- Class: Honors Algebra 2
- Author: Peter Atlas
- Text:
__Algebra and Trigonometry: Structure and Method__, Brown

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- True or false: a system consisting of a linear and quadratic equation could have at most two real solutions.
- True or false: a system consisting of two quadratic equations could never have exactly five real solutions.
- True or false: the intersection of a circle and ellipse both with centers at the origin could contain eactly one point.
- Solve the system over the real numbers: \(y = x^2 - 3\) and \(y = 2x.\)
- Solve the system over the real numbers: \(4y^2 - 25x^2 = 100\) and \(y = 2x.\)
- Find the dimensions of a rectangle whose area is 64 square cm and whose perimeter is 40 cm.
- Solve the system over the real numbers: \(x^2 + y^2 = 9\) and \(y = x^2 - 3.\)
- Solve the system over the complex numbers: \( \displaystyle \frac{x^2}{9} + \frac{y^2}{4} = 1\) and \(x^2 + y^2 =4.\)
- Solve the system over the complex numbers: \( \displaystyle \frac{x^2}{16} + \frac{y^2}{9} = 1\) and \( \displaystyle \frac{x^2}{16} - \frac{y^2}{9} = 1.\)
- Suppose you bought $1200 of stock. When the price per share increased by $1, you sold all but 10 shares for $1380. How much did you originally pay for each share of stock?
- Solve over the complex numbers: \(9x^2 + y^2 = 27,\) and \(y = 3x^2 - 3\)
- If the numerator of a reduced, simplified fraction is increased by 3 and the denominator is decreased by 3, the resulting fraction is the reciprocal of the original fraction. The numerator of the original fraction is 1 more than one half its denominator. What was the original fraction?
- The product of a two-digit number and the number obtained by reversing its digits is 2268. If the difference of the numbers is 27, find the numbers.

True

True

False

\((3, 6)\) and \((-1, -2)\)

No real solutions

16 cm by 4 cm

\( (0, -3),\) \((-\sqrt{5}, 2),\) and \((\sqrt{5}, 2).\)

\((0, 2)\) and \((0, -2)\)

\((4, 0)\) and \((-4, 0)\)

$5

\(( \pm i, -6)\) and \( ( \pm \sqrt{2}, 3) \)

\( \displaystyle \frac{5}{8} \)

63