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th 7 Grade Test Prep Algebra Evaluate 8a – 2b when a = 7 and b = 4 48 Evaluate x² + y³ when x = 3 and y = 2 17 How do you evaluate 6c + d² when c = 9 and d = 5 79 Joanna receives $8 per hour when she works at the coffee shop. Last week she earned $256. Write an equation that can be used to find the number of hours Joanna worked last week. Let h = Hours Joanna worked 8h = 256 Write an equation to represent the following. The sum of 7 and a number, divided by 15, is equal to 33. Let n = the number (7 + n) ÷ 15 = 33 Solve for n: n - 19 = 7 8 Step 1: Start with the term that does NOT include the variable. Use the inverse operation (subtraction) to ‘move’ the 19. n/8 – 19 (+ 19) = 7 + 19 n/8 = 26 Step 2: To isolate the variable, use the inverse operation (multiplication), to ‘move’ the 8. n/8 (* 8) = 26 (* 8) n = 208 Step 3: Check your work by substituting and solving. n = 208 208 / 8 – 19 = 7 √ A car uses 9 gallons of gasoline for a 162-mile drive. How many gallons of gasoline will the same car use in a 216-mile drive? Step 1: Write the ratio given in the problem. The ratio is “162 miles uses 9 gallons.” As a fraction, the ratio miles/ gallons is 162/9 Step 2: Represent the unknown by a variable. g = gallons of gasoline for a 216-mile drive Step 3: Write the ratio and fraction for the unknown variable. The ratio is “216 miles uses ‘g’ gallons.” As a fraction, the ratio miles/ gallons is 216 / g Step 4: Write the ratios as proportions. Cross-multiply to solve. 162 216 9 g 162g = 1944 g = 12 The car will use 12 gallons of gasoline for a 216-mile drive . Eighteen less than twice a number A number squared, plus nineteen 2t - 18 n² + 19 The product of eleven and a number, divided by sixty 11 × k ÷ 60 One hundred more than the quotient of a number and two hundredths n ÷ 0.02 + 100 Polynomial – an algebraic expression that is the sum of any number of monomials. Which of the following expressions are polynomials: 7n - 35 Five less than a number, times seven 7(n – 35) = 63 -m + n2 n>5 Simplify the following expression: 3ac + 4 – 2ac + 9 – 5bc Step 1: Identify the like terms. +3ac - 2ac +4+9 - 5bc Step 2: Combine the like terms + ac + 13 - 5bc Step 3: Rewrite the expression using the combined terms ac + 13 – 5bc Simplify the following expressions: a) 3x + 4y – 4x b) -1/2t + 6t – 6 c) pq – 2pq2 d) 3ab – 3a – 3ab + 2a e) -4t + 26m – mt + tm 2x + 12 = 3 – x +x +x 3x + 12 = 3 - 12 -12 3x ÷3 = -9 ÷3 x = -3 Combine like terms Add x to each side. Simplify Combine the second set of like terms Subtract 12 from each side. Simplify Divide each side by 3 Substitute & complete the check 7 (x – 2) = 5x + 10 7 x – 14 = 5x + 10 - 5x -5x 2 x – 14 = + 14 = 2 x = 24 ÷2 ÷2 x = 12 10 14 Use the distributive property to remove the parenthesis Multiply (x – 2) by 7. Combine like terms Add a negative 5x to both sides. Simplify Combine the second set of like terms Add 14 to each side. Simplify Divide each side by 2 Simplify Substitute & complete the check 1. 2. 3. 4. 7y + 8 = -2y – 64 4 (2b – 6) + 11 = 8b - 13 9y + 3 = 5y – 13 5n + 3 = 2(n + 2) – 3n Solve and graph each of the following inequalities 4g > 28 5+k≤3 2 < 90/j 98 ≥ d - 6 k > 72 ÷ 8 y/2 < 9 g>7 k ≤ -2 2 < 45 104 ≥ 104 k>9 y < 18 John is a data entry professional. His typing rate is 70 words per minute. At this rate, how long will it take to complete a memo of 665 words? 9.5 minutes. The formula for the mass of an object is density times volume (M = DV). What is the mass of a 49-cc object with a density of 63 g/cc? 3,087 g The formula for the mass of an object is M = DV, where m is the mass, d is the density and v is the volume. What is the volume of a 17-kg solid with a density of 0.05 kg/cc 340 cc If a decaminute is equivalent to 10 minutes of time, how many decaminutes are equivalent to 2 hours? 12 decaminutes Complete the tables and graph the equations (on a coordinate plane) 2y – x = 6 x y 1 y=½x 2 x 0 0 6 2 y 4 5 x + 2y = 4 x y -1 -2 2 4 Consider the sequence 3, 5, 7, 9, … Write an expression for the nth term. ** use a table to help you. Consider the sequence 2, 5, 8, 11, … Write an expression for the nth term. ** use a table to help you. Name of Polygon Number of Sides Sum of Measure of Interior Angles Triangle 3 180˚ 4 Pentagon 6 Septagon 8 Nonagon 10 N-gon n Write each equation, then complete the table. y = ___________ x y 7 4 10 7 x y 10 2 2 4 4 16 y = ___________ 8 16 y = ___________ x y 5 2 10 4 6 20