8774 words - 35 pages

What you will learn Expanding binomial products Perfect squares and difference of perfect squares Factorising algebraic expressions Factorising the difference of two squares Factorisation by grouping Factorising quadratic trinomials Factorising trinomials of the form ax 2 bx c Simplifying algebraic fractions: multiplication and division Simplifying algebraic fractions: addition and subtraction Further simpliﬁcation of algebraic fractions Equations with algebraic fractions

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8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9

8.10 8.11

Chapter

Algebraic techniques

What you will learn

8

ISBN 978-0-521-17865-5 Photocopying is restricted under law and this material must not be transferred to another party.

© Greenwood et al. 2011 Cambridge University Press

445

Free falling

Australian curriculum N U M B E R A N D A L G E B R A

P a t t e r n s a n d a l g e b r a

Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate

P a

Ap ex inc wh

s

The distance (x) of an object from the top of a building after it has been dropped (where air resistance is negligible) can be found using the formula x ut

1 2

at 2 where u is the initial velocity of the object, t the time since the object has been dropped and a the acceleration due to gravity, which is approximately equal to -9.8 m/s2. When an object is dropped it has an initial velocity of 0 m/s, so the distance the object has fallen becomes x -4.9t 2. Using algebra, the distance from the building after t seconds can be found or the time taken to reach ground level could be calculated. If the object is instead dropped from a hot air balloon ascending at 10 m/s, the object ﬁrst travels in an upward direction. Its distance (x metres) above or below the height of the balloon from when the object is dropped can be found using x 10t 4.9t 2. Knowing the time taken for the object to reach the ground, we could again use algebra to ﬁnd factors, such as the height of the balloon, the greatest height reached by the object and the time taken for the object to return to the height it was released from.

ISBN 978-0-521-17865-5 Photocopying is restricted under law and this material must not be transferred to another party.

© Greenwood et al. 2011 Cambridge University Press

Chapter 8 Algebraic techniques446 p g q

1 Expand the following. a 2(x 3) b 3(a 5) c 4x(3 2y) d -3(2b 1)

2 Evaluate. a 92 b 42 c 12

d (2x)2 if x 4 e (5a)2 if a -1 f b if b2 49 and b 0 g y if y2 9 and y 0 h m if m2 36 and m 0

3 Write down the highest common factor of: a 4 and 6 b 12 and 18 c 2x and 4x d 3xy and 9y e 10x and 15x2 f 3a2b and 4ab2

4 Factorise by taking out the highest common factor. a 2a 6 b 3x 12y c 5x2 15x d 4m 6mn

5 List the pairs of whole numbers that multiply to each of the following. a 6 b 12 c -10 d -27

6 Simplify:

a 2

7

2

3 b 7

9

1

6

c 3

8

2

9 r d 5

8

5

12 v

7 Expand and simplify. a 3(x 1) ...

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