Unit 1
What is point-slope form?
y - y1 = m (x - x1)
What is the inverse of ex?
ln(x)
What are possible outputs to a system of equations?
No solution, one solution, multiple solutions or infinitely many solutions.
What is the equation of a hyperbola? (a, b =1)
What is the slope of the line of asymptotes for hyperbolas?
a/b or b/a
What is the slope and y-intercept of this equation: 3x + 2y = 18
slope: - 3/2, y-intercept: 9
Solve for x: log5(x-3) = log5(13x)
x = -¼
Solve:
3x + 6y - 7 = 0
3y = 3/2 x - 7/2
Infinite solutions.
What is the standard form equation of a vertical parabola with vertex at (-1, 4)?
What is the eccentricity of a circle? How about a line?
Circle is 0, Line is infinity.
What is the end behavior of y = -7x3 + 5x2 - 2
Up to the left, down to the right.
Expand the expression: log((7a + 12)4 / (8b x c3))
4log(7a + 12) - log (8b) - 3log(c)
y = ½ x - 10
4y - 2x = 3
No solution.
What is the formula for the directrix of a horizontal parabola?
x = h - p
Equation for c, for an ellipse.
c2 = a2 - b2
How does the graph change from y = x3 to y = -(x-4)3
The graph shifts right 4 units and is reflected along the x-axis.
Solve for x: ln(8x) - ln (4) = 2 ln(x) + 4ln(e)
x = 2
Solve (in coordinate form):
5x - 2y = 7
3x + 2y = 9
(2, ⅔ )
Find the length of the major axis of the ellipse with equation y2/ 16 + (x-2)2/ 9 = 1
8 units
What is the value of (-12x2 - ln(8))0?
1
What is the domain of the function: y= 1/(x-1)½
x > 1
Solve for x: ⅓ ( 5 2x + 2 ) = 9
x = 1
Solve: 2x + 4y + 2z = 16
-2x - 3y + z = -5
2x + 2y - 3z = -3
(1, 2, 3)
Find the c-value for the hyperbola: (y-7)2/36 - (x+3)2/64 = 1
c = 10
What is the half-life formula?
N(t) = N0(½)t/ t½