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Download Math 10C – Final “Midterm” Exam Prep Checklist Number – Real
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Math 10C – Final “Midterm” Exam Prep Checklist Topic I’ve Got It! Number – Real Numbers (Rational Numbers) Demonstrate an understanding of whole numbers by determining the: • prime factors • greatest common factor • least common multiple • square root • cube root Represent, using a graphic organizer, the relationship among the subsets of the real numbers (natural, whole, integer, rational, irrational). Determine the prime factors of a whole number. Determine, using a variety of strategies, the greatest common factor or least common multiple of a set of whole numbers, and explain the process. Determine whether a given whole number is a perfect square, a perfect cube, or neither. Determine the square root of a perfect square, without the use of technology. Determine the cube root of a perfect cube, without the use of technology. Solve problems that involve prime factors, greatest common factors, least common multiples, square roots or cube roots. Number – Irrational Numbers and Radicals Demonstrate an understanding of irrational numbers by: • representing, identifying and simplifying irrational numbers • ordering irrational numbers Represent a function using function notation. Evaluate a function given in function notation. Solve relation and function problems in context. Sort a set of numbers into rational and irrational numbers. Determine an approximate value of a given irrational number, without the use of technology. Approximate the locations of irrational numbers on a number line, using a variety of strategies, but without the use of technology. Order a set of irrational numbers on a number line. Express a radical as a mixed radical in simplest form. Express a mixed radical as an entire radical. Explain, using examples, the meaning of the index of a radical. I Need More Practice I Need Help Math 10C – Final “Midterm” Exam Prep Checklist Exponents Demonstrate an understanding of powers with integral and rational exponents. Apply the exponent laws: • Product Law: (am)(an) = am + n • Quotient Law: am ÷ an = am – n, a≠0 • Power Law: (am)n = amn • Power of a Product Law: (ab)m = ambm • Power of a Quotient Law: = 0 , b≠0 • Zero Exponent Law: a = 1 to expressions with rational and variable bases and integral and rational exponents, and explain the reasoning. Explain and use the negative exponent law: • = , a≠0 Explain and use the rational exponent law: • = √ , > 0. Express powers with rational exponents as radicals, and vice versa. Solve a problem that involves exponent laws or radicals. Identify and correct errors in a simplification of an expression that involves powers. Polynomial Operations Demonstrate an understanding of the multiplication of polynomial expressions. Multiply and simplify combinations of 2 or 3 polynomial expressions, including: • monomials • binomials • trinomials • polynomials Relate the multiplication of two binomial expressions to an area model. Identify and explain errors in a solution for a polynomial multiplication. Math 10C – Final “Midterm” Exam Prep Checklist Factoring Demonstrate an understanding of common factors and trinomial factoring. Determine the common factors in the terms of a polynomial, and express the polynomial in factored form. Express a polynomial as the product of its factors. • common binomial factor: ax(bx + c) + d(bx + c) • factor trinomials by inspection: x2 + bx + c • factor trinomials by decomposition: ax2 + bx + c • factor a difference of squares: a2 – b2 Explain, using examples, the relationship between multiplication and factoring of polynomials. Trigonometry Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles. Explain the relationships between right triangles and the definitions of the primary trigonometric ratios. Identify the hypotenuse of a right triangle, and the opposite and adjacent sides for a given acute angle in the triangle. Determine the length of a missing side on a right triangle when 1 side length and 1 acute angle measure are given. Determine the measure of an acute angle in a right triangle when 2 side lengths are given. Solve a right triangle. Solve a problem that involves one or more right triangle.
