# Free Compass Math Test Practice Questions Solutions with Explanations - Sample 5

 Solutions with detailed explanations to compass math test practice questions in sample 5. The solution of the equation - 3x + 7 = 4x - 12 falls bewteen what 2 numbers? A) 3 and 3.5 B) 1 and 2.5 C) 2.1 and 3 D) 4 and 4.5 E) 19 and 7 Solution We first solve the given equation -3x + 7 = 4x - 12 -3x - 4x = -12 - 7 -7x = -19 x = 19/7 ≈ 2.71 The solution x = 19/7 is between 2.1 and 3. Answer C 35x2 -11x - 6 is the product of 5x - 3 and Solution We are given one factor 5x - 3 and we need to find the second factor of 35x2 -11x - 6 as follows 35x2 -11x - 6 = (5x - 3)(7x + 2) So 35x2 -11x - 6 is the product of 5x - 3 and 7x + 2 For all real numbers x, y and z, 3√(64 x3 y z2) = Solution Let us rewrite the given expression as follows 3√(64 x3 y z2) = 641/3 (x3)1/3 y1/3 (z2)1/3 then simplify = 4 x y1/3 z2/3 For all x, 45 x4 - 115 x3 - 60 x2 = A) 45 x2(x + 4)(x - 3) B) 5 x2(9x + 4)(x - 3) C) 5 x2(9x - 4)(x + 3) D) 5 x2(9x - 4)(x - 3) E) 45 x2(x - 4)(x + 3) Solution Factor 5 x2 out 45 x4 - 115 x3 - 60 x2 = 5x2 (9x2 -23x - 12) We now factor the trinominal = 5x2 (9x + 4)(x - 3) Which of the following is one of the factors of the polynomial -3x2 - 7x + 26? A) x + 2 B) x + 1 C) -3x + 7 D) x - 2 E) 3x - 2 Solution Factor -3x2 - 7x + 26 -3x2 - 7x + 26 = (-3x - 13)(x - 2) x - 2 is a factor of the given expressions What is the product of the solutions of the equation 2x2 + x - 15? Solution The product of the solutions of a quadratic equation of the form ax2 + bx + c = 0 is equal to c / a. Hence the product of the solutions of the solutions of the given equation is equal to -15/2 If y = |x - 3|, what is the value of y2 when x = -2? Solution Evaluate y and then y2 y = |-2 - 3| = 5 y2 = 52 = 25 The operation ||| is defined by x ||| y = x + y + xy. If -5 ||| y = -13, then y = Solution Use definition to express -5 ||| y in terms of y -5 ||| y = (-5) + y + (-5)y = -5 + y - 5y = -5 - 4y Use the fact that -5 ||| y = -13 to write an equation -5 - 4y = - 13 Solve for y y = 2 A car uses 15 gallons of gaz to travel 300 miles. How many gallons are needed for this car to travel a distance of 430 miles? Solution Let us first find how many gallons are used to travel 1 mile 15 gallons / 300 miles = 1 /20 gallons per mile The number of gallons needed for 430 miles is given by (1 /20 gallons per mile)*(430 miles) = 21.5 gallons David has 200 books in his library. 30% of these books are about science. Of these books about science, 20% are about mathematics. How many math books does David have? Solution Number of science books is 30% of 200 = 30% * 200 = 60 books Number of math books is 20% of 60 = 20% * 60 = 12 bokks. √32 √2 = Solution Use 32 = 2 * 16 and simplify √32 √2 = √(2*16)√2 = √2 √16 √2 = 4 √2 √2 = 4 * 2 = 8 If a = 3 and b = -1, then -3a2 - 2ab + b3 Solution Substitute -3a2 - 2ab + b3 = -3(3)2 - 2(3)(-1) + (-1)3 Simplify = -3(9) + 6 - 1 = -27 + 6 - 1 = -22 (-3x2 - x - 10) - (- 3x + 8)? Solution Multiply, group like terms and simplify (-3x2 - x - 10) - (- 3x + 8) = -3x2 - x - 10 + 3x - 8) = -3x2 + 2x - 18 (4 - √5)(4 + √5) = Solution Expand and simplify (4 - √5)(4 + √5) = 42 - √5 2 = 16 - 5 = 11 In a standard (x,y) coordinate plane, the point (-2 , -6) is located Solution Both coordinates are negantive, therefore the point (-2 , -6) is located in quadrant III | -7 - 9 | = Solution Simplify as follows | -7 - 9 | = |-16| = 16 If the ratio of 7 to x is equal to 42/30, then x = Solution We are given 7 / x = 42 / 30 Solve for x 7 * 30 = 42 * x x = 5 If x = 1/3, then 4 x2 - 2x + 2 = Solution Substitute 4 x2 - 2x + 2 = 4 (1/3)2 - 2(1/3) + 2 = Simplify using common denominator 4 * (1/9) - 2/3 + 2 = 4 / 9 - 6 / 9 + 18 /9 = 16 / 9 Which equations corresponds to a line that is perpendicular to the line 2y + 3x = 6 A) y = -(2/3)x + 9 B) y = (3/2)x + 4 C) y = -(3/2)x - 5 D) y = 2/3 E) y = (2/3)x + 3 Solution Write in slope intercept form and find the slope of given line 2y + 3x = 6 2y = -3x + 6 y = (-3/2) x + 2 , slope = - 3 / 2 Slope of line perpendicular to the given line is equal to -1 / (-3/2) = 2 / 3 Hence line E) given by y = (2/3)x + 3 is perpendicular to the given line (√128) / 2 + (5√2) / 4 = Solution Use 128 = 2 * 64 to write (√128) / 2 + (5√2) / 4 = (√(2*64)) / 2 + (5√2) / 4 = = (√2 √64) / 2 + (5√2) / 4 = 8 √2 / 2 + 5√2 / 4 = 16 √2 / 4 + 5√2 / 4 = 21 √2 / 4 More ACT, SAT and Compass practice