A1.1 Homework 1 Answers
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1 Cambridge Essentials Mathematics Core 7 A1.1 Homework 1 A1.1 Homework 1 Answers 1 a = 3 b = 12 c = 5 d = 42 2 a 11 b 4 c 6 d = 10 = 10 7 = 70 So = = 30 4 a 21 b 7 c 60 d 25 5 Any three pairs of values that differ by 3. 6 a + 6 b 2 c 3 d 9 7 a p = 3 b t = 11 c f = 7 d k = 18 e m = 12 8 a 26 b 12 c 16 d 10 e 80 f 15 9 Three different values for a and b such that a b = a seven less than x b two more than x c three times x d a quarter of x e x more than eight (or 8 more than x or the sum of 8 and x) 11 a n 2 b 5 n c n + 10 d n 2 e 2 n f n 7 g 12 n h n + 6 i 10 n 12 a ii c = 13 iii c = b 3 iv c + a = 45 b ii Brad s age and Carla s age add up to 29. iii Ahmed is twice as old as Brad. iv Ahmed is 19 years older than Carla.
2 Cambridge Essentials Mathematics Core 7 A1.1 Homework 2 A1.1 Homework 2 Answers 1 a 39, 47 increasing b 18, 10 decreasing c 57, 70 increasing d 30, 36 increasing e 96, 192 increasing f 4, 2 decreasing 2 a 13, 19, 25, 31, 37, 43 Add 6 b 55, 47, 39, 31, 23, 15 Subtract 8 c 14, 23, 32, 41, 50, 59 Add 9 d 3.5, 7, 10.5, 14, 17.5, 21, 24.5 Add , 17, 25, 33, , 14, 28, 56, , 40, 20, 10, 5 6 a 7 circles b 9 circles 11 circles c 3, 5, 7, 9, 11 d Add 2 7 The 5th term is 6 5 = 30 The 10th term is 6 10 = 60 The 100th term is = 600 The nth term is 6 n 8 a i 9, 10, 11, 12, 13 ii 19, 18, 17, 16, 15 iii 4, 8, 12, 16, 20 iv 60, 30, 20, 15, 12 b Sequences ii and iv are decreasing a The number of hexagons in Pattern 4 is = 13 b The number of hexagons in Pattern 10 is = 31 c The number of hexagons in Pattern n is n
3 Cambridge Essentials Mathematics Core 7 A1.2 Homework A1.2 Homework Answers 1 a c b d n 15n a b a 3 15 b a b or c , 17, 29, 41, 53, 65 8 x x or x x
4 Cambridge Essentials Mathematics Core 7 A1.2 Homework 9 a x 3 y b x 10 y c x + 1 y d x + 5 y 10 a x 12 4 x 3 b x x or x x 11 a x y b 12 n 4n 2 Original material Cambridge University Press
5 Cambridge Essentials Mathematics Core 7 A2.1 Homework 1 A2.1 Homework 1 Answers 1 a 16 b 5 c 32 d 33 e 2 f 54 g 13 h 3 i 6 j 6 k 160 l 2 m 2 n 20 o 12 p 6 2 a 10 b 12 c 20 d 5 e 4 f 14 g 7 h 23 i 1 j 7 k 10 l 6 3 a 8 b 2 c 15 d 9 e 0 f 11 g 3 h 35 i 3 j 10 k 5 l 0 4 a x + 11 b x + 3 c x + 12 d 4x e 11x f x g 12x h 3x i 4x + 7 j 2x k x + 3y l 3x y m 2x y + 4 n 7xy o 3xy p 9xyz 5 a = = 76 b = = 168
6 Cambridge Essentials Mathematics Core 7 A2.1 Homework 2 A2.1 Homework 2 Answers 1 a P = 2x + 8y b P = 10x a 7x + 1 b 2x a x + 5 b 2x + 5 c 2x + 3 2x 2x x x x + 2 x + 2 x + 5 2x + 5 2x a d = 20 5 = 100 b d = 80 4 = 320 c d = 35 3 = 105 d d = = a g = 25 1 = 5 b g = = 2.5 or c g = = 0.5 or 20 2 d y = 6 3 = 18
7 Cambridge Essentials Mathematics Core 7 A2.2 Homework A2.2 Homework Answers 1 a The number that goes into a function machine is called the input. b The output is the number that comes out of the function machine. c What happens to the number as it moves through the machine is called the function. d The inverse operation of add 4 is subtract 4. 2 a x + 7 b 4x c x 5 d y 10 e t + 17 f 6m 3 a 3x + 6 b 8(x 4) c d 5(x + 7) e 2 3y f x k a p b y 2 5 c d d x e m 4 5 f t 4 1 g x h x 3 5 i k a Subtract 3 b Add 9 c Divide by 4 d Multiply by 7 e 5 f + 11 g 8 h 4 i 6.1 j 3.8 k l a x b x = 3
8 Cambridge Essentials Mathematics Core 7 A2.2 Homework 7 a i x b i y ii x ii y iii x = 3 iii y = 8 c i m d i t ii m ii t iii m = 5 iii t = 3½ or 3.5 e i x f i d ii x ii d iii x = 30 iii d = 24 g i g h i p ii g ii p iii g = 3 iii p = 6 i i s ii s iii s = 20 Original material Cambridge University Press
9 Cambridge Essentials Mathematics Core 7 A2.2 Homework 8 a Sita is not correct. b 2x + 6 = 16 means x So x = 5 x (x + 6) = 16 means x So x = 2 x Original material Cambridge University Press
10 Cambridge Essentials Mathematics Core 7 A3.1 Homework 1 A3.1 Homework 1 Answers 1 a 3(n 5) b Start with x, add 9 and divide the answer by 4. c 6 2 a 3n is n multiplied by 3. n + 3 is n added to 3. b i 3n 3 n ii n n 3 a 5x x 5 x b x x x c 2(x 3) 2 x x d 6x 7 6 x 7 4 a x = 48 b x = 8 c x = x d x = 12 e x = 20 f x = 7 5 a x 1 + x x = 41 b x = 9 cm c 8 cm, 15 cm, 18 cm 4x + 5 = 41 6 a n + n n + 9 = 74 b n = 20 c 29 3n + 14 = 74
11 Cambridge Essentials Mathematics Core 7 A3.1 Homework 2 A3.1 Homework 2 Answers 1 You can add numbers in any order and you will get the same answers. For example, = 7 and = 7. This is not true with subtraction 8 6 = 2 but 6 8 = 2 2 m = x n and n = x m are true. 3 a 3xy b 3mx + 2my c 3 + 6kt 4 a 32n b 44g c 27a 5 a 7x + 14y + 21 b 13m 12 c 3a + 11b d 11x a 6(2a + 3b) b 12a + 18b 7 a c = 7 b x = 4 c y = 1 d x = 2 8 a 3 + n + n + 5 = 20 b 3n n + 3n + 2 = 24 n = 6 n = 3
12 Cambridge Essentials Mathematics Core 7 A3.2 Homework A3.2 Homework Answers 1 2 a y = 2x 1 b y = 2(x 1) c y = x + 2 d y = 13 x 3 a x 2x 3 x x + 1 x 3x 7 b x 2x 3
13 Cambridge Essentials Mathematics Core 7 A4.1 Homework 1 A4.1 Homework 1 Answers 1 a A(3, 4), B(3, 2) b x = 3 c i x = 1 ii x = 17 iii x = 2 2 a A( 2, 3), B(4, 3) b y = 3 c i y = 1 ii y = 16 iii y = 10 3 a (2, 5) b ( 1, 10) c ( 4, 3) d (4, 4) e (10, 10) f (6, 7)
14 Cambridge Essentials Mathematics Core 7 A4.1 Homework 2 A4.1 Homework 2 Answers 1 a (4, 5) b (4, 3) c (2, 3) 2 a x y b, c y = 6 x d i (6, 0) ii (0, 6)
15 Cambridge Essentials Mathematics Core 7 A4.1 Homework 2 3 a x y b y = 2x 3 c i (1.5, 0) ii (0, 3) iii (1, 1) iv (2, 1) Original material Cambridge University Press
16 Cambridge Essentials Mathematics Core 7 A4.2 A4.2 Homework Answers 1 a i 88 ii 68 iii 34 iv 96 b i 3.7 m ii 1.5 m iii 7.4 m iv 5.3 m 2 a x = 2 b x = 4 c x = 3 d x = 2.5 e x = 1 3 Yes. When x = 5, 12 2x = = 2.
17 Cambridge Essentials Mathematics Core 7 A5.1 Homework1 A5.1 Homework 1 Answers 1 a 5x + 5y b 3x 2y 2 a m + 7 b m 10 c 2m d m a 6ab b 4a + 6b 4 a n + 3 b 2n a a + 2b b i ah ii 1 bh iii ah + bh 2 6 a n + 2 b n + (n + 2) + (n + 4) + (n + 6) = 4n + 12 c n a Q (n + 5, 3n) b R (n + 7, 3n 2) c T ( n 2, 3n)
18 Cambridge Essentials Mathematics Core 7 A5.1 Homework 2 A5.1 Homework 2 Answers 1 C = 2 m = F 30 2 a + b + c 3 3 a Number of tables Number of children b 22 c c = 2t a 14 b 18 c 22 d 4n a b Pattern number Number of white tiles c 26 d Pattern 17 e 2n a 31, 38 b 66 c 7n 4 x x 1 7 a y = 5(x + 3) b y = 4 c y = 3x 5 d y = B = 7(H + 4) 9 a x 2 3 y b i x y ii y = 1 3x y = y
19 Cambridge Essentials Mathematics Core 7 A5.2 Homework 1 A5.2 Homework 1 Answers 1 a x = 2 b x = 5 c x = 7 d x = 9 e x = 12 f x = 3 2 a p = b y = 3 4 c m = d q = 10 9 e t = 1 3 f a = a x = 1.5 b m = 1.3 c n = 2.25 d q = 1.4 e a = 0.8 f c = x + 12 = 40 x = 14 5 a x = 20 b x = 25 6 a 6a + 5 = 38 b 8a = 180 a = 5.5 a = 9 7 a (4x + 3) cm b 4x + 3 = 18 x = 3.75 c 3.75 cm, 6.5 cm, 7.75 cm
20 Cambridge Essentials Mathematics Core 7 A5.2 Homework 2 A5.2 Homework 2 Answers 1 a 3n + 30 b 3n + 30 = 84 n = , 28, 34, 35 3 a x = 5 b x = 14 c x = 8 4 a x = 3 b p = 7 c c = a m = 40 b t = 15 c a = (x + 9) = 80 x = 11 7 a A = 4(y + 5) b P = 2(y + 9) c i 72 cm 2 ii 30 cm 8 3(y + 16) = 120 y = (2x + 3) = 72 x = a 7(n 13) = n = 28.5 b n = 21 n = a 2a b a + 8 c 4a + 8 = 100 a = 23 Ciaran is 31 years old. 12 a The 4th term b 14 terms c When 3(2n + 5) = 54 2n + 5 = 18 2n = 13 n = 6.5 You cannot have a term with position 6.5.
21 Cambridge Essentials Mathematics Core 7 A5.3 Homework A5.3 Homework Answers 1 a 1.5 km b 5 minutes c 7.5 minutes d 30 minutes e 2.5 km f 6.5 km g 10 minutes h 50 minutes 2 C, because the ball is thrown up at a high speed, gradually shows down, stops at the maximum height, then speeds up as it falls. So the speed starts high, slows down to zero, then increases again. 3 a 75 cm b 2 p.m. c 280 cm d 12 noon and 4:30 p.m.
1 a 2 b 10 c 4 d 12. e 7 f 11 g 12 h 30. i 8 j 7 k 5 l a 9 b 14 c 3 d 10. e 11 f 5 g 15 h 1. i 12 j 2 k 35 l 49.
Cambridge Essentials Mathematics Core 7 A1.1 Answers A1.1 Answers 1 a 2 b 10 c 4 d 12 e 7 f 11 g 12 h 30 i 8 j 7 k 5 l 20 2 a 9 b 14 c 3 d 10 e 11 f 5 g 15 h 1 i 12 j 2 k 35 l 49 m 25 n 1 o 1 p 18 3 a
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