Remember, you may not use a calculator when you take the assessment test.

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1 Elementary Algebra problems you can use for practice. Remember, you may not use a calculator when you take the assessment test. Use these problems to help you get up to speed. Perform the indicated operation. Write in lowest terms if necessary. 1) ) ) ) 1 - (-1) + + (-) Evaluate the expression. ) 8 - () (-8) ) Evaluate (x - y) for x = - and y = ,76-2,8-68 Simplify the algebraic expression. 11) (a + 10b) - (10a - 7b) 26a + b 26a + 7b 26a + 17b 6a + 7b Solve the inequality and express the solution set in interval notation. Graph the solution set on the real number line. NOTE: A square bracket, i.e. [, is the same as a filled in circle. A curved bracket, i.e. (, is the same as an open circle. 12) 2x + > 6(6x + ) (-, ) ) (-, -] 6) (-1)(-)(-7) ) undefined (-, -) [-, ) 8) -86 divided by

2 1) -(x + 10) -16x - 2 (2, ) 17) 0. is 1% of a number. Find the number [2, ) (-, 2] (-, 2) Solve the equation. Check your solution. 18) 6x = -.2 {-.8} {-7.2} {-} {-.8} 1) - 1 x = Solve the problem. ) After a 17% price reduction, a boat sold for $ 21,80. What was the boat's price before the reduction? (Round to the nearest cent, if necessary.) $126,1.18 $2, ) 7(p + 2) = 8p 7 - $ $26,000 21) t = 6 7 1) A 12-ft. board is cut into 2 pieces so that one piece is 8 feet longer than times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces. shorter piece: 1 ft.; longer piece: 11 ft. shorter piece: 2 ft; longer piece: ft. shorter piece: 6 ft; longer piece: 6 ft. shorter piece: 28 ft; longer piece: 6 ft. 16) A rectangular carpet has a perimeter of 26 inches. The length of the carpet is 6 inches more than the width. What are the dimensions of the carpet? 1 by 18 inches 12 by 12 inches 7 by inches 1 by 12 inches ) x - 1 = 12 {-1} {7} 1 1 {1} {-7} Evaluate the expression for the given value of the variable. Combine. 2) z2 - z - for z = ) (x + 10x2 + 11) - (x - 7x + 6) -x + 10x2-7x + -x + 10x2 + 7x + -x + 10x2 + 7x x + 17x2 +

3 Multiply. 2) 11x(12x + 2x2 + ) Find the product. Multiply. 26) (x - 8)2 12x8 + 2x2 + 12x8 + 22x7 12x + 22x2 + 12x8 + 22x7 + x x2-80x + 6 x x2-80x + 6 2x ) (y + x)(y - x) Perform the division. 16y2 + 8xy - x2 16y2-8xy - x2 16y2 - x2 8y2 - x2 28) x 2 + 0x - 11 x 7x - 7x x x x 7x2 + 6x - 11 Simplify the expression. All exponents should be positive integers. 2) (8x2y) -1 (2x2y) 1x0 2x0 2x 1x Perform the indicated computation. Write the answer in scientific notation. 0) (6. 10)(2 10-1) Perform the indicated computations. Write the answer in scientific notation. 1) x 10. x 10.0 x Factor the polynomial completely. If the polynomial cannot be factored, say it is prime. 2) x - 81 (x2 - ) 2 (x2 + ) 2 (x2 + )(x + )(x - ) prime ) xy + 10x - 6y - 60 (x + 10)(y - 6) (y - 10)(x + 6) (x - 10)(y + 6) (y + 10)(x - 6) ) x2 + x - ) - m2 (x - )(x + 1) (x - )(x - ) (x + )(x - ) prime (2 - m)(2 + m) (2 - m)2 (2 + m)2 prime 6) 2x2 + 6 (x - 8)2 prime (x + 8)(x - 8) (x + 8)2 7) 1(a + 12) - y(a + 12) (a - 12)(y - 1) (a + 12)(1 - y) (a + 12)(1 + y) prime 8) x2y - 10xy - 00y y(x - 10)(x + 8) y(x - 10)(x - 8) y(x - 0)(x + 8) y(x + 10)(x - 8)

4 ) x2 - x - 6 (x - 7)(x + ) (x + 7)(x - ) (x - 6)(x + 1) prime 0) 8x2 + 18x + (8x + )(x + ) (2x + )(x + ) (2x - )(x - ) prime 1) 10m - 2mn + 10n (2m - mn + 2n) (-m + 2n) (2m + mn - 2n) prime Evaluate the expression for the given values. 2) m - 2n 2 when m = 2, n = -, and p = -1 8p 1 Simplify the rational expression. ) m 2 - m m - m + m 2-6 m - 6 m + Perform the indicated operation. Simplify if possible. 21x 7x ) x2 28x x 28 28x 8 28x 18x 2 16 ) 6) 7) 8) y - 2 y + 2 y + 0 y x2 x x x2 x2-6 6x x + 6 x 2-10x - 16 x x + 8 x - 2 x - 2 x + 8 s - t + 12 t - s -8 s - t -16 s - t ) x + 6 x - 7 (x - 7) x(x - 7) x(x - 7) x 2 undefined 0 Simplify the complex rational expression. 1-1 x2 0) x x - 2 2x 2x x s - t (x + 7) x(x - 7) 2x - 7 x + 2 2x 2x x - 2

5 Solve the equation. 1) x = 20 x2, - -,, - 1, 1 Solve the rational equation. Check your answer. 7 2) x x - 7 = x + 21 x2 + x - 7 {1} { } {0} {-1} Solve the equation for the indicated variable. ) 1 a + 1 b = 1 c for b b = a - c ac b = a + c ac Solve the proportion. ) x + 2 = x - {-6} {6} b = ac a - c b = ac a + c {28} {-28} Given that the pair of triangles is similar, find the missing length. Solve. 6) If apples cost $2.0, how much would 20 apples cost? Solve the problem. $0.0 $0.00 $0.0 $ ) Determine whether the ordered pair (-, ) satisfies the equation x - 6y = -. Yes No 8) If m varies directly as p, and m = 1 when p =, find m when p is. Solve the equation. m = m = 81 m = 2 m = ) x2 = x +, 0, -1, -1, 1 60) 8x + 6x x = 0 {0,, } {-, -} {0, -, -} - 1, - ) 12 Simplify the square root. Assume all variables represent positive real numbers. 61) x = 16 x = 0 x = 2 x = 2 62) 10x2y 6) xy2 6 x2 6y xy 6 x 6y 10x11 6x x10 x 6 x x11

6 Simplify the expression. If necessary, express the result that is not a rational number as a decimal rounded to two decimal places. 6) 2 - ()(-1) 1 not a real number Perform the indicated operation and simplify. Assume all variables represent positive real numbers. 6) Graph the inequality. 66) y x + Perform the indicated operation and simplify. Assume all variables represent positive real numbers. 67) 6 2( 6-7) ) ( ) ) 270x 10x7 x 27 x 11 x 110 x8 11

7 70) ( 7 + )(8 7 + ) 71) Solve the system of equations. 72) y = - x 2 y = x 2-18 (-, 18) (18, ) (2, 1) (18, -) Rationalize the denominator. 10 7) 0 7) Simplify the square root, if possible. 76) 16-/ Solve the system of equations. 77) x - y = -2 x + 16y = 0 (, -12) (-12, ) infinitely many solutions no solution Find the length of the unknown side of the right triangle with sides a, b, and c, where c is the hypotenuse. Solve. 78) Two legs of a right triangle measure inches and 10 inches. Find the exact length of the hypotenuse and then find the decimal approximation to the nearest tenth of an inch in in 8 in 8 in 7) 2x2-8 = 2 {-, } {-8, 8} {} {-} 80) x2 - x + = 0 {, } { 2, -1} {0, } {-, -} Simplify the expression. 7) 20x7 x2 x x7 x2 x x2 81) x2 + 18x + = 0 {-18 +, } { +, - } {- + 22, } { + 22, - 22}

8 Solve the quadratic equation by any method. 82) (x - )(x + ) = 8 {-, } {-, } {} {-} Graph the solution set of the system of linear inequalities. -x + y - 8) y < - x Solve the quadratic equation by any method. 8) p = p {1-1, 1 + 1} - 1, + 1 {1 -, 1 + } , 8) 1 2 y 2 = y 1 -, , , no real solution Solve the problem. 86) The sum of three consecutive integers is 87. Find the numbers. 127, 128, 12 12, 10, , 12, , 12, 11 87) Twice the sum of a number and - equals 12. Find the number

9 88) The length of a rectangular room is 7 feet longer than twice the width. If the room's perimeter is 170 feet, what are the room's dimensions? Width = 26 ft; length = ft Width = 1 ft; length = 6 ft Width = 2 ft; length = 118 ft Width = ft; length = 6 ft 8) The perimeter of a triangle is 8 centimeters. Find the lengths of its sides, if the longest side is 8 centimeters longer than the shorter side, and the remaining side is centimeters longer than the shorter side. 12 cm, 8 cm, 20 cm 12 cm, 8 cm, 2 cm cm, 8 cm, 12 cm 8 cm, 20 cm, 2 cm Find the length of the unknown side of the right triangle with sides a, b, and c, where c is the hypotenuse. 0) Two legs of a right triangle measure inches and inches. Find the exact length of the hypotenuse and then find the decimal approximation to the nearest tenth of an inch in 7 in 20 in in