AM Modulus Misc Ex 5 Q7-11

8/6/2019 AM Modulus Misc Ex 5 Q7-11

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6. (a) Solve the equation Ix2 - lOx + 81 = 8.(b) Sketch the graph of Y = Ix 2 - lOx + 81. Hence, find the range of values of x

for which Ix 2 - lOx + 81 < 8.

7. Solve the following simultaneous equations.(a) Y + 2x = 3 and Y = 12x - 11 (b) 2x + 3y = 19 and Ix - yl = 3

8. Sketch on the same diagram the graphs of y = 12x - 51 and y = 4 - x. Calculatecoordinates of the points of intersection of these two graphs.

9. The graphs of y = 12x - 11 and 2x + 2y = 7 intersect at the points (Xl' Yl) and(x 2, Y2)' Calculate IX2 - xII + IY2 - Yll

10. (a) Solve the simultaneous equations Y = 2x - 1, Y = [x - 21.(b) On the same diagram, sketch the graphs of Y = 2x - 1 and Y = IX - 21.(c) Hence, find the solution set for which 2x < Ix - 21 + 1.

11. The diagram shows part of the graph of y

Y = [x - 21- 5. The graph cuts the x-axis at P and Q.Find the coordinates of P and Q. Hence, write downthe range of values of x for which Y is positive. Q

212. (a) Given that f(x) = Ix - 3xl, find the values of x for which f(x) = x.

(b) A function f is defined by f(x) = Ix - al + b. Given that f(3) = 3 and f(-I) =find the value of a and of b.

CriticaL Thinking

13. Check whether the following statements are correct or not.

(a) H = x (b ) H =xUse a graphing software to plot the graph of Y

=H . Does the shape of this

graph look familiar? What is H ?

Hence, solve the equation ~ ( x - 3)2 + Ix - 41= 312 - x l - 5 given that x < 2.

14. Solve the equation ~ - Ixl - 2 = O.In a group, explore different ways of solving this equation.

AM Misc Ex 5


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AM Modulus Misc Ex 5 Q7-11