Welcome to your Coordinate Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. Which of the following pairs of graphs cannot be used to find the solution to the cubic equation x³ -3x² + 3x - 9 = 0 ? y = x² - 3x + 3and y = 9/x y = x³ and y = 3x² - 3x + 9 y = x³ -3x² and y = 3x - 9 y = x³ -3x² + 3x and y = 9 2. Find the gradients and the intercepts on the y- axis for 5x = 6y m = -1, c= -1 m = 1/6, c= -1 m = 1, c = -1/2 m = 5/6, c= 0 3. A straight line y = ax intersects the parabola y = x² -5x + 6 at points P(1,2) and Q(m,n). The values of m and n are (-2, -4) (3, 6) (6, 12) (-1, -2) 4. In a coordinate system, P = (2, 7) and Q = (2, –3). Which could be the coordinates of R if PQR is an isosceles triangle? I. (12, –3) II. (–6, –9) III. (–117, 2) II only I and III only II and III only I, II and III 5. Which point is the reflection of the point (–7, 5) over the line y = –x? (5, -7) (-5, 7) (7, 5) (7, -5) 6. Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7. Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have? 8 6 9 7 7. The intercept of the line y = 3x on the x-axis is 0 1 1/3 3 8. Find the co-ordinates of a point on x-axis, which is at a distance of 5 units from the point (6, -3). (0,2) and ( 0,10). (2, 10) and (1, 0). (2, 0) and (10, 0). (2, 10) and (0, 0). 9. In the figure, the point on segment JK that is four times as far from K as it is from J is: (0, 2) (-1, 3) (-1/3, 7/3) (2,0) 10. The maximum value of y in the equation y = 1 + x - 4x² is 17/8 2 1 17/16 11. In the x-y plane, point (p, q) is a lattice point if both p and q are integers. Circle C has a center at (–2, 1) and a radius of 6. Some points, such as the center (–2, 1), are inside the circle, but a point such as (4, 1) is on the circle but not in the circle. How many lattice points are in circle C? 109 36 96 89 12. ABCD is a rhombus with the diagonals AC and BD intersecting at the origin on the x-y plane. The equation of the straight line AD is x + y = 1. What is the equation of BC? x + y= -1 x + y = 1 x - y = 1 x - y = -1 13. Find the equations of the straight lines passing through the point (2, -1) and the gradient 2 y = x + 7 y = x +1 y = 2x - 5 y = 4x + 9 14. Find the gradients and the intercepts on the y- axis for y+3= 0 m= 0, c= -3 m = 0, c = 3 m = 3, c = 0 m = -3, c= 0 15. Find the gradients and the intercepts on the y- axis for 3y-2x+5 = 0 m = 1, c = -1 m= 3, c = -5 m = 2/3, c=-5/3 m = 1/3, c = 5/3 16. The points of intersection between a straight line and the curve y = -x² + x + 2 give the roots of the equation x² - 2x - 1 = 0. The equation of the line is y = 1 - x y = 1 + x y = x -1 y = x + 3 17. The points of intersection of the graphs of y = x² + 2 and y = 2x + 5 when drawn on the same set of axes are (3, 0) and (-1, 0) (-1, 3) and (3, 11) (1, 0) and (-3, 0) (-1, 11) and (3, 3) 18. The graph of the function 2y = x² - x - 6 intersects the y axis at the point (0, -3) (2, -3) (0, -6) (-2, 0) 19. The point (1, -2)is located on the graph of a linear function. If y increases by 3 units for each unit increase in x, the equation of the function is y - 3x = 5 3y - x = 5 y - 3x = -5 x -3y = 5 20. The points of intersection of the curve y = -2x² - x + 3 with the coordinate axes are (1, 0), (-3/2, 0) and (0,3) (3/2, 0), (1, 0) and (0, -3) (0,0), (1, 3/2) and (0, -3) (-1, 0), (3/2, 0) and (0,3) 21. Find the co-ordinates of the point of intersection of the medians of triangle MNO; given M = (-2, 3), N = (6, 7), O = (4, 1). (8/3, 11/3) (5/3, 17/3) (5/3, 1/3) (3/8, 3/11) 22. In which quadrant does the point (-3,4) lie? 3rd quadrant 1st quadrant 4th quadrant 2nd quadrant 23. Find the coordinates of the point which will divide the line joining the points (3, 5) and (11, 8) externally in the ratio 5: 2. (49/3, 10) (3/49, 1/10) (5/3, 1/3) (3/5, 4/13) 24. If a graph of the function y = 3x² -5x - 7 is provided, the roots of the equation 3x² - 2x -5 = 0 are given by the points of intersection of the curve y = 3x² -5x - 7 and the line y = 3x - 2 y = 7x - 12 y = -3x - 2 y = -7x - 2 25. Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4 = 0 3y = 5x-2 3y = 2x+5 y = 5/ 3x-2 y = x+2 1 out of 25 Time is Up! Time's up
