C1 1 Worksheet D INDICES AND SURDS a Express ( 23 )−2 as an exact fraction in its simplest form. (2) b Solve the equation 3 x 2 − 27 = 0. 2 (2) a Find the value of x such that 2x − 1 = 16. (3) y b Find the value of y such that 2(3 − 10) = 34. 3 Simplify 12 − a b 4 (2) 5 3 (3) (4 x )3 16 x (2) 7 3 a Express 2 2 − 2 2 in the form k 2 . (2) b Show that ( x + 6)2 + ( 2 x − 3)2 can be written in the form ax + b where a and b are integers to be found. 5 (3) Solve the equation x 12 + 9 = x 3 , giving your answer in the form k 3 , where k is an integer. 6 (3) B A C M The diagram shows triangle ABC in which AB = BC = 4 + 3 and AC = 4 + 4 3 . Given that M is the mid-point of AC, 7 8 a find the exact length BM, (4) b show that the area of triangle ABC is 6 + 2 3 . (2) a Find the value of x such that 82x − 1 = 32. (3) b Find the value of y such that ( 13 )y − 2 = 81. (3) Express each of the following in the form a + b 2 , where a and b are integers. a b 9 48 − 600 12 (3) 2 4+3 2 (3) Find the non-zero value of x for which (2 x )3 = 4x. (4) Solomon Press C1 INDICES AND SURDS 10 a Express 5 3 in the form Worksheet D continued k. (2) b Hence find the integer n such that n < 5 3 < n + 1. 11 a Express (12 14 ) − 12 (2) as an exact fraction in its simplest form. (2) b Solve the equation 3x−3 = 7 19 . 12 Simplify a 192 − 2 12 + b (2 + 13 (3) 75 (3) 3 )(5 − 2 3 ) (2) a Write down the value of x such that 2x = 32. (1) b Solve the equation 32y + 1 = 4y. 14 (3) a Find the value of x such that 3 x 2 = 64. b Find the values of the rational constants a and b such that 3 +1 2 3 −3 15 16 17 = a + b 3. Solve the equation 42y + 7 = 8y + 3. Giving your answer in the form k 2 , solve the equation 2(x − 32 ) = 2 3 2 −4 − 98 − x. (4) Express 3− 2 2 +1 (6) Given that 5x + 1 = 25y − 3, a find an expression for y in terms of x. Given also that 16 x−1 a Express (1 − (3) z =4, b find an expression for z in terms of y. 19 (4) (4) in the form a + b 2 , where a and b are integers. 18 (2) 5 )2 in the form a + b 5 . (3) (2) b Hence, or otherwise, solve the equation y2 = 3 − 5, giving your answers in the form c 2 + d 10 , where c and d are exact fractions. Solomon Press (4)

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