How many times does the number '1' occur in the first 63 terms?

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Question No. 3

The vertices of a triangle are (-1, 3), (1, 1), and (7, 1). Find its area.

ANSWERED

Question No. 4

In the diagram, all the dots are equally spaced. Segment `bar(AB)` is drawn. How many ways are there to choose point C from the remaining points so that triangle ABC is isosceles with AB=AC?

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Question No. 5

In the expression `(a)/(b)+(c)/(d)+(e)/(f),` each letter is replaced by a different number from 1, 2, 3, 4, 5, 6.

What is the largest possible value of the expression?

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Question No. 6

A certain company allows employees to retire when the sum of their age and number of years worked equals 85. Amie is 45 years old and has worked 18 years. If she works continuously until she retires, how old will she be when she can retire?

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Question No. 7

A 1 litre carton for juice uses 500 cm^{2} of cardboard to make and costs $5.25 to buy.

A mathematically similar 500 ml carton for juice uses 300 cm^{2} of identical cardboard to make and costs $2.60 to buy.

Which size carton is better for the environment in terms of cardboard use?

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Question No. 8

If `x=1440-:3` , `y=x-:3` , and `z=x+y` , then the value of `z` is

ANSWERED

Question No. 9

Triangle `ABC` is a right triangle with `/_C=90^O` . If `bar(AB)=13` , `bar(BC)=5` and `bar(AC)=3xxDC` , find `bar(BD)` .