A Tricky 'n' Easy Maths Quiz! (3)

Answer: 18 cm^2

The formula for finding the area of a kite or a rhombus is:
1/2 * (product of diagonals)
The diagonal labelled AC is 4.5 cm long. The other diagonal labelled BD is 3.5 cm longer than the diagonal AC. In other words it is
4.5 cm + 3.5 cm (or 8 cm) long. Then using the formula:
1/2 * (product of diagonals)
= 1/2 * (4.5 * 8)
= 1/2 * (36)
= 18 cm^2.

Answer: 2x^2/3

The best way to simplify an expression is to expand it and then simplify it rather than just simplifying it directly:
5x 6x 5*x*6*x 1*x*2*x 2x^2
-- * -- = ------- = ------- = ----
3 15 3*15 1*3 3

(2x)^2/3 is incorrect because in this expression 2x has been raised to 2 whereas in the correct answer only the x is to be raised to 2. This expression can also be simplified further to 4x^2/3.
(2)^2*x/3 is equivalent to 4x/3 because in this expression, 2 has been raised to the second power.

Answer: 40/240 = 1/6

In this question, we have one event which is made up of two separate events. Be careful with the 'and' in: "What is the probability that Tom draws a red marble 'and' John draws a red one?" This 'and' joins the two separate events and makes it one event. In such cases, we multiply the individual probabilities to get the answer.
P (Tom draws a red marble) = 8/16
P (John draws a blue marble) = 5/15
There are 16 marbles in the jar (5 + 8 + 3), out of which 8 are red. After Tom draws a marble, there will be 15 marbles left, and there are 5 blue marbles.
Therefore 8/16 * 5/15 = 40/240 = 1/6.

Answer: 3.82 inches

The formula for finding the circumference of a circle is "2 Pi r" or "Pi d" where r is radius and d is diameter. 2 Pi r can also be written as Pi d because 2r = d (i.e 2 times a circle's radius is equal to its diameter).
Make "d" the subject of the formula and you get:
d = Circumference
-------------
Pi
Plug in the numbers:
d = C/pi
d = 12/3.14
d = 3.82 inches (correct to 3 s.f.).

Answer: 90%

We can express a fraction as a percentage by multiplying it by 100%. This does not alter its value, since 100% is 1. Therefore, we multiply John's score by 100%: 4.5
----- * 100% = 90%
5
Notice that 4.5 out of 5 means 4.5
----- .
5

Answer: 12.5%

There is a formula for such percentage word problems which is:
Percentage profit = actual profit divided by the original price times 100.

The actual profit is £2 because £18 - £16 = £2. 2 divided by 16 times 100 = 12.5%.

Answer: supplementary

For example, the supplement of 75 degrees is 105 degrees (180 - 75).

Answer: 3500 degrees2

The angles of a triangle add up to 180 degrees. Consider 180 degrees as 18 equal parts (i.e 5 + 7 + 6). Then the first angle has 5 parts, the second angle has 7 parts and the third angle has 6 parts.
Therefore:
5
-- * 180 = 50 degrees.
18

7
-- * 180 = 70 degrees.
18

The product of the smallest and largest angle is 50*70=3500 degrees^2. This is a strange unit but there is a way to prove it. If we had to express the ratio 50 degrees : 70 degrees in its simplest form, we would get 5 : 7 not 5 degrees : 7 degrees because there is degrees in the numerator and there is degrees in the denominator, and thus they get cancelled.
Notice that the word 'product' in mathematics means "to multiply".

Answer: 10800

The volume of the box = cubic centimetres of rice which can be put in the box. In this case, since it is a rectangular box, we can find the volume by multiplying the three dimensions together.
This tells us that "volume" in mathematics means the space occupied by an object.

Answer: 25

This question could also be written as: "If one pair of jeans cost £5, how much do 5 pairs of jeans cost?".
5*5 = £25.
Therefore, Jill needs to earn £25 to buy 5 more pairs of jeans. An easy question to end with, right? ;)