# 2015 MTAP Reviewer for Grade 9 With Solutions(11-15)

We’re done with 20% of the elimination paper of 2015 MMC (MTAP) for grade 9, now we will continue learning how to deal with mind boggling problems to win the competition next year.

**Problem 11:**

If , solve for x in

**Solution:**

To solve equations, we always eliminate fractions. By multiplying the whole equation by we can remove all fractions.

Now, since the right side of equation is radical, we raise both sides by 2,

By factoring we have,

These factors will immediately tell us that the values of x are 1 and 9/4. By quick check however, 9/4 fails to satisfy the original equation. Thus, the only solution is **1**.

**Problem 12:**

Evaluate

**Solution:**

This is a nested radical and I already have a tutorial on how to solve this problem. If you’re used to see problem like this, you might be able to solve it in less than 3 seconds. For real.

To solve this though, we let x be equal to

Square both sides,

Now, recall that

The square root of a positive number will always be positive. Thus, the answer is **2**. -1 is an extraneous root.

**Problem 13:**

Find the two consecutive integers whose product is 506.

**Solution:**

Let x be the smaller integer. Since we are looking for the two CONSECUTIVE integers, the other number must be x+1.

It is stated that their product is 506, thus

Therefore, the numbers that we are looking for are are **22** and **23**.

**Problem 14:**

If and if , what is the larger root of

**Solution:**

Let x and y be the roots of equation.

By Vieta’s formula, we have

*

**

From the relationship of the coefficients, we solve for c in terms of a and b.

***

We substitute *** to c of *,

****

From ** we solve for b/a,

We substitute this to ****

By factoring,

Since the roots are equal, there is no greater root. The answer is **-1**.

Problem 15:

Solve for x in

Solution:

We also provided the easiest way to solve this quadratic inequality in this site. But let us demonstrate the answer to this problem.

In this format, the answer is in the form of a<x<b, where b>a and a and b are the roots of inequality.

The roots are supposed to be 3/2 and -2. Thus, the solution set is** -2<x<3/2 or (-2,3/2)**