2.
Solving Equations <br />Solve for a certain variable, which is normally x. <br />Involves re-arranging the equation to get x by itself.<br />E.g. 2x + 6 = 4,<br /> 2x = -2<br /> x = -1 <br />
3.
Solving using the null factor law<br />If the product of any two numbers is zero, then one or both of the numbers is zero.That is, if ab = 0, then a = 0 or b = 0 (which includes the possibility that a = b = 0).<br />E.g if (x-6)(x-3) = 0 then x is said to be 6 or 3.<br />Helps us to find the x intercepts and y intercepts of a graph as the graph will intersect the axis when x or y equal zero.<br />
4.
Solving Exponential and Logarithmic Equations <br />a^x = a^y, implies x=y<br />E.g. 3^(x-1) = 256 <br /> 3^(x-1) = 3^4<br />x – 1 = 4, x = 5<br />Sometimes you need to re-arrange the equation back into its logarithmic form, using the rule <br />logax = y if ay = x<br />E.g. Solve the equation 0=-5e(x/2) for x:<br /> (Do Question Together as a Class)<br />(Solution Page 157 Notes Book)<br />
5.
Book Questions:<br />Complete;<br />Exercise 5.C; Q3.a, c, e, k <br />
6.
Solving Logarithmic Functions Cont.<br />E.g. Log2x = 5<br /> x = 25 , x = 32<br />Logx27 = 3/2<br /> x3/2 = 27<br /> x = 272/3 , x = 9<br />Loge(x-1) + loge(x+2) = loge(6x-8)<br /> loge(x-1)(x+2) = loge(6x-8)<br /> x2 + x – 2 = 6x – 8<br /> x2 – 5x + 6 = 0<br /> (x-3)(x-2) = 0, x = 3 or x = 2<br />
7.
Book Questions <br />Do Question 4.e, page 175<br />Complete;<br />Exercise 5.D; Q3.a, c, e, i. Q4. a , b, c,<br />
8.
Solving using the Solve( command<br />Enter solve( by pressing F2 and then 1. Next type your equation in, and then put a comma and type in x (or whatever variable your solving for). Then close the brackets.<br />E.g. for Loge(x-1) + loge(x+2) = loge(6x-8) you would type solve(ln(x-1) + ln(x+2) = ln(6x-8),x)<br />
9.
Solving Circular Functions<br />Involves re-arranging to get x by itself.<br />Do example 18b, page 214 on the board.<br />Solve this equation individually;<br /> solve √2sinx + 1 = 0 for x. <br />
10.
Book Questions <br />Complete;<br />Exercise 6.H; Q.1. a, c, e – only finding x interecepts.Q2. a, c, e – only finding x intercepts for the interval [0,2π]<br />
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