# Trigonometry / PreCalculus Q1 benchmark performance

Results for Trigonometry / PreCalculus Q1 benchmark performance (10/26/2010):

Standards/Clusters Tested | ||
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Standard/Cluster | Description | # Items |

California MA.8-12.AI.16.0 ( 8, 9, 10, 11, 12 ) |
Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. | 5 |

California MA.8-12.AI.14.0 ( 8, 9, 10, 11, 12 ) |
Students solve a quadratic equation by factoring or completing the square. | 2 |

California MA.8-12.AI.11.0 ( 8, 9, 10, 11, 12 ) |
Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. | 2 |

California MA.8-12.AI.7.0 ( 8, 9, 10, 11, 12 ) |
Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. | 5 |

California MA.8-12.AI.8.0 ( 8, 9, 10, 11, 12 ) |
Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. | 2 |

California MA.8-12.AII.10.0 ( 8, 9, 10, 11, 12 ) |
Students graph quadratic functions and determine the maxima, minima, and zeros of the function. | 4 |

California MA.8-12.AII.17.0 ( 8, 9, 10, 11, 12 ) |
Given a quadratic equation of the form ax² + by² + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation. | 1 |

California MA.8-12.AII.2.0 ( 8, 9, 10, 11, 12 ) |
Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. | 1 |

California MA.8-12.AII.5.0 ( 8, 9, 10, 11, 12 ) |
Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane. | 3 |

California MA.8-12.AII.4.0 ( 8, 9, 10, 11, 12 ) |
Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. | 5 |

California MA.8-12.AII.6.0 ( 8, 9, 10, 11, 12 ) |
Students add, subtract, multiply, and divide complex numbers. | 4 |

California MA.8-12.AII.9.0 ( 8, 9, 10, 11, 12 ) |
Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x – b)² + c. | 1 |

California MA.8-12.G.17.0 ( 8, 9, 10, 11, 12 ) |
Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. | 2 |

California MA.8-12.G.8.0 ( 8, 9, 10, 11, 12 ) |
Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. | 4 |