Elementary Algebra Review for Exam 1
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1 Elementary Algebra Review for Exam 1 1) The area of a triangle with base b and height h is given by the formula A = 1 2 bh. Simplify. 12) a) b) Find the area of a triangle when the base is 7.8 cm and the height is 18.9 cm. Round your answer to the nearest hundredth. 2) The area of a rectangle of length l and width w is given by the formula A = lw. Bill's deck is rectangular with a length of 27.1 yards and a width of 20.2 yards. Find the area of Bill's deck. 3) In one store, bananas cost 60 cents per pound. The cost, in dollars, of x pounds of bananas is 0.6x. What is the cost of 2.6 pounds of bananas? Perform the indicated operation and, if possible, simplify. 13) a) 40x y z 24 c) e) 14x 9 14) a) b) d) f) b) Translate to an algebraic expression. 4) The sum of a number and 12 c) d) ) 5 less than y e) f) ) Three fourths of x 7) A number divided by six Divide, if possible. 15) a) b) 12 0 c) ) 2 less than 5 times a number 9) The quotient of a number and 8 10) The product of 14 and the sum of two numbers. Find the following. 11) a) Find the prime factorization of the numbers b) Find the LCD (least common Use the distributive law to multiply. 16) a) 4(x + 8) d) 3(9r s) b) (y + 6)7 e) (5 + u + v)8 c) 4(7x + 4) f) (7l + m + 5)9 Use the distributive law to factor the given expression. Check by multiplying. 17) a) x b) 6x + 30y c) 7m + 35n + 14 Find the absolute value. 18) a) -65 b) 29.2 c) denominator) of 1 16 and 1 70.
2 Elementary Algebra Exam 1 Review Page 2 Use <, >, or = to make a true sentence. 19) a) -9 3 b) -3 3 c) Pick the requested numbers from the given list. 20) -104,-19.8, 0, 7, π, 54, 19.69, 96 9 Natural, Whole, Integers, Rational, Irrational Find the perimeter of the figure. 21) Evaluate. 29) 6(-5) + 8(-9) 30) 8x - (3x - 4) - (-7x + 1) 31) 3x 2 + x - 2(3x 2-8x) 32) 2m2-3mn + 2n2-6(9m2 + 5mn - 8n2) 33) x + y, for x = 15 and y = n 34) 8m n, for m = 14 and n = ) (-x) 2-2x, for x = -5 3n 6n 36) 2x - 6x 2 x 2, for x = Combine like terms. 22) a) 8a - 6a + 2 b) -7 + (-6x) + 9x + 2 c) 6x - (-8x) (-9x) + 6 Write exponential notation. Simplify. 23) a) x x x x x x b) c) 2m 2m 2m 2m 2m 24) a) 13 2 b) ) a) (-3x)3 b) (-3x)4 26) 4 (5 + 4) 2-3 (6-3) 2 27) ( ) 28) (-4)2 37) -21 x(x + 13)2, for x = -3 38) Nikki is fishing from a bank 28 feet above water level. In this location, the fish tend to feed at 35 feet below the surface. How long must Nikki's fish line be to reach the fish? 39) The lowest point in Africa is Lake Asaal, which is 156 m below sea level. The lowest point in South America is the Valdes Peninsula, which is 40 m below sea level. How much lower is Lake Asaal than the Valdes Peninsula? 40) A container of liquid hydrogen flouride is at a current temperature of -90 C. The boiling point for hydrogen flouride is 19 C. What is the difference between the boiling point of hydrogen flouride and its current temperature?
3 Elementary Algebra Exam 1 Review Page 3 Solve the equation. (Do not convert fractions into decimals when you are solving.) 41) -28 = x ) M = e + h + y 9 for h 42) m = 0 43) x = ) 29 = 5x ) 2y + 5 = -1-2y 46) 20y - 6 = 17y 47) 7 8 x = 49 48) 5(2z - 2) = 9(z + 3) 49) 1 3 x x = 2 50) 1 4 x x = x 59) c = 3a + 3b for b 60) At many colleges, the number of "full-time-equivalent" students f is given by f = n, where n is the total number of 15 credits for which students enroll in a given semester. Determine the number of full-time-equivalent students on a campus in which students registered for a total of 23,010 credits. 61) When a ball is thrown upward at a speed of 19 m/s, its height s above the ground (in meters) after t seconds is given by the formula s = 19t - 4.9t2. Find the height of the ball after 3 seconds. Round to the nearest hundredth, if necessary. 62) What is 35% of 460? 51) 5 6 3x + 1 = 20 63) What number is 140% of ) -4.6q = q 53) -5x + 5(-3x - 7) = -50-5x 54) 9x - (4x - 1) = 2 55) 0.4(5x + 15) = (x + 3) Solve the formula for the indicated letter. 56) V = 1 Bh for h 3 57) a + b = s + r for s 64) 90% of what number is 56? 65) 61 is 0.82% of what number? Round to the nearest tenth of a percent. 66) What percent of 145 is 8.7? 67) is what percent of 980? Write as a decimal. Do NOT round your answers. 68) a) 94% b) 750% c) 0.32% d) 3 5 %
4 Elementary Algebra Exam 1 Review Page 4 Write as a percent. Do NOT round your answers. 69) a) 0.46 b) c) 17 d) ) The parking lot at a grocery store has 80 cars in it. 25% of the cars are blue. How many cars are blue? 71) A chemical solution contains 9% salt. How much salt is in 1.5 ml of solution? 72) Charlie purchased a digital camera. The cost of the camera, including 7.5% sales tax was $ What was the cost of the camera before tax? 73) If Gloria received a 11 percent raise and is now making $24,420 a year, what was her salary before the raise?
5 Answer Key Testname: EAREVIEW1_SP2013 1) cm2 2) square yards 3) $1.56 4) x ) y - 5 6) 3 4 x 7) x 6 8) 5x - 2 9) x 8 10) 14(x + y) 11) a) 16 = = b) LCD: = ) a) ) a) 5xz 3y c) e) - 2x 27 14) a) 7 6 c) e) b) b) d) f) b) d) f) ) a) -7 b) undefined c) 0 16) a) 4x + 32 b) 7y + 42 c) 28x + 16 d) 27r s e) u + 8v f) 63l + 9m ) a) 3(3 + 7x) b) 6(x + 5y) c) 7(m + 5n + 2) 18) a) 65 b) 29.2 c) ) a) > b) = c) < 20) Naturals: 96 Wholes: 0, 96 Integers: -104, 0, 96 Rationals: -104, -19.8, 0, 7 9 Irrationals: π, 54 21) 12n ) a) 2a + 2 b) 3x - 5 or x c) 23x ) a) x6 b) 143 c) (2m)5 or 25m5 24) a) 169 b) ) a) -27x3 b) 81x4 26) ) ) ) 42 30) 12x ) 3x3-6x2 + 17x 32) -52m2-33mn + 50n2 33) 6 34) 56 35) 35 36) 60 37) ) 63 feet 39) 116 m 40) 109 C 41) ) ) ) 7 45) ) 2 47) 56, 19.69, 96
6 Answer Key Testname: EAREVIEW1_SP ) 37 49) 42 50) 16 51) ) 5 53) 1 54) ) ) h = 3V B 57) s = a + b - r 58) h = 9M - e - y 59) b = c - 3a 3 60) ) 12.9 meters 62) ) ) ) ) 6.0% 67) 124% 68) a) 0.94 b) 7.5 c).0032 d) ) a) 46% b) 0.133% c) 1700% d) 48% 70) 20 cars 71) ml 72) $312 73) $22,000
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