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Ahrens Math Review Pg. 1 of 5 Math Concept Review (7th) Number Sense and Operations. Classify numbers. Counting numbers (also called natural numbers): 1, 2, 3, etc. Whole numbers: 0, 1, 2, 3, etc. Integers: positive and negative whole numbers, and 0: …-3, -2, -1, 0, 1, 2, 3…, etc. Write the prime factorization of a number. A number in prime factorization form is written as the product of prime numbers. Example the prime factorization of the number 20 is 2 x 2 x 5 = 22 x 5. Write 28 in prime factorization form. How is the number -7 classified? Understand exponents. An exponent represents repeated multiplication. Example base →43←exponent 43 means 4 x 4 x 4 = 64 Example 4 squared = 4 x 4 = 42 The base 4 is multiplied 3 times, indicated by the exponent 3. 3 What is the value of 2 ? Use scientific notation. In scientific notation, a number is written as the product of: A number that is greater than 0 and less than 10 And a number that is a power of 10 Example 5,280 = 5.28 x 10 Write the square of a number. The square of a number is the product of a number times itself, usually written with an exponent. 3 Write 460 in scientific notation. Identify prime numbers. A prime number is a whole number greater than 1 that has only two factors: itself and the number 1. Example the number 7 is a prime number. The only factors of 7 are 1 and 7. 7 = 1 x 7 Name all prime numbers that are less than 10. What is the value of 62? Find the square root of a number. The square root of a number is one of its two equal factors. To find the square root, ask, “What number times itself equals this number?” the symbol for square root is √. Example √36 = 6 because 6 x 6 = 36. What is the square root of 25? Write a ratio. A ratio compares two numbers by division. Example in a group of 6 girls and 8 boys, the ratio of girls to boys is six to eight: which reduces to . What is the ratio of boys to girls? Ahrens Math Review Pg. 2 of 5 Understand the concept of rate. A rate is a ratio that compares quantities of different units. Example miles per hour, price per pound, and beats per minute. What two units are compared in the rate feet per second? Solve a simple proportion. A proportion says that two ratios are equal. A proportion is written as two equivalent fractions. Example Determine absolute value. Absolute Value is a number’s value when the sign of the number (positive or negative) is ignored. The symbol for absolute value is ││. Absolute value is the distance from 0 to the number on the number line. Example │+7│ = 7 and │-7│ = 7 What is the │-8│? Understand decimal forms of a fraction. A terminating decimal has digits that do not repeat indefinitely. Examples ½ = 0.5; ¼ = 0.25. = In the proportion = , what is the value of x? A repeating decimal has digits that repeat without end. Examples 1/3 = 0.333…; 2/3 = 0.666…, and so on. Identify percent as part of a whole. Percent (%) means parts out of each 100 equal parts. Written as a decimal, is 1/6 terminating or repeating? Example 5% is 5 parts out of each 100 equal parts. 5% of $1.00 is $0.05. What is 65% of $1.00? Order numbers on a number line. Positive number any number greater than zero, located to the right of zero on a number line. Negative number any number less than zero, located to the left of zero on a number line. Negative numbers │ Positive numbers •---•---•---•---•---•---•---•---•---•---• -5 -1 0 1 5 Place -2 and 4 on the number line. Understand order of operations. The order of operations is the order in which an expression is evaluated: 1st Find the value of the number within parentheses. nd 2 Find the value of the numbers with exponents. rd 3 Perform multiplication or division, working left to right. th 4 Perform addition or subtraction, working left to right. Example 2(8 – 5)2 + 3 = 2(3)2 + 3 =2(9) + 3 =18 + 3 =21 Find the value of 3(6 – 4)2 – 9 Ahrens Math Review Pg. 3 of 5 Algebra Represent a number by a variable. A variable is a letter that stands for a number. Example x + 7 The value of an expression is known only when the value of each variable is given. Solve a one-step equation. A one-step equation is solved in one inverse operation. Example x + 5 = 9 To find x, subtract 5 from each side: x+5–5=9–5 x=4 Solve for x: x – 8 = 10 Find the value of x + 7 when x = 4. Use substitution to evaluate an algebraic expression. An algebraic expression contains one or more variables and constants (numbers). To evaluate an expression, substitute a number for each variable. Example 3x – 9; When x = 5, the value of 3x – 9 is 3(5) – 9 = 15 – 9 = 6. If n = 3, what is the value of 2n + 6? Evaluate a formula. A formula is a rule that shows a relationship. Example P = 3s (The perimeter P of an equilateral triangle equals 3 times s, the length of each side.) Using A = πr2, find the value of A when r = 6ft, and π = 3.14. Understand inverse operations. An inverse operation undoes another operation. Addition and subtraction are inverses: 4–2+2=4 Multiplication and division are inverses: 4x2÷2=4 What is the inverse operation of multiplying by 9? Solve a one-step inequality. An inequality compares two numbers. Examples n > 4 says that n is greater than 4; x + 3 < 8 says that x plus 3 is less than 8 To solve a one-step inequality, perform the inverse operation on each side of the inequality. Example to solve x + 3 < 8, subtract 3 from each side: x+3–3<8–3 x<5 Solve the inequality x – 3 > 2. Geometry Identify parts of a circle. The parts of a circle are indicated below. A chord is a line segment that connects any two points on the circle. radius diameter chord What is the ratio of the diameter of a circle to its radius? Ahrens Math Review Pg. 4 of 5 Use circle formulas to find unknowns. Example If the circumference = 6, what is the diameter, d? Use C = πd First solve for d: C ÷ π = πd ÷ π C÷π=d Substitute 6 for C. 6 ÷ 3.14 ≈ 1.9 Calculate volume. The volume (V) of a rectangular prism is given by the formula V = lwh (length x width x height) The volume (V) of a cylinder is given by the formula V = πr2h (area of circular base x height) r Example h V= lwh V = πr2h Find the volume of the rectangular prism shown above. Identify the faces and bases of 3dimensional shapes. base ↓ Find the area and surface area. The surface area of a figure is the sum of the area of each surface of a figure. Rectangular Prism. Surface area = 2lh + 2lw + 2hw Cylinder r h Surface area = 2πr2 + 2πrh What is the surface area of a rectangular prism that is 8 feet long, 3 feet wide and 2 feet high? Understand similar figures. Similar figures have the same shape but may not have the same size. Corresponding sides are in proportion, and corresponding angles are equal. Vertex→ ←face Example. Edge→ 6 faces B Y ↑ base How many faces does the pyramid have? (Be sure to count any faces you cannot see!) X Z A C ∆XYZ is similar to ∆ABC Which side of triangle ABC corresponds to side YZ of triangle XYZ? Ahrens Math Review Pg. 5 of 5 Statistics and Probability Identify coordinates of a point. A coordinate plane uses two axes to locate a point. The point (x,y) is an ordered pair in which the x-coordinate is written first, followed by the y-coordinate. Example point A has coordinates (-4,3) name the coordinates of point B. Find the mean, median, mode, and range of a set of data. Consider the set: {1, 1, 5, and 9} To find the mean, add the numbers and then divide the sum by the number of addends (numbers added). Example mean: (1 + 1 + 5 + 9) ÷ 4 = 16 ÷ 4 = 4 The median is the middle value, or the average of two middle values. Example median: (1 + 5) ÷ 2 = 3 Name the coordinates of point B. Measurement Understand weight/mass units. Customary units of Weight 1pound (lb) = 16 ounces (oz) 1 ton (t) = 2,000 pounds Metric Units of Mass 1 gram (g) = 1,000 milligrams (mg) 1 kilogram (kg) = 1,000 grams Comparing Units 1 pound ≈ 450 grams 1 kilogram ≈ 2.2 pounds Understand central angle. A central angle has its vertex at the center of a circle; its sides are radii. ←central angle The mode is the number t hat occurs most frequently in a set of numbers Example mode: 1 The range is the difference between the greatest and least values. Example range 9 – 1 = 8 For the set {3, 4, 6, 7, 7, 9} find: mean _____ median _____ mode _____ range _____ List all outcomes (sample space) in a probability experiment. An outcome is a possible event. The sample space is a list of all possible outcomes. Example the sample space for tossing two coins is: (H, H), (H, T), (T, H), (T, T). List the sample space for tossing three coins.