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REVISION HOMEWORK ADOLYGU GWAITH CARTREF Rational and Irrational Numbers HIGHER TIER MARK Enw: _____________________________ % Dosbarth:_____________________________ Target Target Practice Writing examples of irrational numbers 1,2 Changing fractions to recurring decimals 3,4 Changing recurring decimals to fractions 5,6 Simplifying surds 7 to 10 Substitution 11 Met Classwork Questions Rational and Irrational Numbers 1. Give an example of an irrational number (i) whose square is rational (ii) whose square is irrational 2. Write these numbers as recurring decimals (i) (ii) 13 99 7 9 3. Express 0.1 2 as a fraction 4. Express 0.83 7 as a fraction 5. Express 0.864 as a fraction 6. Show clearly that 15.4 07 is a rational number 7. Express 192 in the form a b , where a is a whole number and b is a prime number. 8. Find the value of ( 50 2 ) 2 9. Show that ( 72 2 ) 2 50 10. Given that d 5 , e 2 and f 20 . Simplify each of the following and indicate in each case whether your answer is rational or irrational. (i) 3d 2 (ii) f de Revision Homework GCSE Questions 1. Indicate with a tick ( ) in the appropriate box whether the number belongs to one or more or more of the categories: Integer Rational Number Irrational Number e.g 0.6 Integer Rational Number Irrational Number -6½ 64½ 12π (5) 2. Give an example of an irrational number whose cube is rational ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (1) 2 3. Write down a value of x (where x>1) for which x 3 is rational ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (1) 5 4. Write 6 as a recurring decimal ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (1) 23 5. Write 99 as a recurring decimal ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (1) 6. Express 0.65 2 as a fraction ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………………….. ………………………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………………………. (2) 7. Express 0.8 3 as a fraction ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) 8. Express 180 in the form a b , where a is a whole number and b is a prime number. ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) 9. Express 243 in the form a b , where a is a whole number and b is a prime number. ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) 10. Find the value of ( 32 2 ) 2 ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) 11. Find the value of ( 18 2 ) 2 ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) 12. Show that ( 3 12 ) 2 27 ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) 13. Given that a 3 , b 7 and c 21 . Simplify each of the following and indicate in each case whether your answer is rational or irrational. (i) ab 3c ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………………… (2) (ii) abc ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) b (iii) ac ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) 14. Given that p 2 3 and q 2 3 , determine whether each of the following expressions is rational or irrational. (i) p q ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) (ii) pq ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… (2) (iii) p 2 ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………………………… (2) Target Practice 1. Write down a value of x (where x 1 ) for which x 3 2 is rational 2. Write down an Irrational Number between 3 and 4 4 3. Write 9 as a recurring decimal 3 4. Write 11 as a recurring decimal 5. Express 0.6 3 as a fraction 6. Express 0.342 7 as a fraction 7. Express 320 in the form , where is a whole number and is a prime number. 8. Express 108 in the form , where is a whole number and is a prime number. 9. Simplify ( 75 3 ) 2 10. Simplify ( 3 5 ) 2 8 expressing your answer in surd form. 11. Given that d 3 , e 6 and f 12 , simplify each of the following, indicating in each case whether your answer is rational or irrational. (i) e f d e (ii) (d e)( d e)
