WCGS Mathematics Lower Sixth Bridging Work 2018

Transcription

1 WCGS Mathematics Lower Sith Bridging Work 08 To be successful in Mathematics, students need to be confident in certain aspects of algebra, coordinate geometry and trigonometry before starting the course. All students wishing to study Mathematics in the Lower Sith are required to have completed this pack before joining the course.. Students are often rusty after the summer, so this pack should be completed between Results Day and the first day back to ensure your skills are up to scratch right at the start of the course. We do not advise students to do it earlier than this unless they will be away during the last few weeks of the holidays.. Students need to be able to write their solutions clearly and in full, with the work well set out. Work should be written on A4 lined paper and your name written at the top. Full working must be shown, with each line of working below the previous one, that is, you need to work down the page. Question numbers should be put in the margin. Only one column is to be used on a page. Failure to show full working will result in your being asked to redo the pack. Answers are given at the end and students must MARK their work before it is handed in. Marking should be done clearly in RED. Any questions that are not initially solved correctly should be retried until the correct answer is obtained. If you cannot obtain the correct answer, after retrying the question, a red circle should be put around that question number. Work that is not marked in this way will not be accepted.. The topics covered in this pack will be considered assumed knowledge when the course begins. If there are topics in this pack that you are uncertain of then you should visit the BBC Bitesize website ( for support. 6. There will be a TEST on this work at the beginning of the term. The results of this test, together with public eam results, will be used to put you into sets. These sets will be adjusted after a further assessment that will take place 4 weeks into the term.

2 Wallington County Grammar School Lower Sith Maths Bridging Work 08 The rules of indices Eercise Simplify these epressions ( p ) 4 p. 9 ( ). 7 a 4 4 a ( ) ( 4y ) y Epanding brackets Eercise epand and simplify 4( + ) -( 7). ²( + ) ²( 4). (a b + c)(a + b c) (² + + )( ² ) Factorising epressions Eercise factorise completely ( + ) 7( + ) Solving quadratics Eercise 4 solve using factorising. Some will need to be rearranged first. ) ² ) ² ) ² ) 6² 8( + ) ) ² 4 0 6) 4² 0 Using the Quadratic Formula Eercise solve using the Quadratic Formula (give your answers to sf) ) 6² 0 0 )

3 Wallington County Grammar School Lower Sith Maths Bridging Work 08 Completing the square Eercise a Convert these epressions to completed square format ) + + ) 8 7 ) + 0 4) 4 Etending the rules for indices Eercise 6 - Evaluate without using a calculator Using surds and irrational numbers 7 8 Eercise 7 - simplify ( + ). Find the value of when +

4 Wallington County Grammar School Lower Sith Maths Bridging Work 08 Rationalising the denominator Eamples a. b. c Eercise 8 rationalise the denominators.. Changing the subject of a formula 4 Eercise 9 Make y the subject. a y ay b. 4 y a y y m( y n). p y y Inequalities Eercise 0 Solve these inequalities. ( ) ( ). - < + < 6 4

5 Wallington County Grammar School Lower Sith Maths Bridging Work 08 Algebraic fractions Eercise Simplify as far as possible Simultaneous Equations Eercise Solve to find both and y.. y 4 y. 4 y 0 y 9 y 4 y 6 y y

6 Wallington County Grammar School Lower Sith Maths Bridging Work 08 Coordinate Geometry Eercise Straight Lines... 6

7 Wallington County Grammar School Lower Sith Maths Bridging Work 08 Eercise 4 Trigonometry... End of bridging work. 7

8 Wallington County Grammar School Lower Sith Maths Bridging Work 08 Lower Sith Mathematics Bridging Work 08 Solutions Eercise Eercise Eercise Eercise 4 p 4² ( + 7 )( ) -, -/ 8 7-9³ + ² ( )( ) -4, / 6a a b c ab + bc ( + )( 4 ) /, 6 4 y ( 8 + )( + ) 4 -/, ± 6 - /, / Eercise Eercise a Eercise 6-76, ( + ) + 8 ( ) , 94 ( ) 4 ( + ) Eercise 7 Eercise Eercise 9. ( a ab)/( b ) y. /( a ). / mn/( p m) Eercise < 7. 4 Eercise ( )/( ). ( ) /( ). ( 7 )/ 0. ( )/ 0 6. / ( 9)/ 0 Eercise, y 4., y. (-4, ) and (-,) (, ) and (,) Eercise a: F & G; C & D b: B & H; A& E c: I. y. a: a: (4, ). a: y 0 8

9 Wallington County Grammar School Lower Sith Maths Bridging Work 08 Eercise 4 a: cm b: 9m c: 8cm a: 7. b: 97 c: 6.8 a:.6m b: 070cm c: cm 4 a: 7.7miles b: 09 9cm 9