Practice questions 14.7 1. Given the formula x = −b ± √


(i) 2 x2 (ii) 5 x2 (iii) 4 x2


+ 4x − 1 = 0 + 3x − 1 = 0 + 4x − 5 = 0


2. Solve the following using the quadratic formula, leaving your answers in surd form.


(i) x2 (ii) 3 x2 (iii) −t = − t2


+ 4x − 3 = 0 − 8x + 1 = 0 + 1


3. Solve the following using the quadratic formula, leaving your answers correct to two decimal places.


(i) 12 n2 (ii) 6 x2 (iii) 7 x2


+ n − 5 = 0 + 4x − 6 = 0 = 2x + 6


4. Solve the following, leaving your answers in surd form.


(i) x2 (ii) 2 x2


+ 6x + 1 = 0 − 2x − 3 = 0


(iii) − 30a + 9 a2 + 23 = 0


5. Solve the following, leaving your answers correct to two decimal places.


(i) x2 − 2x − 9 = 0 (ii) 7 b2 (iii) 10a + 3 a2


− 25b + 2 = 0 − 2 = 0


6. Shown is a right-angled triangle.


(i) Find the value of x , correct to two decimal places.


(ii) Write down the lengths of the three sides of the triangle.


(i) Find the value of x , correct to two decimal places.


(ii) Hence write down the length of side b .


244 Linking Thinking 2 b x + 5 2x + 1 x + 5 x – 2


___________ 2a


_ b2


− 4ac , solve


the following quadratic equations. Leave your answers correct to three signifi cant fi gures.


8. A rectangular fi eld is 15 m longer than it is wide. The area of the fi eld is 800 m².


(i) Letting x equal the width of the fi eld, write an expession for the length.


(ii) Calculate the length of the fi eld. Give your answer to one decimal place.


9. A rocket is launched at 푡 = 0 seconds. Its height, in metres above sea level, is given by the equation h(t) = − 4·9 t2


+ 52t + 367


How long does it take for the rocket to hit the ground? Give your answer to two decimal places.


10. The revenue, 푅, of producing and selling 푥 Farrigans jumpers is modelled by the function, R(x) = − 4 x2


+ 120x


How many Farrigans jumpers need to be produced and sold to earn a revenue of €880 ? You may have more than one answer. Give your answer(s) to the nearest whole number.


11. A rocket launch sequence starts at 푡 = 0 seconds, and lift off occurs at t = 0·71 seconds. Its height, in metres above sea level, is given by the function, h(t) = − 4·9 t2


+ 325t + 227


How many seconds after lift off does the rocket hit the ground? Give your answer to two decimal places.


12. The revenue, R , of producing and selling + 105x


푥 round bales of hay is modelled by the equation, R(x) = − 5 x2


How many round bales need to be produced and sold to earn a revenue of €531 ? You may have more than one answer. Give your answer(s) to the nearest whole number.


7. Shown is a triangle with area 20 cm². x + 6


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