Slope Of A Line - College Level

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Find the slope of the line going through the following points:

(3, 6) and (-2, -4)

The term “Slope” usually refers to an incline of a straight line. In order to visualize a straight line that is drawn at an incline, it is important to note that this line will travel a certain horizontal distance while rising up or down a certain vertical distance. The horizontal distance is called the “run” and the vertical distance is called the “rise”. The ratio between the two is called the “slope” which also represents the steepness of that line.

The formula used for calculating the slope of a straight line is as follows:

Where m represents the slope going through two points that are indicated as:

In order to calculate the slope we use the above formula as follows:

Therefore, the slope of the line = 2

© Copyright 2008.Najwa S. Hirn. All rights reserved.

Solving for a Variable - Middle school math

Solve for t in the following equation:

3t + b = 5

When a problem asks to solve for a particular variable, it means to isolate that variable on one side of the equation (equal sign) and isolate the other terms on the other side of the equal sign.

In order to isolate the t term in the above problem, we must eliminate b from the left side of the equation. This can be accomplished if b is subtracted from both sides of the equal sign as follows:

3t + b – b = 5 – b

It is important to remember that whatever is done to the right side of the equation must be done to the left side also.

At this point b is eliminated from the right side of the equal sign and the resulting problem is:

3t = 5 – b

It is necessary at this time to eliminate the number 3 from the left side of the equation. There are two ways that may be used to accomplish this. Either multiply both side of the equation by (1/3) or divide both side of the equation by 3.

Lets divide each side by 3 as follows:

(3t) / 3 = (5 - b) / 3

The 3’s on the left side of the equation cancel out and the problem is finalized as follows:

t = (5 - b) / 3

©Copyright 2008.Najwa S. Hirn. All rights reserved.

Number Sense - Elementary School Math

There were 35 pizzas at Andrew’s birthday party and 16 of them had only pepperoni topping while the rest had a mushroom topping. How many pizza had the mushroom topping?

a. 12
b. 19
c. 21
d. 8

Answer:  (b)  19 pizzass had only a mushroom topping.

The student needs to recognize number sense and know how to add, subtract, multiply and divide mathematical expressions.

In order to solve this problem, it is important to realize that the total number of pizza’s were 35 and since 16 had only pepperoni that means that the student must subtract 16 from the total of 35 to obtain the number of pizza’s with the mushroom topping.

35 – 16 = 19 pizzas with a mushroom topping.

©Copyright 2008.Najwa S. Hirn. All rights reserved.

Fractional Expressions - College Level Math

Multiply the following fractional expression and simplify:

Answer:

In order to solve this problem, we first must factor the numerator and denominator of each fraction. Once they are factored the problem will look like the following:

Now it is time to multiply the numerators and multiply the denominators as follows:

It is obvious from the above that several factors can be cancelled. It is noted that the(a-1) factors can be cancelled from both numerator and denominator and one (a +4) can be cancelled from the numerator. The final simplified answer will look as follows:

© Copyrightreserved 2008.Najwa S. Hirn. All rights

Volume Of A Cube - High School Math

One face of a cube has an area of 64 cm square – What is the volume of this cube?

Answer : 512 cm cubed

In order to calculate the volume of a cube, the length, height and width of the cube must be known since the formula for finding the volume is:
V = l w h
The problem does not provide information about the length, width or height; therefore they must be calculated using the information we were given about the area.

In this problem, we are given the area of one face. We know that the formula for calculating an area for any two dimensional figure is:
A = l w
Since each face of a cube is constructed from a square, then we know that the length and width of this square must be the same and by multiplying the two, the area can be found.

Lets apply what we have:
64 cm square = l w
Since we know that the length and width must be equal for a square, we can take the square root of the area in order to calculate the length of width:

square root of 64 = 8

Therefore, the length and width of each face is 8 cm. Therefore, the height of this cube will also be
8 cm. The volume can now be calculated as follows:

V = (8cm)(8cm)(8cm) = 512 cm cubed.

©Copyright 2008.Najwa S. Hirn. All rights reserved.

Reflection Of An Object - Middle School Math

If triangle ABC shown in the figure below is reflected about the y-axis what would the coordinates of the new triangle vertices be?

a. (-3, 3) (-5, 6) (-5, 3)
b. (-3, -3) (-5, -6) (-5, -3)
c. (3, -3) (6, -5) (3, -5)
d. (-3, -3) (-6, -5) (-3, -5)


























Answer: (a) (-3, 3) (-5, 6) (-5, 3)


In order to solve this problem, it is important to understand what happens when an object is reflected about an axis. When an object is reflected about an axis the vertices of the new object will have the same distance from that axis like the original object.

The reflection of triangle ABC is done about the y-axis in this problem. Therefore, the distances each ordered pair has from the y-axis will be the same in the new triangle. This means that the y-coordinate of each ordered pair will be the same in the new triangle like they are in triangle ABC. However, the reflection will mean that the x-coordinates of these points will have the opposite sign in the new object from the original one. In this case, the positive x-coordinates will change to negative x-coordinates.

To simplify this, we’ll look at the location of each ordered pair in the original triangle as follows:

Ordered pair (A) has the original points of (3, 3) therefore the reflected pair will be (-3, 3)

Ordered pair (B) has the original points of (5, 6) therefore the reflected pair will be (-5, 6)

Ordered pair (C) has the original points of (5, 3) therefore the reflected pair will be (-5, 3)

Note in all of the above points, the x-coordinate changed from a positive to a negative while the y-coordinate remained unchanged.

© Copyright 2008.Najwa S. Hirn. All rights reserved.

Elementary Math - Recognizing number sense

While visiting a historic district during a field trip, the students were told the dates that four of the historic houses were built. The chart below list those dates. According to the list, which house was built last?

a. House no. (1)
b. House no. (2)
c. House no. (3)
d. House no. (4)

Answer : ( c ) – House no. (3)

In order to solve this problem, a student must recognize which number in the table represents the highest number. That number will indicate the year the last house was built. By examining the table, it is determined that 1853 is the highest number in the table. Therefore House no. (3) was built last.

The student can list the numbers in ascending or descending order to assist in identifying the highest number.

In order to list the numbers in ascending order, they can be written as follows:

1803 - 1819 - 1836 - 1853

In order to list the numbers in descending order, the can be written as follows:

1853 - 1836 - 1819 - 1803

Both of the above cases indicates that the highest number is 1853 and the lowest number is 1803.

©Copyright 2008.Najwa S. Hirn. All rights reserved.