A Tricky 'n' Easy Maths Quiz! (6)

Answer: infinite

I did not ask to find the diameter of the circle - I asked how many diameters a circle has. The radius was just given to confuse you, so that you could click on 20. Remember that a circle has an unlimited number of diameters and radii, and infinite lines of symmetry, as well. A 'diameter' is defined as a chord that passes through the centre of a circle. It is also the longest chord in a circle. A 'radius' is the distance between the centre of a circle and any point on the circumference (The plural of radius is radii).
Also remember that Diameter = 2 * Radius, and Radius = 1/2 * Diameter.

Answer: From 1 to 69

Remember that Percentage Increase = Increase/Original Number * 100, and Percentage Decrease = Decrease/Original Number * 100, where Increase is New Number - Original Number and Decrease is Original Number - New Number.
In this case, as all of them are percentage increases, we first use the 'Increase = New Number - Original Number' formula to know how great the new number is.
We just plug in the numbers and we get:
81 - 13 = 68, 80 - 12 = 68, 69 - 1 = 68. In all the cases, the new number is 68 more than the old number. But what about the percentage increase?
Using the formula 'Percentage increase = increase/old number * 100', we get:
68/13 * 100 = 523.076923...%
68/12 * 100 = 566.6...%
68/1 * 100 = 6800%
Therefore, the percentage increase from 1 to 69 is the greatest.

Answer: 7.00 cm

A cube has six faces which are all squares. If y cm is the length of a square, then the area of that square is y^2 cm^2. Similarly, the area of six such squares will be 6y^2 cm^2 or (y^2 + y^2 + y^2 + y^2 + y^2 + y^2)cm^2.
Remember that cm^2 (centimetres square) is a unit of area, and that a cube is a solid. When we talk about the surface area of a solid, we talk about the area covered by the outside of the solid. The area covered by the inside of the solid is called the volume.
Surface area of a cube = 6y^2 cm^2 (where y cm is the length of cube)
294 = 6y^2
294/6 = y^2
49 = y^2
y = 7.
So y = 7.00 cm (correct to 2 decimal places).

Answer: Cannot be determined

This cannot be determined as it is not specified what type of a heptagon it is. I never said that the heptagon was regular, did I? IF it was a regular heptagon (a seven-sided closed polygon with all sides and interior angles equal), then we could have divided 84 cm by 7 to get 12 cm as the length of a side of a heptagon. And as the length of a side of the heptagon was equal to the length of a side of the square, we would square 12 cm to get 144 cm^2 as the area of the square.
Sorry for that tricky question! I hope many of you got that one right!

Answer: (x^2 - 256) cm^2

Your first task is to find t. t is the negative sq. rt. of 36, which is -6. Remember that every natural number has two roots - a positive root and a negative root. 36 has two roots, +6 and -6. But we are concerned with the negative sq. rt., so we use -6 in our equation to find y.
y = 2t + 28
= 2*(-6) + 28
= -12 + 28
= 16.
Using y as 16 cm, we then multiply the length by the width to get its area:
(x + y) (x - y) [We can use the identity x^2 - y^2 = (x+y) (x-y) to get the area)
> (x + 16) (x - 16)
> x^2 - 16^2
> x^2 - 256.
Therefore, the area of the rectangle is (x^2 - 256) cm^2.

Answer: 56 cm

Remember that any number raised to the power 0 is equal to 1. (1.12 * 10^0) can also be written as (1.12 * 1), which is 1.12.
The stick is divided between Anne, Carol and Ben in the ratio 1:3:4. The first name corresponds to the first ratio, the second name to the second ratio and the third name to the third. Therefore, Ben receives 4 parts of the total 8 parts (1 + 3 + 4), which is:
4/8 * 1.12 m = 0.56 m = 56 cm. (1 m = 100 cm)

Answer: 266

2^(x + y) can also be written as 2^x * 2^y.
If 2^x = 7, and 2^y = 38, then 2^(x + y) is (7 * 38), which is 266.

Answer: 290,000,000

A year that is divisible by 4 is a leap year. As 2000 is 500 times greater than 4, 2000 was a leap year. In a leap year, there are 29 days in February. If the factory produces 10000 litres of milk in a day, then in 29 days, it produces 290000 litres of milk, which is equal to 290000000 millilitres of milk.
Remember that 1 litre = 1000 millilitres. The question stated to determine the number of 'MILLILITRES' of milk produced by the factory in February 2000, NOT the number of litres.

Answer: 2.2

The arithmetic average or mean is found by adding up all the elements in the set and dividing by the number of elements in the set.
(2 - [- 8]) = 2 + 8 = 10. There is a negative sign outside the bracket and there is one inside. When two negative signs are multiplied, they become positive.
So - 8 + 10 + 3 + 7 + - 1 = 11. When you divide 11 by 5, you get 2.2, which is the mean of the set of numbers, in this case.

Answer: All of these

You don't need graph paper to get this one right! In the ordered pairs (3, 119.5), (- 415, - 925.5) and (- 14, 77), the x co-ordinates are 3, -415 and -14, and the y co-ordinates are 119.5, -925.5 and 77. You just have to substitute either the x or the y co-ordinate in the equation and solve to find out whether the point lies on the line or not.
y = 2.5x + 112
= 2.5 (3) + 112
= 119.5
y = 2.5x + 112
= 2.5 (- 415) + 112
= -925.5
y = 2.5x + 112
= 2.5 (- 14) + 112
= 77
In all the above cases, you will see the that y = 119.5, -925.5 and 77! I just substituted the x-coordinates, i.e. 3, -415 and -14 in the equation and I got the corresponding y - coordinates!
That was easy, wasn't it? I hope you enjoyed this quiz. Please send me your compliments and comments. I would be delighted to read them and I am also ready to help you out if you had a problem with any of the above questions. Bye bye till next time! ;p