Common Student Misconceptions
The incorrect simplification of (a + b)2.
What is a2 + b2?
Find the zeros of y = x2 - 9.
x = -3, 3
Name the Sequence: 2 3 5 7 11 13 17 19 23 ...
The Prime Numbers
The process of finding the numbers or expressions that multiply together to equal a given number or algebraic expression
Factoring
Regarding the lengths of sides of a triangle: a2 + b2 = c2.
The Pythagorean Theorem
The commonly missed solution of x2 = 4.
What is -2?
The area of a circle with diameter 46.
529 * Pi
Name the sequence: 1 1 2 3 5 8 13 21 ...
The Fibonacci Sequence
The FOIL acronym stands for these four words to describe multiplying two binomials.
First, Outer, Inner, Last
There are exactly n solutions to a (single-variable) polynomial equation of degree n.
The Fundamental Theorem of Algebra
The incorrect simplification of -102.
What is 100?
Evaluate the least common multiple: lcm(3, 11, 132)
132
Identify the type of series, and the value it converges to: 2 + 2/3 + 2/9 + 2/16 + 2/25 + ...
Geometric series/sum, 2 / (1 - 1/3) = 3
Name this form of a quadratic equation: ax2 + bx + c = 0
The Standard Form of a Quadratic Equation
Two triangles are congruent if two corresponding sides and the included angle are congruent.
SAS (Side-Angle-Side)
The incorrect simplification of (a + b)(c + d).
What is ac + bd?
Find the derivative of f(x) = loga(x3).
3x2 / (x3ln(a)) or 3 / xln(a)
Identify f(x) = 1 + x2/2! + x3/3! + x4/4! + ... + xn/n!
f(x) = ex
Explain the difference between complementary angles and supplementary angles.
Complementary angles add up to 90 degrees; Supplementary angles add up to 180 degrees
The two-part theorem which relates the derivative and integral as inverses.
The Fundamental Theorem of Calculus
The commonly forgotten term of an indefinite integral.
+ c
x2ex - 2xex + 2ex + c
Identify: f(x) = (x - 1) - (x - 1)2/2 + (x - 1)3/3 - (x - 1)4/4 +...
f(x) = ln(x)
A value that appears to be a solution during the algebraic process of solving an equation, but does not satisfy the original equation when checked
Extraneous Solution
No three positive integers a, b, and c satisfy the equation an + bn = cn for n > 2.
Fermat's Last Theorem