2x – 4y – 20 = 0
(c) x2 + y2 – 6x – 2y – 15 = 0 (d) x2 + y2 – 4y – 6 = 0
17. (a) x2 + y2 – 8x – 10y – 59 = 0 (b) x2 + y2 – 8x – 4y – 80 = 0
(c) x2 + y2 + 8x – 10y – 59 = 0
18. (a) x2 + y2 – 6x – 2y + 9 = 0 (b) x2 + y2 – 6x – 8y + 16 = 0

19. (a) 2 units (b) 2 2 units
20. (a) x2 + y2 + 6x – 8y + 9 = 0
(b) ± 24 (c) 4, 4

Exercise 5.1

1. (a) (i) 24 , 275, 24 (ii) 120 , – 119 , – 120 (iii) 24 , 275, 24
25 7 169 169 119 25 7

354 Infinity Optional Mathematics Book - 10

(b) (i) 1, 0, ∞ (ii) 1 , – 1 , –1 (iii) 1, 0, ∞

2 2

9. (a) 3sinq – 4sin3q (b) 4 cos3q – 3cosq (c) cot3q – 3 cotq
3 cot2q – 1

(d) 3tanq – tan3q (e) 1 – 8 cos2q + 8cos4q
1 – 3tan2q

Exercise 5.2

1. (a) 2245 , 275, 24 (b) 120 , – 119 , – 120 (c) 24 , – 275, – 24
7 169 169 119 25 7

2. (a) 1,0, ∞ (b) 1 , – 1 , –1 (c) 1 , – 1 , –1

2 2 2 2

Exercise 5.3 (b) 1 – sin40º 11
(c) 2 2 + cos10º
1 (e) sin 8 q + sin2 q (f) sin16 q – sin2 q
1. (a) 2 + sin 20º 1
(h) 2 (cos3A – cos21A) (c) 2cos6q.cos3q
(d) 21 (cos20º + 1) (f) – 2sin75º.sin35º
(g) sin12q – sin2q

2. (a) 2 cos25º (b) 2sin40º.cos15º
2. (d) – 2sin9q.sin2q (e) – 2cos10q.sinq
(g) 0 (h) 2sin75º.cos40º

Exercise 5.5

1. (a) 30°, 150° (b) 45°, 315° (c) 30°, 210° (d) 240°, 300°

(e) 60°, 240° (f) 225°, 315° (g) 135°, 315°

(h) 60°, 120°, 240°, 300° (i) 30°, 150°, 210°, 330° (j) 60°, 120°, 240°, 300°

(k) 60°, 120°, 240°, 300° (l) 45°, 135°, 225°, 315°

2. (a) 30°, 90°, 150° (b) 30°, 120°, 150° (c) 45°, 150° (d) 120°

(e) 0°, 30°, 150°, 180° (f) 30°, 150° (g) 30°, 150° (h) 45°, 135°

(i) 45°, 135° (j) 30°, 150° (k) 60°, 120° (l) 60°

(m) 0°, 60° (n) 30°, 150° (o) 120°, 0° (p) 60°, 135°

(q) 120°, 150° (r) 45°, 135° (s) 45° (t) 120°

3. (a) 10° (b) 10° (c) 5° (d) 15°, 45°

(e) 30°, 150° (f) 45°, 135° (g) 45° (h) 0°, 180°, 120°

(i) 45° (j) 0°, 45°, 180° (k) 60°, 90° (l) 0°, 180°

(m) 30°, 90°, 150° (n) 0°, 90° (o) 30° (p) 120°

4. (a) 0°, 90°, 360° (b) 105°, 15° (c) 90°, 330° (d) 90°, 150°

(e) 15°, 255° (f) 0°, 360° (g) 75°, 165° (h) 0°, 120°, 360°

Infinity Optional Mathematics Book - 10 355

(i) 0°, 360° (j) 60° (k) 120° (l) 15°, 195°
5. (a) 10°, 50°, 90°, 270°
(d) 0°, 180°, 270° (b) 45°, 60°, 135°, 300° (c) 0°, 45°, 180°, 315°, 360°
(g) 18°, 90°, 270°
(e) 45°, 120°, 135°, 225°, 240° (f) 0°, 90°, 360°

Exercise 5.6

1. (a) 69.28m (b) 30.72m (c) 96.6m (d) 55.98m

(e) 60º, 37.72m

2. (a) 157.73m (b) 230.9m (c) 273.2 m (d) 315.47m

(e) 50.72m

3. (a) 68.3m (b) 236.6m (c) 273.2m (d) 42.3m

(e) 819.67m (f) 2.366km (g) 146.4m (h) 320ft

(i) 106.47 m (k) 18.3 m (l) 68.3m, 68.3m (m) 29.28m

(n) 9.56 m (o) 6.28m (p) 62m, 43.92m

(q) 73.2m

4. (a) 84.53 m (b) 42.26m (c) 60 m (d) 473.2 m

(e) 40.98 m (f) 546.4m (g) 118.3 m, 68.3 m (h) 59.15m, 59.15m

(i) 81.96m. (j) 40m (k) 30° (l) 28.28 m

5. (a) 8.66 m (b) 21.65m,12.5m away from one of the houses

(c) 39.32m (d) 47.32m, 94.64m (e) 47.32m

6 (a) 3m (b) 15m (c) 24m (d) 12m

(e) 178.89m (f) 20.125m (g) 19m (h) 60°

(i) 37.32m (j) 34.64m (k) 623.5 km/hr.

(l) 264.1 m/sec (m) 30º (n) 30°, 28.87 m

Exercise 6.1

1. (c) 45 (d) 36 (e) 10

2. (a) 10 (b) 22 (c) 3 (d) –26 3. (a) 7

4. (a) 60° (b) 30° (c) 90° (d) 90 ° (e) cos-1 11
(f) cos-1 5
8. (a) –3 1
65 7. (a) m = –2 (b) p = –10

(b) 3 (c) x = 4 9. (a) a2 = 13, b2 = 10

10. (a) 6 (b) – 10 12. (a) 60°

13. (a) 60° (b) 60° 15. ∠ABC

Exercise 6.2

1. (a) MN = 1 BC , MN //BC (b) 90° (c) EF ⊥GF.
2

356 Infinity Optional Mathematics Book - 10

2. (a) 2i – 5j (b) 5i + 6j (c) (6, –3) (d) i

3. (a) 12 i – j (b) 251, 158 (d) –331, 2
5

4. (a) 5 (2 i + j ) (b) (1, 2) (c) – i – 10 j
3 3

6. (a) 3b – 2a (b) a – b + c (c) 31(2a + b)

Exercise 7.1

2. (a) A''(–2, –7) (b) B''(–5, –3) (c) P''(3, 2) (d) (–2, 4)
3. (a)
4. (a) (5, 3) (b) A''(–1, 8) (c) P''(–2, 9) (d) (8, 5)
(e)
5. (a) (5, –2) (b) (–3, 3) (c) (0, 5) (d) (–2, –5)
6. (a)
(b) (–6, –4) (f) (3, 6)
(c)
7. (a) R[(0, 0), +90°], A(3, 2) (b) (5, –6) (c) (–2, 3) (d) 3

(b) A'(1, –2), B'(4, 1), C'(2, –5); A''(–1, –2), B''(–4, 1), C''(–2, –5)

(c) M'(–4, 3), N'(–1, –2), O'(–6, –1); M''(–4, –7), N''(–1, –2), O''(–6, –3)

A'(2, 6), B'(2, 10), C'(4, 11), D'(4, 5); A''(2, –6), B''(2, –10), C''(4, –11), D''(4, –5)

A'(–4, 3), B'(–6, 5), C'(–3, 5); A''(–4, 1), B''(–6, –1), C''(–3, –1); R[(–1, 2), 180°]

X'(–2, 0), Y'(0, 2), Z'(–2, 3); X''(4, 0), Y''(2, 2), Z''(4, 3); Translation by T = 8 .
0

P'(0, 1), Q'(–1, 2), R'(–3, –4); P''(–1, 0), Q''(–2, 1), R''(4, 3); R[(0, 0), +90°]

8. (a) R[(0, 0), 180°], P'(–4, –3), Q'(–1, –1), R'(–5, 1)

(b) R[(0, 0), +90°], A'(–2, 2), B'(–2, 6), C'(–4, 7), D'(–4, 3)
(c) Translation by vector T = 0 ; E' (2, –1), F'(–1, 6), G'(3, 7)

2

Exercise 7.2

3. (a) A''(–2, 5) (b) (8, –6)

4. (a) A''(–6, –3) (b) B''(5, –3)

5. (a) (–3, 1) (b) (–5, 8) (c) (–9, –4) (d) (–2, 3)

(e) (1, –4) (f) (–2, –6)

6. (a) (–2, –5) (b) A(3, –4)

7. (a) A'(3, –2), B'(1, –5), C'(4, –6); A''(–3, 2), B''(–1, 5), C''(–4, 6); R[(0, 0), +90°]

(b) P'(6, 3), Q'(2, 3), R'(3, 0); P''(–3, 6), Q''(–3, 2), R''(0, 3); R[(0, 0), –90°]

8. (a) R[(0, 0), +90°]; A'(–5, 2), B'(–2, –6), C'(0, –4), D'(–3, –4)

(c) R[(0, 0), –90°]; W'(1, –5), X'(–3, 4), Y'(3, 2), Z'(2, –3)

Exercise 7.3 (b) B''(–4, –2) 3. (a) (–1, 10) (b) P'(3, –1)
(b) (0, 10)
2. (a) A''(3, 8)
4. (a) 6, 4

Infinity Optional Mathematics Book - 10 357

5. (a) P'(3, 2), Q'(0, 5), R'(4, 6); P''(3, –1), Q''(0, 2), R''(4, 3)
(b) A'(–5, 3), B'(–8, 5), C'(0, 4); A''(–7, 2), B''(–10, 4), C''(–2, 3)

6. (a) E'(–4, 8), F'(–4, 6), G'(0, 6) (b) P'(0, 4), Q'(3, 4), R'(3, 5), S'(0, 5)

Exercise 7.4

2. (a) A'(6, –9) (b) B'(9, –18) 3. ( a) M'(–3, –2) (b) N'(24, 23)
4. (a)
6. (a) (–5, –7) (b) (32, 52) 5. (a) (1, –3) (b) (1, 2)
7. (a)
8. (a) A'(–12, –4), B'(–4, –6), C'(–8, –10) (b) P'(6, 12), Q'(12, –6), R'(12, 0)
(b)
X'(7, 0), Y'(–5, 6), Z'(1, –4) (b) A'(–7, 12), B'(–11, –8), C'(–11, –4)

A'(–2, 0), B'(–4, –2), C'(–6, 2); A''(–2, 0), B''(–4, –2), C''(–6, 2)

O'(0, 3), A'(4, 3), B'(6, 5), C'(2, 5); O''(0, 9), A''(12, 9), B''(18, 15), C''(6, 15)

Exercise 7.5

2. (a) (–3, 4), (–4, –3) (b) A'(–1, –3), A''(–3, –4) (c) A'(4, –1), A''(12, –3)

3. (a) A'(–6, –3), A''(–6, 3) (b) (–3, –4), (–1, 1) (c) B'(3, 5), B''(3, 5)

4. (a) F'(2, 8), F''(–2, 8) (b) A'(4, –8), A''(10, 0) (c) M'(–8, 3), M''(–3, –8)

5. (a) A(11, –9) (b) (4, 3) (c) 3, 0

6. ( a) A'(–5, –6), B'(–7, –4), C'(–9, –6); A''(–6, –5), B''(–4, –7), C''(–6, –9)

(b) P'(0, –2), Q'(1, –3), R'(1, –1); P''(2, 0), Q''(3, –1), R''(1, –1)

(c) D'(2, –1), E'(5, –3), F'(7, 1); D''(4, –2), E''(10, –6), F''(14, 2)

7. (a) A'(–2, –1), B'(4, –3), C'(0, 4); A''(–3, 2), B''(3, 0), C''(–1, 7)

(b) M'(–3, –1), N'(–1, 4), O'(–5, 2); M''(–6, –2), N''(–2, 8), O''(–10, 4)

(c) P'(0, –6), Q'(4, 6), R'(–10, –2); P''(4, –1), Q''(8, 11), R''(–6, 3)

Exercise 7.6

3. (a) 3 units (b) 6 units (c) 3.2 units
4

4. (a) A'(0, 3), B' –2198, 45 (b) (3,4), (6,8)
29

5. (a) P' (14, 15), Q' –38 , 27 (b) –223, 31 , (–2, 7)
41 41 2

6. (a) M' 6, –1 , N'(–3, –1) (b) (–5, 3) , –2361, 105
2 26

Exercise 7.7

3. (a) A'(3, 5), B'(–5, 4) (b) A'(4, 4), B'(–4, 3)

(c) A'(0, 7), B'(–8, 6) (d) A'(–1, 0), B'(–9, –1)

4. (a) 2 , (5, –2) (b) 3 , A'(7, 1)
–3 –4

5. (a) 0 1 (b) 01 –10
–1 0

6. (a) 3 0 , (6, 15) (b) 1 –1 , (–6, –17)
0 3 2 3

358 Infinity Optional Mathematics Book - 10

7. (a) 0 –1 , A'(5, –3) (b) 0 1 , (–9, 8)
–1 0 –1 0

8. (a) Reflection on x-axis, A'(–2, –5) (b) E[(0, 0), –2], (6, –18)

9. (a) –5, –4 (b) –1, –14

11. (a) P'( 4,7), Q'(6, 11), R'(10, 17), S'(8, 13) (b) A'(–3, 3), B'(–9, –2), C'(0, –6)

12. (a) (0, 0), (4, 1), (6, 3), (2, 2) (b) (0, 0), (1, 3), (2, 5), (1, 2)

13. (a) 6 2 (b) 20 20
14. (a) 2 4
15. (a)
1 0 , Reflection on x-axis. (b) 0 1 , Reflection on y = x.
0 –1 1 0

1 0 (b) 10 –01
0 1

Exercise 8.1

4. (a) 20, 0.36 (b) 12.5, 0.33 5. (a) 50, 0.11 (b) 42, 0.14
6. (a) 20, 50 (b) 30, 58 7. (a) 27, 18 (b) 38.66, 18.66
8. (a) 14, 0.4 (b) 6.86, 0.18 (c) 2.32, 0.13 (d) 201.5
9. (a) 1.255 (b) 16, 0.36
10. (a) 10.23, 0.33 (b) 10.09, 0.33 (c) 10.72 yrs, 0.34

11. B has more variable.

Exercise 8.2

4. (a) 5.6, 0.1867 (b) 24.5, 0.45

5. 0.64, 0.64

6. (a) 11.667, 0.259 (b) 7.27, 0.21 (c) 503.59, 0.401 (d) 9.56, 0.34

7. (a) 9.44, 0.303 (b) 11.6, 0.09 (c) 6.56, 0.29

8. (a) 10.08, 0.30 (b) 10.3, 0.37 (c) 10.52, 0.25

9. (a) 9.44, 0.36 (From mean) (b) 11.8, 0.295 (From median)

10. (a) 11.13, 0.45 (b) 12.4, 0.243, 12.3, 0.23

11. 13, 0.43

Exercise 8.3

3. (a) 4.049 (b) 2.37, 0.1185
4. (a)
5. (a) 2.68 (b) 1.73, 2.9929 (c) 12.37
(c)
6. (a) 15.48, 0.28 (b) 12.96, 0.41
7. (a)
8. (a) 28.35, 0.19 (d) 12.96, 0.42
(b)
272.20, 44.45% (b) Rs. 111.43, 21.35% (c) Rs. 11.88. 52.1%

11.458, 0.502, 50.2% (b) 12.96, 0.42, 42%

(i) 4.8, 4.6 (ii) P shows greater consistency because c.v of p is less than c.v of Q.

(i) A (ii) B

Infinity Optional Mathematics Book - 10 359

360 Infinity Optional Mathematics Book - 10 Specification Grid

Knowledge Understanding Application Higher
Ability
S.N. Contents Each 5 Total Total
Marks Questions Marks
Each 1 Each 2 Marks Each 4 Marks
Marks 1 8 21
25
1 Algebra 23 2 1 49
6 15
2. Limit and Continuity 1 1 1 8 20
1 4 10
3. Matrix 12 1 3 10
4 3 10
4. Co-ordinate Geometry 2 2 1 20 38
100 100
5. Trigonometry 23 3

6. Vectors 12

7. Transformation 1 1

8. Statistics 1 2
Total 10 13 11
Marks 10 26 44