Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

The presentation includes all the necessary material for review of Chapter 2.2 Harder Surds for A-level Pure Mathematics Cambridge International Examinations. It will be useful for students as the review materials and also for teachers as the teaching tips and presentations in the class. The presentation was made by Oleksii Khlobystin (Alex) - Mathematics Teacher at Depu Foreign Language School, Chongqing City, China. Personal website: www.visualcv.com/o-khlobystin Personal email: o-khlobystin@yandex.comPresentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709 Made by Oleksii Khlobystin (Alex) - Mathematics Teacher at Depu Foreign Language School – Cambridge International Centre, Chongqing City, China. Personal website: www.visualcv.com/o-khlobystin Personal email: o-khlobystin@yandex.com

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

We met surds when solving quadratic equations. e.g. Find the roots of the  x 2 equation Using the formula for :02cbxax21x xaacbbx242Solutio 222482222x Simplifying the surd: 2  2  )1(2 )1)(1(4   1 0  x   x  n: 2  2 2 )2( 8

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

We can also simplify surds which are in the denominators of fractions. 21e.g.1 Write the expression in the form pp and the denominator by : 221212222222A fraction is simplified if there are no surds in Solution: Multiply the numerator the denominator.

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

e.g.2 Simplify the expression 2032 Solution: We first simplify the surd.20325432523255531Multiply the numerator and the denominator by 511155

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

e.g.3 Write the expression in the form qp))((babaMethod: We know 22ba 321 So, )32)(32( 22)3(2341By multiplying the expression by the surd has disappeared. )32( )32( )32( However, if we multiply the denominator by we must multiply the numerator by the same amount. that

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

: 3432323232 321321Solution The process of removing surds from the denominator is called rationalising.

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

Exercises: Simplify the following by rationalising the denominators: 1. 232333331292232222326221332232323229)23(27)23(2 312. 1823.

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

We can also surds which are in the denominators of fractions. 21e.g.1 Write the expression in the form pp and the denominator by : 221212222222A fraction is simplified if there are no surds in Solution: Multiply the numerator the denominator.

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

e.g.2 Simplify the expression 2032 Solution: We first simplify the surd.20325432523255531Multiply the numerator and the denominator by 511155

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

: 3432323232 321321Solution The process of removing surds from the denominator is called rationalising.

Presentation POWER POINT Chapter 2.2 Harder Surds, A-level Pure Mathematics CIE 9709

SUMMARY fraction of the form qpba. . . multiply the numerator and denominator byqp  To rationalise the denominator of a SUMMARY

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17.05.2018