9. Solve the following equations. (i) 1


__ 2 x2


(ii) 1


__ 3 x2


__ 2 x 2


− 1 __


(iii) 0·5 x2 (iv) 1


2 x − 3 = 0 − 3x + 6 = 0


+ 2·5x + 2 = 0 = 5·5x − 14


10. Seán is y years old. His brother Michael is four years older than Seán. The product of their ages is 780.


(i) Set up an equation to represent this information.


(ii) Solve your equation from (i) to fi nd Seán’s age.


11. A ball is thrown upwards from a rooftop, 80m above the ground. It will reach a maximum vertical height and then fall back to the ground. The height of the ball from the ground at time t is h , which is given by: h(t) = − 16 t2


+ 64t + 80


(i) What is the height reached by the ball after 1 second?


(ii) How long will it take for the ball to hit the ground?


12. The equation P(t) = t2 + 4t − 5 is the profi t in


€1 000s made by a company after t months. (i) Find the profi t made after two months.


(ii) After how many months did the company make €55 000 profi t (i.e. when P(t) = 55 )?


13. The following picture shows the shape of a certain grass patch.


k – 3 x x


(i) By letting x equal the width of the path, fi nd an equation, in terms of x , for the area of the path Finnbar can make.


(ii) Given the amount of gravel Finnbar has, fi nd the width of the path he can make.


k – 9


Taking it FURTHER


10 n – 2


14. A right-angled triangle is shown.


n (i) Using Pythagoras’s theorem, fi nd n.


(ii) Hence fi nd the value of the lengths of the two unknown sides of the triangle.


15. Finnbar wishes to make a gravel path around his rectangular pond. The path must be the same width all the way around as shown in the diagram. The pond measures 4 metres by 9 metres and he has enough gravel to cover an area of 48 m2


. x 9 m 4 m x


(i) Find an expression that describes the area of the patch of grass.


(ii) By letting the equation from part (i) equal zero, fi nd two possible values for k .


242


Linking Thinking 2


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