Recurring Decimals. Mathswatch. Clip ) a) Convert the recurring decimal 036. to a fraction in its simplest form.
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1 Clip Recurring Decimals ) a) Convert the recurring decimal 06. to a fraction in its simplest form. 8 b) Prove that the recurring decimal 07. = ) a) Change 4 9 to a decimal. 9 b) Prove that the recurring decimal 07. = ) a) Change to a decimal. b) Prove that the recurring decimal 04. = 4) a) Change 6 to a decimal. b) Prove that the recurring decimal 0. = 7 ) a) Convert the recurring decimal 06. to a fraction in its simplest form. b) Prove that the recurring decimal 07. = 8 6) a) Convert the recurring decimal. to a fraction in its simplest form. b) Prove that the recurring decimal 06. = Page 48
2 Clip 6 Fractional and Negative Indices a a y a a y = a +y = a y (a ) y = a y a 0 = a - = a y y = ( a ) a = a y ( a ) y ) Simplify a) (p ) c) e) (m - ) - b) k k d) (p ) - f) (y ) ) Without using a calculator, find the eact value of the following. a) c) 7 7 e) (8 ) b) 4 - d) f) ( ) ) Work out each of these, leaving your answers as eact fractions when needed. a) 4 0 e) 4 i) 49 m) 49 b) 7 0 f) 8 j) n) c) 0 g) k) 7 o) 7 d) 9 0 h) 0 l) 6 p) 6 4) can be written in the form n. Find the value of n. ) 8 = m Find the value of m. 6) Find the value of when = 7) Find the value of y when 8 = y 8) a =, b = y a) Epress in terms of a and b i) + y ii) iii) + y ab = 6 and ab = 6 b) Find the value of and the value of y. Page 49
3 Clips 7, 8 Surds is not a surd because it is equal to eactly. is a surd because you can only ever approimate the answer. We don t like surds as denominators. When we rationalise the denominator it means that we transfer the surd epression to the numerator. ) Simplify the following: a) 7 7 b) c) 0 d) 4 e) 7 f) 00 g) ) Simplify the following: a) 8 b) 8 c) 99 d) 4 0 e) 8 8 f) 8 7 ) Epand and simplify where possible: a) ( ) b) ( 6+ ) c) 7( + 7) d) ( 8) 4) Epand and simplify where possble: a) ( + )( ) b) ( + )( ) c) ( + )( + 4) d) ( )( + ) e) ( + 7)( 7) f) ( 6 ) ) Rationalise the denominator, simplifying where possible: a) b) c) d) e) f) g) ) 7 = n Find the value of n 7) Epress 8 8 in the form m where m is an integer. 8) Rationalise the denominator of giving the answer in 8 8 the form 9) Work out the following, giving your answer in its simplest form: a) b) c) d) e) f) ( + )( ) ( 4 )( 4+ ) ( )( + ) 4 ( + ) ( + ) 0 p ( )( + ) 0 Page 0
4 Clip 9 Direct and Inverse Proportion ) is directly proportional to y. When =, then y =. a) Epress in terms of y. b) Find the value of when y is equal to: (i) (ii) (iii) 0 ) a is inversely proportional to b. When a =, then b = 4. a) Find a formula for a in terms of b. b) Find the value of a when b is equal to: (i) (ii) 8 (iii) 0 c) Find the value of b when a is equal to: (i) 4 (ii) 4 (iii). ) The variables u and v are in inverse proportion to one another. When u =, then v = 8. Find the value of u when v =. 4) p is directly proportional to the square of q. p = 7 when q = a) Epress p in terms q. b) Work out the value of p when q = 7. c) Work out the positive value of q when p = 7. ) y is directly proportional to. When =, then y = 6. a) Epress y in terms of. z is inversely proportional to. When = 4, z =. b) Show that z = c y n, where c and n are numbers and c > 0. You must find the values of c and n. Page
5 Clip 60 Upper and Lower Bounds ) A =. correct to decimal place B = 00 correct to significant figure C = 9 correct to the nearest integer a) Calculate the upper bound for A + B. b) Calculate the lower bound for B C. c) Calculate the least possible value of AC. d) Calculate the greatest possible value of A + B B + C ) An estimate of the acceleration due to gravity can be found using the formula: L g = T sin Using T =. correct to decimal place L = 4.0 correct to decimal places = 40 correct to the nearest integer a) Calculate the lower bound for the value of g. Give your answer correct to decimal places. b) Calculate the upper bound for the value of g. Give your answer correct to decimal places. ) The diagram shows a triangle ABC. C AB = 7mm correct to significant figures. BC = 80mm correct to significant figure. Diagram NOT accurately drawn A (a) Write the upper and lower bounds of both AB and BC. B AB upper =... BC upper =... AB lower =... BC lower =... (b) Calculate the upper bound for the area of the triangle ABC....mm Angle CAB = (c) Calculate the lower bound for the value of tan. Page
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