Math Placement Exam Practice Problems Georgia State University.docx, Exams of Biology

Download Math Placement Exam Practice Problems Georgia State University.docx and more Exams Biology in PDF only on Docsity! Math Placement Exam Practice Problems Georgia State University Part 1 - answer Part 1 Simplify (2a^3b)^-3 - answer (2^-3 * a^(3 *-3) * b^-3) 2^-3 a^-9b^-3 1/8a^9b^3 Simplify (-4x^2y^-3)^-2 - answer *y^6/16x^4* Simplify Radical 1/64 - answer Radical 1/Radical 64 1/8 ^3 Radical -27 - answer *-3* Complex numbers: - answer Complex numbers Find x and y such that the following is correct: 3x + 5yi= 15 + 5i - answer 3x + 5yc= 15 + 5c i^47 - answer *-i* Solving Quadratic Equations by Factoring - answer Solving Quadratic Equations by Factoring Solve for x in 3x^2 + 8x + 4 = 0 - answer 3x^2 + 8x + 4 = 0 (3x + 2)(x+2)= 0 3x + 2 = 0 of x + 2= 0 *x= -2/3 or x= -2* Solve for x in x^2 + 4 = 0 - answer *x= +/- 2* Solving Quadratic Equations that are irreducible - answer Solving Quadratic Equations that are irreducible Solve for x in x^2 + 7x + 3 = 0 - answer x^2 + 7x + 3 = 0 x= -7+/- Radical 49 -4(1)(3)/2*1 *x= -7 +/- Radical 37 /2 * Solve for x in 2x^2 + 10x -1 = 0 - answer 2x^2 + 10x -1 = 0 x=b-10 +/- Radical 108 / 4 Solving and graph in Equalities - answer Solving and graph in Equalities Solve and graph 2-4x > 10 - answer 2-4x> 10 -4x >8 *x < -2 * Solve for x and graph the solution on number line for x^2 -2 >/eqaul to 1 - answer x^2 -2 >/ equal to 1 x >/equal to radical 3 or x </ equal to - radical 3 Solve the following equations for x and y 3x +2y =5 7x - y = 1 - answer 3x + 2y = 5 7x - y =1 z= 5 Graph the function f(x) = x^2 + 2 and identify x and y intercepts - answer x=0 f(x)= x^2 + 2 y= x^2 + 2 y= 0^2 + 2 y= 0 +2 *y= 2* y-intercept = (0, 2) When y = 0 *f(x) = 0 never occured* Graph the function f(x) = 3x-9 and identify x and y intercepts - answer f(x) = 3x - 9 f(0) = 3(0) -9 Set y=0 0= 3x - 9 9=3x x=3 *(3, 0) y intercept* Set x=0 y=3(0) -9 y=-9 *(0.-9) x-intercept * Solve for x in 0.3x+ 0.2 = 0.5 - answer x=1 Solve for x in 0.5x + 0.4 = 1.2 - answer x=1.6 Solve for x in x+3/x-9 =0 - answer x+3/x-9 =0 Numerator must be zero (x-9)(x-3)/x-9 0 * (x-9) x+ 3 = 3 Use the coordinates (2, 6) 6 = 2 (2) + yintercept 6= 4 + yintercept 2 = y intercept Equation *y= 2x+ 2 * For a right triangle, ABC with a= 3 and c=5, where c is the hypotenuse, find b. - answer a^2 + b^2= c^2 3^2 + b^2 =5^2 9 + b^2= 25 b^2= 16 *b = 4* For a right triangle ABC with a=13 and b=14 find the hypotenuse c. - answer a^2 + b^2= c^2 13^2 +14^2= c^2 169 + 196 = c^2 365 = c^2 *19* Write in interval notation { x E R: 10 < x < 20} where R denotes the set of all real numbers - answer *x E (10, 20)* Write x E (- affinity, 0} - answer *x </= (0) * Algebraic Solving - answer Algebraic Solving Solve ( radical x - 3 radical y ) * ( radical x + radical 9y) - answer ( radical x - 3 radical y ) * ( radical x + radical 9yx) (radical x radical x) + (radical x radical y) + (-3 radical y radical x 9y) (x) + ( radical 9 xy ( -3 radical yx + (-9y) x + 3 radical xy - 3 radical xy -9y *x - 9y * Multiply out the product ( superscript radical x + 2) (x^2-4) - answer *(superscript radical x + 2)(x^2 - 4) = x^7/3 -4 superscript radical x + 2x^2 - 8 * Simplify by placing over a common denominator 3/x-1 + x/x+4 - answer 3/x-1 + x/x+4 2x = 3 *x = 3/2 * Solve for x and y in x + y= 12 y-x= 4 - answer y=x + 4 and y= 3x + 1 x + 4=3x + 1 2x=3 x=3/2 y=(3/2) + 4 = 5.5 *x=1.5 and y=5.5* x + y= 12 and y - x = 4 - answer x + y= 12 and y- x=4 x= 12 - y y - (12 -y) = 4 y - 12 + y 2y -12 2y = 16 *y=8 * y-x=4 8-x *x=4* * x=4 and y=8* f(x) = 12x + 3 Find f(2) - answer f(2) = (12 * 2) + 3 = *27 * Let g(x) = 10x - 30 Find g(3) - answer Let g(x) = 10x -30 g(3) = ( 10 * 3) -30 *0* Solve for x in Radical x + 11 + 2= 0 - answer Radical x + 11 +2 = 0 lxl = 1 * x = 1 or 3 * Solve for x in l x - 4 l = 1 - answer l x + 4 l = +/- 1 *x = - 3 or 5* Write .0000045 in scinetific notation. - answer *4.5 * 10^-6* Write 4, 500, 000 in scientific notation - answer *4.5 * 10 ^6* Polynomial Division - answer Polynomial Division Perform the polynomial division (x-1) Radical x^3 - 3x^2 + x + 1 - answer (x-1) Radical x^3 - 3x^2 + x + 1 *x^2 - 2x - 1* Perform the polynomial division (x-1) Radical x^3 + 3x^2 - 4 - answer *X^2 + 4x + 4* Solve for j in 7i + 2k - 3j = 0 - answer 7i + 2k - 3j = 0 7i + 2k = 3j *7i/3 + 2k/3 = j* Solve for a in 8p + 2O -3a=0 - answer 8p + 2O -3a=0 8p + 2O = 0 +3a *8p/3 + 2O/3= 0 * Simplify x-2/2-x - answer x-2/2-x x-2/-1(x-2) 1 x- 2/-1 x-2 -1 * 1 *-1* Simplify -x + 8/x-8 - answer -x + 8/x-8 *-1* Evaluate