7.3.5 Practice

Complete the following questions to practice the skills you have learned in this lesson.

1. Sketch or describe the figure in Step 4 and Step 15.
   
   

1. How many small squares are in Step 4?

2. How many small squares are in Step 15?

3. Which equation represents the relationship between the step number, $n$, and the number of small squares, $y$, in each step?

1. $y=n^2-<!--\; -\; -->n$
2. $y=n^2-<!--\; -\; -->1$
3. $y=n^2+1$
4. $y=n^2$

2. Each figure is composed of large squares and small squares. The side length of the large square is $x$. Choose the correct expression that represents the area, $y$, of the shaded part of each figure.

1. Figure A
   
   

1. $y=x^2-<!--\; -\; -->8$
2. $y=x^2-<!--\; -\; -->4$
3. $y=x^2-<!--\; -\; -->1$
4. $y=x^2$

2. Figure B
   
   

1. $y=2x^2$
2. $y=x^2+8$
3. $y=2x^2+8$
4. $y=x^2$

3. Use the sequence below to answer questions a and b.

1. How many squares are in Step 5?

2. Choose the correct expression that represents the area, $y$, of the shaded part of each figure for $n$ steps.

1. $(n+1{)}^2-<!--\; -\; -->1$
2. $(n+1{)}^2$
3. $n^2-<!--\; -\; -->1$
4. $n-<!--\; -\; -->1$