King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 181 Recitation (1.1)
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1 Recitation (1.1) Question 1: Find a point on the y-axis that is equidistant from the points (5, 5) and (1, 1) Question 2: Find the distance between the points P(2 x, 7 x) and Q( 2 x, 4 x) where x 0. Question 3: If the point (1, 4) is 5 units from the midpoint of the line segment joining (3, 2) and (x, 4), then x is equal to (a) either 7 or 9 (b) 15 (c) either or (d) either 7 or 9 (e) 15 Question 4: If M(6, 8) is the midpoint of the line segment AB and if A has coordinates (2, 3) then the coordinates of B is (a) (4, 11 2 ) (b) (16, 25) (c) (10, 13) (d) (13, 10) (e) (4, 5)
2 Recitation (1.2) Question 1: Sketch the graph of the following equations: (a) x = y 1 (b) y = 4 x (c) y = x (d) y = 9 x 2 Question 2: Find the general form of the equation of a circle with center at (-3, 5) and tangent to the y-axis. Question 3: If x 2 + y 2 4y = 5 k 2 is the equation of a circle which is tangent to the x-axis, then k = (a) ± 5 (b) 0 (c) ± 2 (d) ± 5 (e) ± 1 Question 4: Find an equation of the circle that has the points P( 1, 1) and Q(5, 9) as the endpoints of a diameter. Question 5: Let M be the midpoint of the line whose endpoints are (1, 2) and( 3, 6), and let C be the center of the circle x 2 + 4x + y 2 8y + 2 = 0. Then, find the distance between M and C. Question 6: Discuss the symmetry of the following relations: (b) x 2 = x y (d) xy + x y = 1 is symmetric with respect to both the x-axis and the origin. (e) x 4 y 4 + x 2 y 2 = 1 is symmetric with respect to x axis, y-axis, and the origin.
3 Recitation (1.3) Question 1: If A( 1, 2), B( 10, 5), and C( 4, k) are the vertices of a right triangle, where the right angle is at B, then find the value of k. Question 2: Find k so that the line passing through ( 2, 11) and (k, 2) is perpendicular to the line passing through (1, 1) and (5, 1) Question 3: The equation of the line passing through (4, 1) and parallel to x = 5 is (a) x = 5 (b) y = 1 (c) x = 1 (d) x = 4 (e) 4x + y = 5 Question 4: The line with x-intercept 1 and y-intercept the point (p, q). The value of p is intersects the line y = 2 at (a) 5 4 (b) 1 (c) 5 2 (d) 1 2 (e) 3 4 Question 5: Find an equation for the line tangent to the circle x 2 + y 2 = 25 at the point (3, 4) Question 6: A point that lies on the line that is perpendicular to the line 3y 2x + 6 = 0 and passes through the point (2, 3) is (a) ( 2, 1) (b) (1, 5) (c) (4, 3) (d) (6, 5) (e) (3, 3 2 )
4 Recitation (1.4) Question 1: For the given equation 7x 2 + 6x 7 = 0, state the number of distinct solutions, and whether they are rational, irrational, or non-real complex. Question 2: The product of all the solutions of the equation 1 r r = 4 r 2 is (a) 16 (b) 4 (c) 4 (d) 25 (e) 9 Question 3: When completing the square in the equation 4x(x 2) = 7, we get (x + a) 2 = b, then a + b 2 = (a) (b) (c) (d) 7 16 (e) Question 4: If the quadratic equation kx 2 = kx 16 has a double solution (two equal solutions), then k = (a) 0 and 64 (b) 0 (c) 64 (d) 16 (e) 0 and 16 Question 5: (a) If the sum and the product of the two roots of the equation 0.9x 2 + bx + c = 0 are 4 3 and 1 respectively, then find the values of b and c. (b) For the equation 9x 2 1 4xy = 3y 2, solve for y in terms of x. (c) Find the length of the rectangle if its area is 150 ft 2 and its perimeter is 50 ft.
5 Recitation (1.5) Question 1: If 3 ( 125 i 25 1 ) (2i 1)(2i+1)( i) 103 = x + iy, then y x = Question 2: If Z = ( 2+i 1 i )2 + ( 1+i 1 i ) 21, then find Z. Question 3: Find the reciprocal of the complex number 3 ( )i + ( 5) 2. Question 4: Find the sum of all roots of the equation 7x 2 + 2x + 3 = 1
6 Recitation (1.6) Question 1: Solve the following equation: (a) x 4 5x = 0 (b) 4x + 4 = 8 x 1 x+1 x 2 1 (c) ( x x+2 )2 = 4x 4 x+2 Question 2: Find the sum of all solutions of the following equation: (a) x + 2 = 1 3x + 7 (b) x x = x (c) + x = 1 x 5 5 x Question 4: Solve the following equation 3(2x 1) (2x 1) 1 3 = 6
7 Recitation (1.7) Question 1: Find the solution set of the following inequalities: (a) x (b) 4x 2 + 3x 1 (c) (x 8) 8 x 2 +7x+12 0 Question 2: The solution set of the inequality 0 < x is (a) ( 3, 2] (2, 3] (b) ( 3, 3] (c) ( 3, 3) (d) [ 3, 2) (2, 3] (e) ( 3, 2] Question 3: If the solution set of the inequality x(5x + 3) 3x 2 + 2, is given by the interval [m, n], then calculate m n. Question 4: Solve the following inequality. x 2 5 x
8 Recitation (1.8) Question 1: Solve the following: (a) x + 3 = 2x + 1 (b) x > 5 9 (c) 3x + 2 < 1 Question 2: Find the sum of all solutions of 3 2 x 2 7 x 2 = 6. Question 3: If x 5 < 1 2 m and n are (a) 1, 1 (b) 1 2, 1 2 is equivalent to m < 2x 3 < n, then the values of (c) 6, 8 (d) 3, 4 (e) 9, 11 Question 4: If A is the solution set of x2 +14x+49 x 2 +x 12 (a) [ 7, 7) (b) ( 4, 3) (c) { 7} ( 4, 3) (3, 7) (d) ( 4, 3] { 7} (e) ( 7, 3) (3, 7) 3 x 7, then A B = 0, and B is the solution set of
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