The parallel sides of a trapezium are in the ratio 3:4. If the distance between the parallel sides is 9cm and the area is 126cm², find the length of its parallel sides.

The functions f and g are defined by f(x) = 4x and g(x)= x². For what value of x does f (x)– g( x) =4 ?

Note:
Instead of solving the equation   in the above way, we could also use the quadratic formula, given by


Where the quadratic equation is given by
Or we could simply observe that it the expression of a perfect square

Find the co-ordinates of the mid-point of AB, if A ≡ (1, 10) and B ≡ (3, -8).

The adjacent sides of a parallelogram are 8cm and 9cm. The diagonal joining the ends of these sides is 13cm. Calculate the area of the parallelogram.

Note:
Instead of adding 2 on both sides, we can also understand the concept by taking  -2 of the right hand side on the left hand side and then the sign changes to + 2 . Similarly, instead of subtracting both sides by , we can understand it by saying that we take + x  from the left hand side to the right hand side, and here it becomes  - x .
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.

Find the value of x that satisfies the equation 7x + 22 = − 27 .

The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10cm . If its altitude is 8cm, what is its area?

Joe’s age is 16 years less than 5 times Jim’s age. Find Jim’s age if Joe is 9 years old.

Are the two polygons congruent? Explain why or why not.

Which of the following expressions is equivalent to the expression above?

Note:
Another way of solving this problem is to expand all the terms in the expression

Then we get,

Thus, we will get that

Can be written as

This also gives the same answer as above. No matter which method we use to simplify the expression, we will always get a unique answer.

△ DEF ≅ △ LMN
m∠D = m∠L = 70°
m∠F = m∠N = 30°
Which of the following statements is NOT true?

The parallel sides of a trapezium are 30cm and 10cm and the other two sides are 13cm, 21cm .find its area?

Draw the line of reflection for the word MOM

One hundred park-district members will be selected to participate in a survey about selecting a new park-district coordinator. Which of the following methods of choosing the 100 members would result in a random sample of members of the park district?

Note:
The method given is option A is called simple random sampling. Some other methods of random sampling are stratified random sampling, cluster random sampling and systematic random sampling.
Infact, there is further categorisation of simple random sampling- probability and non-probability sampling.