Cambridge International Mathematics

Challenge

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12 Find the quadratic function with vertex(¡ 4 ,15)andy-intercept¡ 17. Give your answer in the

form f(x)=ax^2 +bx+c.

13 The sum of a number and five times its square, is equal to four. Find the number.

14 Two numbers differ by 3 and the difference between their reciprocals is 4. Find the exact values

of the numbers given that they are both positive.

15 Kuan has$ 180 to share amongst his grandchildren. However, three of his grandchildren have

misbehaved recently, so they will not receive any red packets with money in them. As a result, the

remaining grandchildren receive an extra$ 5 each.

16 A 90 m£ 90 m block of land is to be divided into three

paddocks using two straight pieces of fencing as shown.

Given that all three paddocks must have the same area,

determine where the fencing needs to be placed. To do this

you need to find the lengths of CX and AY.

AB

DC

Y

90 m X

90 m

How many grandchildren does Kuan have?

(Give AY to the nearest mm.)

1aShow that y=x^2 ¡x meets y=3¡x^2 when x=¡ 1 and x=1^12.

b Find the maximum vertical separation between the two curves for ¡ 16 x 6112.

2 A manufacturer of refrigerators knows that ifxof them are made, the cost of making each one of

them will be

μ

100 +

2000

x

¶

dollars.

The receipts for selling all of them will be

¡

1300 x¡ 4 x^2

¢

dollars.

How many should be produced to maximise his profits?

3 800 m of fencing is available for constructing six identical

rectangular enclosures for horses.

What dimensions would maximise the area of each

enclosure?

454 Quadratic equations and functions (Chapter 21)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_21\454IGCSE01_21.CDR Monday, 27 October 2008 2:10:29 PM PETER