Preparing for an examination is never easy. The situation becomes graver if the subject that we are talking about is mathematics. The reason for the same may be attributed to the fact that mathematics is still one of the most feared subjects of the country.

When hundred students, who will be appearing for their board exams later this month, were quizzed on what it was that scared them the most, over 80% of them replied that it was the mathematics exam.

Now for those students who intend to secure pass mark, the easiest resort is the short MCQ or the 1 or 2 marks questions. To come to the aid of people appearing for the board exams and make matters easier for them, in this article we have compiled a list of important short questions that one must keep in mind while appearing for their board exams.

## 1. Linear Equations

Solve the following system of linear equations by substitution method

2 x - y = 2

x + 5 y = 15

The first equation can be written as y = 2x - 2. This value of y can be substituted in the second equation. This will give us the value of x. On knowing x, we can put it back in the first equation to solve the same.

## 2. Arithmetic Progression

Find the value of p for which the numbers 2 p - 1, 3 p+ 1 and 11 are in arithmetic progression. Also find the numbers.

When the numbers are in arithmetic progression, it means that they have a common difference. Make use of this fact to establish the value of p. Then substitute the value of p to find out the two numbers.

## 3. Probability

A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a king nor an ace.

In a pack of 52 cards, there are 13 aces and 4 kings. But one of the kings is an ace itself. Hence, the number of cards which are either a king or an ace is 16. The probability of finding a king or an ace when picking up a card at random from a packet of 52 cards is 16 / 52.

Since the maximum probability of an event is 1, the probability that a card that is picked at random is neither a king nor an ace is 1 - ( 16 / 52 ).

## 4. Coordinate Geometry

Find the coordinates of the point on the x-axis, which is equidistant from the points A ( - 2, 5) and B ( 2, - 3)

Take the point to be P (x, y). Now apply the distance formula to find out PA and PB. Now equate these two to find the value of x.

## 5. Linear Equations

If x = y, 3 x - y = 4 and x + y + z = 6, then find the value of z.

Substitute the first equation in the second to get 2 y = 4, this will give you y = 2. On substituting this to the first equation you get x = 2. Substituting these two values to the third equation you will get the value of z.

## 6. Arithmetic Progression

Find the number of all three-digit natural numbers that are divisible by 9

This question is easy to answer. 9, 18 and 27 are the first three natural numbers (ones that are divisible by 9). Then find the last such number. All such numbers will be in progression. Apply the formulae for sum of an arithmetic progression and you will get an answer.

## 7. Coordinate Geometry

Find the coordinates of the points of trisection of the line segment joining the points A (7, -2) and B (1, -5)

To solve this problem, find the distance between A and B. Then divide the distance by three. Let the value be L. Now if P (x1, y1) and Q ( x2, y2) are the points of trisection, then we know that AP = L and BQ = L. Also PQ = L. Substitute the values into the equations to get the result.

## 8. Quadratic Equation

The sum of two numbers is 18. The sum of their reciprocal is 14. Find the two numbers.

In this case you can take the two numbers to be x and y. Then you can form the two equations x + y = 18. The other equation will be (1 / x) + (1 / y) = 14. Substitute one value for the other in these two equations and you will arrive at the result.