Classify the triangle ABC by its sides if A ≡ (4, − 5), B ≡ (2, − 6) and C ≡ (−3, 0).

The line graph above shows the average price of one metric ton of oranges, in dollars, for each of seven months in 2014.
Between which two consecutive months shown did the average price of one metric ton of oranges decrease the most?

Note:
A simpler way of solving this question is to check where the decrease in the graph has the steepest slope between two months. It is clearly between the months June and July. Here, it is obvious; but that may not be the case in other problems. So, we need to always calculate the actual decrease in the value.

The scatterplot above shows the total number of home runs hit in major league baseball, in ten-year intervals, for selected years. The line of best fit for the data is also shown. Which of the following is closest to the difference between the actual number of home runs and the number predicted by the line of best fit in 2003?

Note:
A line of best fit is also called a trendline. The equation of a line of best fit can be represented as y = m x +  b , where m is the slope and b is the y-intercept. This is the equation of a line. It is a line that minimizes the distance of the actual homeruns from the predicted homeruns.

Classify the small and big triangular shapes by their sides shown in the diagram.

Equilateral triangle is also ______.

The function g is defined as  . What is the value of ?

Note:
We can be given any function and asked to find the value of any expression like , etc. The process is similar to above. Just carefully find the value of g  at the different values of x  given and calculate the final expression.

ABCD is a parallelogram,  and 
If  AB = 12cm, AD = 8cm and AL =6cm, find the measure of AM.

Name the theorem or postulate that justifies the given statement.
∠1 ≅ ∠2

A rope joins the points P ≡ (-10, 5) and Q ≡ (6, 9). At which point should we cut the rope to get two equal parts?

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 .