A Level Mathematics for OCR A Student Book 1
Mixed practice 2 2 1 Express (n + 5 ) in the form a + b
5.
2 If z = xy2 and y = 3x express z in terms of x only. 10 3 Show that can be written in the form a + b . 28 − 8 4 If y = 2 , write y - 4 in the form kxa. x 5 If 3 x 8 = x 2 + 32 , find x. 6 Simplify:
a ( 3 x )6
b
3 y 4 × (10 y ) 2y5 © OCR, GCE Mathematics, Paper 4721, January 2009 [Question part reference style adapted] 3
7 Express each of the following in the form 3n: a 1 9 b 3 3
c 310 × 9135 © OCR, GCE Mathematics, Paper 4721, June 2009 [Question part reference style adapted] −1 2 8 Simplify x 4 + 7 x 3 × x . 9
(
)
9 Rationalise the denominator of n + 1 . n −1 10 a Find and simplify an expression for (a + b 5 )2.
26
b By considering (2 − 5 )4 show that 5 < 161 . 72 c By considering (2 − 5 )3 show that 5 > 38 . 17 3 d i E xplain why considering (3 − 5 ) gives a worse upper bound on 5 than found in part b. ii E xplain why considering (4 − 5 )4 would not give as good an upper bound on 5 as found in part b.
Elevate For more challenging questions on indices and surds, see Extension sheet 2.