|
 |
|
Lesson Plan 1: The X Factor - Trinomials and Algebra Tiles
The questions below dealing with factoring polynomials have been selected from various state and national assessments. Although the lesson above may not fully equip students to answer all such test questions successfully, students who participate in active lessons like this one will eventually develop the conceptual understanding needed to succeed on these and other state assessment questions.
Taken from the New York Regents High School Examination, Mathematics (August 2002):
A rectangular park is three blocks longer than it is wide. The area of
the park is 40 square blocks. If w represents the width, write an equation
in terms of w for the area of the park. Find the length and the
width of the park.
Solution: w(w + 3) = 40, w2 + 3w - 40 = 0, (w + 8)(w - 5) = 0, w + 8 = 0 or w - 5 = 0, w = -8 or w = 5. The width must be positive, so w = 5 and l = 8. The width of the park is five blocks and the length of the park is 8 blocks.
Taken from the New York Regents High School Examination (January 2003):
What are the factors of x2 - 10x - 24?
A. (x - 4)(x + 6)
B. (x - 4)(x - 6)
C. (x - 12)(x + 2) (correct answer)
D. (x + 12)(x - 2)
Taken from the Virginia Standards of Learning Assessment (Spring 2002):
Which property justifies the following statement?
If 3a + 3b = 12, then 3(a + b) = 12
A. Commutative property of multiplication
B. Distributive property for multiplication over addition (correct answer)
C. Multiplicative identity property
D. Associative property of addition
Taken from the Virginia Standards of Learning Assessment, Algebra I (Spring 2002):
Which is the complete factorization of 2x2 + 5x + 3?
A. (2x + 1)(x + 2)
B. (2x + 1)(x + 3)
C. (2x + 2)(x + 1)
D. (2x + 3)(x + 1) (correct answer)
Taken from the Virginia Standards of Learning Assessment, Algebra I (Spring 2002):
Taken from the Virginia Standards of Learning Assessment, Algebra II (Spring 2001):
Which is a zero of the function f(x) = x2 + 6x + 8?
A. -8
B. -4 (correct answer)
C. 2
D. 4
|
|
 |
|
|
|
|
|
