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Practice

7.3.5 Practice

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.

    Three steps of a growing pattern
    1. How many small squares are in Step 4?
    1. How many small squares are in Step 15?
    1. 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
  1. 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.
Figure A

Large square with 1 by 1 small squares removed from each corner.
  1. y = x 2 − 8
  2. y = x 2 − 4
  3. y = x 2 − 1
  4. y = x 2
Figure B

2 large squares side by side. On the side of the right square, there are 2 small squares stacked vertically, each with dimensions 2 by 2.
  1. y = 2 x 2
  2. y = x 2 + 8
  3. y = 2 x 2 + 8
  4. y = x 2
  1. Use the sequence below to answer the following two questions.

DIAGRAM WITH 3 FIGURES, SHOWING STEPS 1 THROUGH 3. STEP 1 HAS A RECTANGLE WITH 1 ROW AND 2 COLUMNS. 1 SQUARE IS ADDED TO THE TOP RIGHT. STEP 2 HAS A RECTANGLE WITH 2 ROWS AND 3 COLUMNS. 2 SQUARES ARE ADDED TO THE TOP RIGHT. STEP 3 HAS A RECTANGLE WITH 3 ROWS AND 4 COLUMNS. 3 SQUARES ARE ADDED TO THE TOP RIGHT.

    1. How many squares are in Step 5?
    1. 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