1. (a) 10, 5, 1, 0, 2, 3 (b) 12, 5, 3, 0, 3, 10 (c) 7, 3, 1, 2, 4, 10 (d) 31, 21, , 21, 41

Size: px

Start display at page:

Download "1. (a) 10, 5, 1, 0, 2, 3 (b) 12, 5, 3, 0, 3, 10 (c) 7, 3, 1, 2, 4, 10 (d) 31, 21, , 21, 41"

Myrtle Allen
5 years ago
Views:

1 Practice Book UNIT 0 Equations Unit 0: Equations 0 Negative Numbers (a) 0 0 (b) 0 0 (c) (d) 4 (a) 4 (b) 0 (c) 6 4 (d) 4 (a) < (b) < 4 (c) > 8 (d) 0 > 0 (a) 0 (b) 0 (c) July (d) 0 Arithmetic with Negative Numbers (a) (b) 6 (c) 6 (d) (e) (f) 4 (g) (h) (i) (j) (k) (l) (m) 4 (n) (o) 0 (p) (q) (r) 0 (a) 0 (b) (c) (d) (e) (f) 0 (g) 6 (h) 0 Simplifying Epressions (a) (b) 6 (c) + 6 (d) 6a + 4 (e) 9a + b (f) a + y (g) y + 4 (h) + 0y + (i) 6q (j) 9 0y (a) + 7 (b) 4 (c) y y (d) y (e) (f) y + + y (g) 4 + (h) 9ab 7bc ac (a) (b) + 0 (c) + 6 (d) 8 8 (e) + y (f) 7 4y (g) + y (h) + y (i) + 6y 6 (j) + + y (k) + y (l) + 6y 4 (a) (b) 8 + (c) 7 + y (d) 7y (e) 0a + b (f) + y (a) p + 7q (b) + y (c) w

2 Unit 0: Equations 04 Simple Equations (a) = (b) = 9 (c) = (d) = 4 (e) = (f) = (g) = 7 (h) = (i) = (j) = (k) = (l) = 0 (a) = (b) = (c) = 4 (d) = 4 (e) = 4 (f) = (g) = (h) = (i) = 6 (j) = (k) = (l) = = ; = = 0 ; = years old (a) p (b) (i) = 6 (ii) y = 8 (c) r = 96 (a) + ( or + ) (b) cm 0 Solving Equations (a) = (b) = 4 (c) = (d) = (e) = (f) = 6 (g) = 4 (h) = (i) = (j) = 9 (to dp) (k) = (l) = 6 (a) = 0 (b) = (c) = 8 (d) = 0 (e) = 0 (f) = 8 (g) = (h) = 8 (i) = 08 (j) = (a) = 6 (b) = 4 (c) = (d) = (e) = 7 (f) = (g) = 0 (h) = 8 (i) = 7 (j) = 7 (k) = 4 (l) = 4 = 6 Bobby is 9 years old Ahmad is 8 years old and John is years old 6 Janet is now 4 years old Mary will be years old in 7 years' time 7 After about 0 mins 8 60 km/h 9 (a) = 6 (b) y = 0 = 7 (a) (b) (i) = (ii) = km

3 Unit 0: Equations (a) 7 (b) 4 (c) (a) (b) (c) 06 Trial and Improvement Method (a) (b) 7 (c) (d) 4 (a) 06 or 46 (b) 6 or 08 (c) 9 or 69 (d) 044 or 46 < < ; = to dp 4 (a) 6 (b) 6 < 40 < 6 (c) 6 < < 6; = 6 to dp and 6 < < 6; = 6 to dp (a) < < (b) = 84 to sf 6 (a) 7 (to dp) (b) 4 6 < < 4 67 = 4 to the nearest integer (we can't give an approimation to dp because we don't know whether 46 < < 467 or 46 < < 46 ) 07 Epanding Brackets (a) + (b) 4 + (c) (d) (e) 0 (f) + (g) + + (h) (i) + (j) + 6 (k) a + a + (l) y + (m) ac + bc ad bd or ac bc ad bd (n) + + (a) 8 + 6y (b) z 0zy (c) y yz (d) 9p + qr qs (e) pr + ps + qr + qs (f) z + w + yz + yw (g) a + ac + ba + bc (h) pm + qm + 4pr + 6rq (i) ac + ad bc bd (j) 4eg eh fg + fh (k) ps pt 4qs + 4qt (l) ab + a + 4b + (m) (n) a + a (o) + 4 (p) c + c + 8 (q) 9y + y + 4 (r) p + p + (s) 8 + y + y

4 Unit 0: Equations (t) d d + (u) a + 0a + (v) (w) b + 4b + 4 () e 8e + 6 (y) (z) (a) 9p + pq + 4q (b) 6m 4mn + 9n (c) (d) y 49 (e) a 9 (f) 6 y (g) 4 (h) a 4 (a) ( + ) (b) Use = 0 : 9 = 0 0 Hence by putting = 0 in we get 667 (a) (i) 4 + (ii) ( + ) ( + ) + = + (b) + ; (a) d + 6d (b) g 8 (c) 8p (a) + 4 (b) 4 = + 08 Simultaneous Equations (a) = 9 y = (b) = y = (c) = y = 78 (d) = y = (e) = y = (f) = y = (g) = y = (h) = y = 4 (i) = y = (j) a = 4 b = (k) = y = 9 (l) m = n = 4 (m) = y = (n) u = v = 7 = 4 y = 6 (a) = y = (b) = y = (c) = 6 y = (d) = y = 7 (e) = y = (f) = 6 y = (g) = 0 y = 4 (h) = y = (i) = y = (j) = 7 y = (k) = y = (l) = y = 4 + y =00 + y = y = 600 = 60 y = y = 0 = 40 y = 00 6 stands for David's money and y for John's money + y = 4; + y = 4 ; = 6 y = 8 7 The cost of a television set is 900 and the cost of a video-recorder is 60 4

5 Unit 0: Equations 8 The toothbrush costs 9 and the tube of toothpaste costs kg of the spice which costs per kg and 4 kg of the spice which costs per kg 0 (a) + y = 6; 4 + y = 8 (b) = 6 y = 4 = y = 7 = y = and = y = 09 Factorisation (a) a + b (b) ( p q) (c) 6( y) (d) 7y( z) (f) a( + b) (g) ( + z) (h) 9mn ( mn) (e) 4 4 (j) a( a) (k) y (i) 4q p q (m) 4pq + 4p (a) a b (l) 7 r ( m ) (b) 0 p( y ) (c) 8ab( c ) (d) 6bc( a + d) ( ) (f) py+ y (e) 44m + n (i) c c (g) 6st( s t) (h) a( + a) (j) abb ( 4) (k) mn( m l) (l) ( y y + ) (n) bac+ a + c (m) pqr+ p+ r (p) st s 4t (a) y m n (o) abc 4 + b + c ( + ) (b) ( a + b) ( k + l) (c) ( + y) ( a b) ( ) (d) c + d y (e) a + b y (g) + y a b ( + ) (f) ( y) ( k + l) ( ) (h) ( p + q) ( b ab) = b( p + q) ( a) = + ( ) (i) c + d 0a a a c d a 4 (a) + 6 (b) a 00 Factorisation ( ) (c) ab( a + b) ( + ) ( ) = ( + )( ) (j) m + n 4 8z 4 m n z ( + ) ( ) (a) (b) + (c) (d) + 6 ( + )( + ) (e) + ( )( ) (h) ( ) ( + ) (f) + 4 (g) ( + ) ( ) (i) + 7 (j) +

6 Unit 0: Equations ( ) (b) ( ab + c) ( ab c) (c) ( + t) ( t) (a) ( ) (e) ( 6b + a) ( 6b a) (f) a 9 = ( a + ) ( a ) (d) ( ) = = (a) 6 6 = ( ) = = (b) 9 9 = ( ) = = (c) 48 4 = ( ) = = (d) = ( ) = = (e) = (f) 6 4 = = = ( + ) ( + ) ( + ) ( ) ( ) (e) ( + ) ( + ) (f) ( a + ) ( a + ) ( y + )( y + ) (h) ( n ) ( n ) (i) ( g ) ( g ) (j) ( r 6) ( r ) ( b + )( b + ) (l) ( d ) ( d ) (m) ( p 7) ( p + ) ( 9) ( + 4 ) (o) ( ) ( ) (p) ( s + ) ( s ) ( f + )( f ) (r) ( e ) ( e + ) 4 (a) k + k (b) m + 8 m 4 (c) + 4 (d) y y (g) (k) 6 (n) h h (q) ( ) ( + ) ( ) (a) p q p q (b) y 4z y z (c) k l k l ( + ) (d) m 7n m n (e) + y y ( + ) 6 (a) 8 y (b) y y ( + ) (f) ( + y) ( + y) 0 Solving Quadratic Equations by Factorisation ( ) = = = ( + ) = = = (a) (b) ( + ) = = = ( + ) = = = (c) (d) ( + ) = = = ( ) = = = (e) (f) ( ) = = = ( ) = = = (g) 0 (h) 0 ( + ) = = = ( ) = = = (i) (j) ( ) = = = (k)

7 0 Unit 0: Equations ( ) = = = (l) + 0 ( ) = = = (m) 0 ( + ) = = = (n) (o) ( + ) = = = (a) = = 4 (b) m = m = 7 (c) p = 0 p = (d) = = 4 (e) = 4 = (f) p = 9 p = (g) a = 8 a = 7 (h) q = 8 q = (i) y = y = (j) = = (k) m = m = (l) z = z = 4 (a) y = 8 y = 7 (b) w = w = (c) y = y = 4 6 (d) c = c = (e) q = q = 4 (f) d = d = (g) = = 7 (h) y = 6 y = (i) p = 0 p = 4 (j) = = 4 (k) = = (l) = = 4 (m) y = y = 4 (n) y = y = (o) a = a = (p) = = 4 (a) =±4 (b) =±7 (c) =±4 (d) =± (a) q = (b) = 9 (c) y = (d) = (e) y = 6 (a) =± (b) a =±6 (c) y =± (d) b =±4 (e) a =±8 (f) =± 9 (g) y =± (h) =±4 (i) p =± (j) p =± (k) p =± (l) b =± 7 The height is cm 8 The length is cm and the breadth is 8 cm 9 r = 7 cm (to 4 dp) 0 The height is 7 cm 7

8 Unit 0: Equations The dimensions of the rectangle are 7 cm and cm ( ) (a) (b) + 7 (c) 7 (a) (b) = 0 or = (c) > or < 0 Solving Quadratic Equations using the Formulae (a) = = 6 (b) y = 68 y = 8 (c) = 0 44 = 44 (d) = 4 79 = 0 09 (e) = = 4 0 (f) y = y = 4 (a) t = 8 t = 0 8 (b) y = 0 8 y = (c) = 08 = 99 (d) = 06 = 8 (e) t = 0 86 t = 86 (f) t = 76 t = = = 4; + = = 4 and 4 + = = 4 4 r = 864 cm (to dp) = m 6 = 76 cm (to dp) 7 The height is about cm and the base is about 6 cm 8 = 09 cm 9 y = 4 cm = cm + y = ( ) cm 0 (a) 8 + y (b) y + = cm + y = = 9cm Hence = 9 y The dimensions of the rectangular card are 8 + y and + Hence A its area is given by: A = 8 + y Its area is also given by: A = ( + ) cm ( + ) = = 644 cm Hence 8 + y 644 cm (c) Putting = 9 y into the above equation gives: ( + ) = 8 + y 8 y 644 cm ( ) = 8 + y y 644 cm 8

9 Unit 0: Equations Simplify the left-hand side of the equation: Subtract 644 from both sides: Divide both sides by : 4y + 0y + 94 = 644 4y + 0y 0 = 0 y y + = 0 (d) y = or y = Hence the possible dimensions of the card are either cm ( length) 8 cm when y = and = 6 or 8 cm (length) cm (when y = and = 4) (a) 8a (b) 4± 6 (c) y 0 Algebraic Fractions = 0 (d) = y = 4 or = 6 y = (a) y 0 (b) y 0 (c) b a 0 (d) y 0 and z 0 z (e) 4e c 0 and d 0 (f) a b (g) 4s t (h) a b + (i) b 4 (j) c 8 (k) 0 (l) (m) (n) 0 d d and c b (o) c y z (a) (d) z z (b) z and (e) (g) c + c (h) m + n m n (i) p 4p p + a a 0 and a (c) + 4p p 0 (j) (k) a (l) m m (f) y + y + q q and q (m) and and (n) = + and (o) and (p) ( m + ) = m m + (q) q 6 q 6 (r) p p n 9

10 0 Unit 0: Equations (a) (d) (g) (j) (l) a b (b) a + b a b a b (c) 4 and 4 (e) + 4 8a a a b (h) a ± 4 (i) a and 7 (k) 7 and 4 a + b a b a b and a b a a b a ± b (f) + and 0 b a b a b + y 6 y y y and (a) a 0 and a (b) (d) (f) (h) (k) u u + p p + 9 yy a 4 a u (e) 0 and (c) 7 + b b 0 and b 7 b yy+ p 0 p and p 7 (g) y 0 y and y (i) y 0 y and y + and p ± (j) 4 p a 0 and a 4 (l) y 0 and y + n n (a) (c) y + y + y and y (b) y y ( + ) ( ) ± 4 (d) a + 4a 4 a a ( ) a and a c + 4c + 0 c and c c c ( + ) (e) u 6u 8 u + u ( ) u and u (f) ( + ) and 6 (a) (c) (e) 4 + a 4 a + b ( ) a + a a ( + ) a b (b) + ( ) and (d) a ± (f) 4( a + ) ( a 4) ( a + 4) and ( + ) a ± 4 and 4 0

11 Unit 0: Equations (g) ( p ) ( p + ) ( p ) p ± (h) 7 a b a b (i) ( c) ( + c) c ± (j) 7 0 and Completing the Square (a) a = a = (b) m = m = (c) p = 0 p = (d) y = 4 y = 0 (e) = = (f) a = a = 7 (g) y = y = (h) a = a = (i) = = (j) b = b = 4 = = (a) (b) 4 06 (c) y = y 4 y (d) 9 y 77 = y 0 y (e) ( t ) = 8 t 48 t 08 (f) p 7 = p 46 p 04 4 (a) y + 4 = y 08 y (b) t 7 = t 8 t (c) p 7 = p 78 p 08 (d) + 0 = (e) ( ) = 8 04 (f) 9 y 6 = y (g) 77 = (h) + 4 = (a) 4 + (b) + 6 = 0 ; ; = 8 (to dp) (a) = ( ) = By multiplying and simplifying we get 6 8 Hence = 0 (b) = cm (c) By setting = in PQ = 4 we get PQ = 444 cm + =

12 Unit 0: Equations 6 (a) 6π 9π cm (b) 00 6π 9π cm cm or 600π 900π (c) 600π 900π = 000π cm By dividing both sides by 00π we get = 0 cm hence 0 = 0 By completing the square we get 4 89 = hence = 0 (to dp) 6 0 Algebraic Fractions and Quadratic Equations (a) =±6 (b) =± (c) y =± (d) =± (a) a = a = 7 (b) = = (c) y = y = (d) c = c = (e) t =± (f) = = 6 (g) = = (h) c = c = 0 (to dp) (a) = 8 (b) =± (c) = 4 = (d) = 6 = 4 (a) = 8 = 7 (b) =±9

Expanding brackets and factorising

Expanding brackets and factorising CHAPTER 8 Epanding brackets and factorising 8 CHAPTER Epanding brackets and factorising 8.1 Epanding brackets There are three rows. Each row has n students. The number of students is 3 n 3n. Two students