Measurements - Middle School Math

A long piece of wood is 8.25 feet long. If this piece were to be cut into 5 equal pieces how long will each piece be?

a. 11.25 inches
b. 19.80 inches
c. 22.75 inches
d. 27.15 inches

Answer : 19.80 inches (answer b)

The student must notice that the dimension of the original piece of wood is in feet units while the answers are in inch units. This is an important observation since all units must match in order to solve the problem. Therefore, as a starting point, we will convert the 8.25 feet into inches. In order to do that, the student must realize that each 1 foot = 12 inches. Therefore:

8.25 feet x [12 inch/1 foot] = 99 inches
(note here that the units for feet are eliminated and we are left with only the inch units we need to continue solving the problem).

Since we need to cut this piece into 5 equal pieces then we must divide the 99 inches by 5 to reach the final answer:

99 inches / 5 = 19.8 inches

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

Subtraction - Elementary School Math

There are a total of 72 cars parked in the used parking lot 8 of them are blue. How many cars are not blue?

a. 58
b. 62
c. 64
d. 68

Answer: 64 (c )

This is a subtraction problem. The student must subtract the 8 blue cars from the total 72 cars in order to come up with what is remaining. The remaining number will be the number of cars that are not blue. Here is the step:

72 - 8 = 64

For additional interactive practice visit: Aplusmath.com

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

Functions - College Level Math

If

f(x) = (x-3)

and

g(x) = (2x + 4)

Evaluate:

(f + g) (2)

Answer : 7

The above two equations are examples of the use of the Algebra of functions.

A function is a relation that does not repeat any first coordinates.

The problem is asking the student to evaluate (f+g)(2). This is the same as saying take the sum of functions f(2) and g(2) respectively and evaluate the result.

The steps involved in solving this problem are as follows:

• Substitute the equation of f(x) for the (f) value of the function.
  
• Substitute the equation of g(x) for the (g) value of the function.
  
• Add the two equations.
  
• Take the function with respect to (2) Evaluate the answer.
  

Here is the algebraic solution for the problem.

f(2) = ( 2 - 3) = -1

g(2) = ( 2(2) + 4 ) = ( 4 + 4 ) = 8

(f + g) (2) = ( -1 + 8 ) = 7


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

Parallel Lines - High School Math

The line shown on the Cartesian coordinate graph below passes by points AB. Another line needs to be drawn parallel to line AB and passes by point C shown on the graph and point D.

What coordinates should point D have that will make line CD parallel to line AB?

a. (-3, 4)
b. (-5, 2)
c. (-6, 0)
d. (-9,-1)

Answer: The coordinates for point D are (-9,-1).

In order to solve this problem the student must recall that parallel lines have the same slope. Therefore, the slope that is calculated for line AB will be the same slope for the line parallel to it that passes through point C.

Therefore, step one is to calculate the slope for line AB.
The coordinates for point A are (6,1)
The coordinates for point B are (1,0)

The slope formula states that:

Let apply the formula to find the slope for line AB:

m = (0 - 4)/(1 – 6) = (- 4)/(- 5) = 4/5

An examination of point C on the graph reveals that the coordinates for this point are:
(- 4 , 3).

The student must now use this point and check each of the above coordinates provided as a possible answer to determine which pair resulted in a slope of 4/5.

Once the coordinate pair of (-9 , -1) is checked, it reveals the following:

m = (- 1 – 3)/ (- 9 – [- 4])
m = (- 1 – 3)/ (- 9 + 4) = (- 4)/(- 5) = 4/5

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

Finding Angles of a Triangle - Middle School Math

In the following triangle, if angle ABC equals 80 degrees and angle BAC equals 40 degrees, what does angle ACB equal to?

Answer:

Angle ACB equals 60 degrees.
The measures of the three interior angles of a triangle must equal to a total of 180 degrees. Therefore we must add the two shown angles and subtract that number from 180 in order to find the correct answer. The step is as follows:

180 - (80 + 40) = 60

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