Power of Maths: Paper 1 – Answers Exercise 2
1. (a) 3(x + 2y) (b) x(x + 3) (c) a(b – c) (d) 4x(x – 4y) (e) 3(x2 + 3x – 6) (f ) 3(x – 3y) (g) 8a2(1 – 2b2) (h) 7x2y (y – 2) (i) (x – 2y)(3 – 5x) ( j) (a + b)(m – 3n) 2. (a) (x + 2)(ax + 1) (b) (x + y)(a + b) (c) (a – b)(x + y) (d) (b + 7)(a – 3) (e) (p + 2q)(3n – a) (f ) (x + 1)(2x – 3y) (g) (x – 3)(2 – b) (h) (z – 2)(x2 + y2) (i) (3x – 2)(1 + 4y) ( j) (7 – ax2)(3 – 2b) 3. (a) (x + 7)(x + 5) (b) (x + 9)(x + 3) (c) (x + 9)(x + 2) (d) (x + 18)(x + 2) (e) (x + 18)(x + 3) (f ) (x – 5)(x – 10) (g) (x – 11)(x + 10) (h) (x + 11)(x – 10) (i) (x – 10)(x – 11) ( j) (x – 15)(x – 3) (k) (2x + 1)(x + 2) (l) (3x + 4)(2x + 5) (m) (4x + 7)(3x + 8) (n) (8x + 3)(2x + 5) (o) (3x – 2)(2x + 3) (p) (4x – 3)(3x + 2) (q) (3x – 8)(2x + 3) (r) (5x – 2)(x + 7) (s) (6x – 11)(2x + 3) (t) (7x – 2)(6x + 1) 4. (a) (x + 3y)(x + 2y) (b) (x + 7y)(x + 2y) (c) (x – 3y)(x – 2y) (d) (x – 2y)(x + 7y) (e) (5x – 1)(2x + 3) (f ) (2x + 5)(x – 3) (g) (7x – y)(x – 3y) (h) (2a + 3b)(a – b) (i) (6x – 1)(5x – 2) ( j) (bx + c)2 (k) (2p – 1)2 (l) (9x – 1)(2x + 3) 5. (a) (2x – 1)(2x +1) (b) (5x – y)(5x + y) (c) (3x – 4)(3x + 4) (d) (x – ab)(x + ab) (e) (2m – 9n)(2m + 9n) (f ) (x + y – z)(x + y + z) (g) (x + 1 – 3z)(x + 1 + 3z) (h) (Yoke – Thing)(Yoke + Thi ng) 6. (a) 200 (b) 600 (c) 400 (d) 80 (e) 60 (f ) 8000 (g) 240 (h) 28 7. (a) 2(x – 2)(x + 2) (b) 2(3a – 2b)(3a + 2b) (c) 3(4x + 3y)(3x – y) (d) (y + 2)(x – 1)(x + 1) (e) 7(2 – x)(2 + x) (f ) 4(x – 3y)2 (g) –2(x – y)2 (h) (a – 2)(a + 4) (i) 4(2x – 3)(2x – 1) ( j) 2(a – 17)(a + 17)
Exercise 3
1. €(98y – 30x) 2. (a) P = (2x + 4y + 6) m (b) A = (xy + 2 + 2y) m2 3. D = xy2 – x2y = xy( y – x) 4. A = (2000 + 4000y + 2005x) c 5. (a) (i) P = (2x + 2y) m (ii) A = (xy) m2 (b) 100 m; 600 m2
6. (a) L = (4y + 2x + 6) m (b) A = (2xy + 4y) m2 7. (a) (i) x + 1 (ii) 2x + 1
(b) Number Sum x = 1 x = 2 x = 3 x = 4 x = 5 x = 6 x = 7
3 5 7 9
11 13 15
The sum of two consecutive whole numbers is odd. 8. (a) 2πr (b) 8r (c) πr2 (d) 4r2 (e) 4r2 – πr2
342
9. (a) (2x + 1·5y) m (b) (1·8x + 1·3y + 41) m 10. (a) x (x + 2) = (x2 + 2x) m2 (b) (x – 2) x = (x2 – 2x) m2 (c) 4x m2
Chapter 4
Exercise 4 1. (a) 8x + 9 (b) 5x – 6 (c) 21x + 28 (d) –3x – 13 (e) 13x – 23 (f ) 28x – 24 (g) 12 (h) 2x + 3 2. (a) x2 + 2x (b) 3x2 + 3x (c) –2x2 + 4x (d) x2 + 3x + 2 (e) 2x2 + 11x + 5 (f ) 15x2 + 31x + 14 (g) x2 + 3x – 4 (h) 8x2 – 2x – 3 (i) –25x2 + 45x – 18 ( j) 36x2 – 49 3. (a) x + 4 (b) x – 2 (c) x + 3 (d) x – 3 (e) 2x – 1 (f ) 5x – 1 (g) 2(x + 1) (h) 3 – x (i) 2x – 1 ( j) x – 1 (k) x + 2 (l) –x
Exercise 5 1. (a) 3x + 2
_____ 6
(g) x − 3 ____
6
(o) (r)
(l) 2x + 1 ______
(b) 5x − 3 _____
15
(h) 8x + 17 _____
15
_________ (x + 1)(x − 1) (s)
3x − 19 2x2
2. (a) 17x ___
(h) 7x2 ___
x − 1
10 (b) − x _
45 (i) 11x2 ___
(l) 2(2x + 1) ______
(r) 21 ____
x + 2 (s) 5 _
Exercise 6
1. (a) 4 (b) 9 (c) 16 (d) 27 (e) 32 (f ) 625 (g) 100 000 000 (h) 1 (i) 1 ( j) –1 (k) 16 (l) –243 (m) 1
_ 4 (n) 4
2. (a) 1 _
(i) 2 _
_ 9 (o) 64
2 (b) 1 _
3 ( j) 6 (k) 1 _
( j) 28 (k) 3 _
(p) 3 _
2 (q) 2 _
4. (a) 2 (b) 3
__ 2
7
(k) a (l) a (d) 1
__ 3
2
___ 2x2
(k) 5
___ 2x2
__ 2
__ 27 (p) − 1
9 (c) 1 __
_ 8 (q) 16
64 (d) 1 __
(b) 5 (c) 125 (d) 16 (e) 1 _
2 (l) 1 _
__ 2
5
3 (r) − 2 _
3 (s) − 3 _
(c) 1 __
(c) a4 (d) a4 (e) a (f ) a 23
__ 3
1 2
(m) 1 __
(e) 2 (f ) 2x5y (g) 22x (h) x × 24x (i) 2 __
a3 (n) a
(l) (a + 3b)5 (m) b __
xy (n) 1
____ 2y2a2
__ 2
6 (l) 6 (m) 1 __
__ 25 (r) 49
25 (e) 1 __
6 (f ) 1 _
5 (d) 7 3
__ 2
__ 2
7
__ 6
13
64 (n) − 1 __
__ 4 (s) 121
16 (f ) 5 __
18 (g) 4 _
27 (o) 8 __
___ 16 (t) − 125
3 (h) 3 _
2 27 3. (a) 27 4 (g) 1 (h) 8 (i) 3
2 (t) 1 (u) 3 (v) –3 (w) 2 _
(e) 5
__ 2
3
(g) a12 (h) 1 __
a2 (i) a ( j) a5
__ 2
___ 500
3 (m) 106 = 1 000 000 (n) –32 (o) 1 __
10
3 (x) 9 _
5
5. (a) a9 (b) a21 3
6. (a) x4y (b) 2x5 (c) 4x x3
(o) 2a2y2 (p) 5 _
___ 8
(c) 9x __
x(x + 1) (m) 5x + 13 _________
8x
14 (d) 7x __
(i) 13x + 5 _____
_________ (x + 2)(x − 3) (p) 3(x + 1)
3 (c) 2 _
= 4x + 2 _____
9 (d) 1 _
4 ( j) x2 + x ____
x − 1 (m) 1 _
3 (t) – (x + 2) (x + 2)(x + 3) (n)
12 (e) 2x __
12 ( j) −x − 5 _____
12
______ x(2x − 3) (q)
_________ (x − 2)(x + 2) (t)
15 = x(x + 1) ______
15
2 (n) 1 _
3 (f ) −5x + 12 ______
12
(k) −3x + 4 ______
4
__________ 6(x + 1)(x + 2)
13x + 22
___________ 5(x − 1)(2x + 3)
___________ (3x + 1)(3x − 1)
x + 14 −12x
4 (e) − 2 _
7 (f ) x2 __
2 (o) 3x __
15 (g) 10x2 ___
21
(k) x2 − 1 ____
21 = (x + 1)(x − 1) _________
21
2 (p) 5 _
3 (q ) –2
( j) x8y4 ____
81z12 y
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