PRAXIS 5001 Math Questions and Answers 100% Pass

PRAXIS 5001 Math Questions and Answers 100% Pass How to add fractions. -4/9 + -9/10 = -103/90 Rational Numbers Include fractions, integers, mixed numbers, and terminating and repeating decimals. Integers The positive and negative whole numbers and zero Ex: -6, -5, -4, 0, 1, 2, 3, 4, .... Whole Numbers Natural Numbers and zero. Ex: 1, 2, 3, 4, 5, 0.... Natural Numbers Counting Numbers 1, 2, 3, 4, 5, 6, .... Irrational Numbers Real numbers that cannot be written as a ratio of two integers, they are infinite, non repeating decimals. Mixed Number Has a integer part and a fraction part 5 1/2 Exponent Shortcut method to writing repeated multiplication. four squared, 2 would be the exponent. 4 would be the base Exponent Product Rule 4[2] * 4[2] = 4[2+2] Exponent Quotient Rule 4[2]/4[2] = 4[2-2] Rule of Negative Exponents 4[-2]/4[-3] = - 4[3]/4[2] Scientific Notation A convenient method for writing very long numbers. Each exponent equals a zero. Order of Operations Parenthesis, Exponents, Multiplication and Subtraction (Left to Right), Addition and Subtraction (Left to Right) Four Quadrants Quadrant I (Top Right), Quadrant II (Top Left), Quadrant III (Bottom Left), Quadrant IV (Bottom Right) Prime Factors are 1 and itself Composite Any number that is not prime Monomials, Binomials and Trinomials Polynomials Monomials (1x) Binomials (1x + 3) Trinomials (1x + 3 + 4[2]) Axioms Property's of Math Closure For all real numbers a and b, a + b is a unique real number. Commutative Commutative means that the order does not make any difference in the result. Note: Commutative does not hold for subtraction ab = ba Because the numbers can travel back and forth like a commuter. Associative Associative means that the grouping does not make any difference in the result. The grouping has changed (parentheses moved), but the sides are still equal. Ex: (ab)c = a(bc) Inverse Operation The operation that reverses the effect of another operation. Example: Addition and subtraction are inverse operations. Start with 7, then add 3 we get 10, now subtract 3 and we get back to 7. Another Example: Multiplication and division are inverse operations. Start with 6, multiply by 2 we get 12, now divide by 2 and we get back to 6. Algorithms An algorithm is a set of rules for solving a math problem which, if done properly, will give a correct answer each time. Algorithms generally involve repeating a series of steps over and over, as in the borrowing and carrying algorithms and in the long multiplication and division algorithms. Rectangular Arrays array. (ə-rā') Mathematics A rectangular arrangement of quantities in rows and columns, as in a matrix. Numerical data ordered in a linear fashion, by magnitude. Unit Rate or Unit Ratio A ratio with a denominator of one. This can be found by simplifying any ratio to having 1 as a denominator. Rate: 2/1 Ratio 3:5 Expressions •Can only be simplified. For example:◦Order of operations (aka PEMDAS/GEMDAS ◦Reduce fractions ◦Rationalize denominators •Express an idea. Examples:◦Twice a number: 2x ◦3 less than the square of a number Equations •Can be solved. •Make a statement. Examples:◦Twice a number is 26: 2x = 26 ◦3 less than the square of a number is 6: x%5E2+-3+=+6 •Are formed by two expressions separated by an equals sign. Linear Equation Y=MX + B Independent and Dependent Variables •Independent variables - The values that can be changed in a given model or equation. They provide the "input" which is modified by the model to change the "output." •Dependent variables - The values that result from the independent variables. 12 inches equals 1 foot 3ft equals 1 yard 1760 yards equals 1 mile Area of Triangles Triangle Area = ½ × b × h b = base h = vertical height Area of Rectangle/Parallelogram Rectangle Area = w × h w = width h = height Area of a circle Circle Area = π × r2 Circumference = 2 × π × r r = radius Area of a square Square Area = a2 a = length of side Area of a Rectangular Prism Right rectangular prism •Find the area of two sides (Length*Height)*2 sides •Find the area of adjacent sides (Width*Height)*2 sides •Find the area of ends (Length*Width)*2 ends •Add the three areas together to find the surface area •Example: The surface area of a rectangular prism 5 cm long, 3 cm. wide and 2 cm. high = 5*2*2 + 3*2*2 + 5*3*2 = 20 + 12 + 30 = 62 cm2. Area of a trapezoid The area of a trapezoid equals one/half the sum of the bases time the altitude.