22/9/24
SECTION & MIDPOINT FORMULA
1) The centroid of the triangle whose vertices are (3,7),(-8,6) and (5,10) is
a) (0,9) b) (0,3) c) (1,3) d) (3,3)
2) A line interestc the y-axis and x-axis at the points A and B respectively. If (2,-5) is the midpoint of AB, then the coordinates of A and B are, respectively :
a) (0,-5) and (2,0) b) (0,10) and (-4,0) c) (0,4) and (-10,0) d) (0,-10) and (4,0)
3) If O (a/3,4) is the midpoint of a line segment joining the point X(-6,5) and Y(-2,3), then the value of a is
a) -4 b) -6 c) 12 d) -12
4) If the centroid of the Triangle formed by (7,x),( y,- 6) and (9,10) is (6,3), then the values of x and y respectively are:
a)( 5,3) b) ( 5,2) c) (-3,2) d) (6,5)
5) The ratio in which the point (3/4, 5/12) divides the line segment joining the point A(1/2, 3/2) and (2,-5) is
a) 1:2 b) 3 : 2 c) 1:5 d) 2 :3
6) The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2,3), B(6,7) and C(8,3) is
a) (0,1) b) (0,-1) c) (-1,0) d) (1,0)
7) The ratio in which the point P(4, m) divides the line segment joining the points A(2,3) and B(6,-3) is
a) 1:2 b) 2:1 c) 1:3 d) 1:1
8) If A(m/2,5) is the midpoint of the line segment joining the points Q(-6,7) and R(-2,3), then the value of m is
a) -8 b) -4 c) 12 d) 6
9) The midpoint of the line segment joining the points(-5,7) and (-1,3) is
a) (-3,7) b) (- 3,5) c) (- 1,5) d) ( 5,-3)
10) In the figure,
AB is a diameter of the circle with centre O(4,5). If A is (1,1), then B=
a) (6,9) b) (7,9) c) (-7,9) d) (7,-9)
11) The ratio in which P(m,4) divides the line segment joining the points A(2,5) and B(6,-3) is
a) 1:2 b) 2: 1 c) 1:3 d) 1 :7
12) if the midpoint of the line segment joining the points P(6, b - 2) and Q(- 2,4) is (2,-3), then the value of b=
a) -5 b) -6 c) -7 d) - 8
13) If the coordinates of one end of a diameter of a circle are (2,3) and the coordinates of its centre are (-2,5), then the co-ordinates of the other end of the diameters are:
a) (-6,7) b) (6,-7) c) (6,7) d) (-6,-7)
14) The point which lies on the perpendicular bisector of the line segment joining the points A(-2,-5) and B(2,5) is
a) (0,0) b) (0,2) c) (2,0) d) (-2,0)
15) The vertices of a parallelogram in order are A(1,2), B(4, y), C(x, 6), D(3,6). The value of x and y respectively are:
a) 6, 2 b) 3, 6 c) 5, 6 d) 1,4
16) If A(1,3), B(-1,2), C(2,5) and D(x, y) are the vertices of a parallelogram ABCD, then the value of x is
a) 3 b) 4 c) 0 d) 3/2
SHORT ANSWER TYPE QUESTIONS
1) Find the ratio in which the line segment joining (-2,5) and (-5,-6) divided by the line y= -3. Hence find the point of intersection .
2) P(1,-2) is a point on the line segment joining A(3,-6) and B(x, y) such that AP: PB is equal to 2:3. Find the coordinates of B.
3) In what ratio is the line segment joining P(5,3) and Q(-5,3) divided the y-axis ? Also find the coordinanates of the point of intersection.
4) In what ratio does the point C(3/5,11/5) divide the line segment joining the points A(3,5) and B (-3,-2)?
5) Find the coordinanates of the point of trisection (i.e., points dividing into three equal parts) of the line segment joining the points A(2,-2) and B(-7,4).
6) Find the ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1,-4). Also, find the point of intersection.
7) If the points A(6,1), B(8,2), C(9,4) and D(p,3) are the vertices of a parallelogram, taken in order, find the value of p.
8) In the figure, 
line APB meets the x-axis at A and y-axis at B. P is the point (-4,2) and AP: PB= 1:2. Write down coordinanates of A and B.
LONG ANSWER TYPE QUESTIONS
1) Find the ratio in which the point (-3, p) divides the line segment joining the points (-5,-4) and (-2,3). Hence, find the value of p.
2) If the co-ordinate the midpoints of the sides of a triangle are (1,2),(0,1) and (2,-1), find the coordinates of its vertices.
3) The base BC of an equilateral triangle ABC lies on y-axis. The co-ordinates of point C are (0,-3). If the origin is the mid point of the base BC, find the coordinates of the points A and B.
4) P and Q are the points on the line segment joining the points A(3,-1) and B(-6,5) such that AP= PQ= QB. Find the co-ordinates of P and Q.
5) Find the length segment joining P(-4,5) and Q(3,2) intersects the y-axis at R. PM and QN are perpendicular from P and Q on x-axis. Find
a) the ratio PR: RQ.
b) the co-ordinates of R.
c) the area of the quadrilateral PMNQ
6) The line segment joining the points (3,-4), and (1,2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, find the value of p and q.
Day - 5(2/6/24)
1) In what ratio is the line joining (2, -3) and (5,6) divided by x-axis. 1:2
2) In what ratio is the line joining (2, -4) and (-3, 6) divided by x-axis. 2:3
3) Calculate the Co-ordinates of the point P which divides the line joining A(-1,3) and B(5,9) in the ratio 1:2. (1,5)
4) The line joining the points A(-3, -10) and B(-2,6) is divided by the point P such that PB/AB = 1/5. Find the coordinate of P. (-11/5, 14/5)
5) P is a point on the line joining A(4,3) and B(-2,6) such that 5AP/2BP. Find the coordinates of P. (16/7,27/7)
6) In what ratio does the point P(3,3) divide the join of A (1,4) and B(7,1)? 1:2
7) In what ratio does the point (1,a) divide the join of (-1, 4) and (4,-1)? Also find the value of a. 2:3, 2
8) In what ratio does the point (a,6) divide the join of (-4,3) and (2,8)? Also find the value of a. 3:2, -2/5
9) In what ratio is the join of (4,3) and (2, -6) divided by x-axt. Also find the Co-ordinates of the point intersection. 1:2, (10/3,0)
10) Find the ratio in which the join of (-4,7) and (3,0) divided by y-axis. Also find the coordinates of the point of intersection. 4:3, (0,3)
11) Points A, B, C and D divide the line segment joining the point (5, -10) and origin in five equal parts. Find the coordinates of A, B , C and D. (4,-8), (3,-6),(2,-4),(1,-2)
12) Find the Co-ordinates of the points of trisection of the line joining the points (-3,0) and (6,6). (0,2),(3,4)
13) Show that the line segment joining the point (-5,8) and (10,-4) is trisected by coordinate axes.
14) Show that A(3,-2) is a point of trisection of the line segment joining the point (2,1) and (5,-8).
Also, find the coordinates of other point of trisection . (4,-5)
15) Given , two fixed points A(0,10) and B(-30 ,0). Calculate the coordinates of a point P which lies in the AB such that:
a) 2AP 3PB.
b) 3AP = AB
c) 7PB = AB
16) Given two fixed points P(-3,4) and Q(5,-2). Calculate the coordinates of points A and B in PQ such that:
5PA= 3PQ and 3PB = 2PQ.
17) The line segment joining A(2,3) and B(6,5) is intersected by x-axis at point K. Write down the ordinate of K. Hence, find the ratio in which K divides AB.
18) The line segment joining the points M(5,7) and N(-3,2) is interesting by y-axis at point L. Write down the absicca of L. Hence, find the ratio in which L divides MN.
Also the Co-ordinates of L.
19) Calculate the coordinates of points which devide the join of (8, 6) and (2,.3) into 4 equal parts. (13/2,21/4),(5,9/2) and (7/2,15/4)
20) A(2,5), B(-1,2) and C(5,8) are the coordinates of the vertices of the triangle ABC. Points P and Q lie on AB and AC respectively, such that :
AP: PB = AQ : QC= 1:2.
a) calculate the Co-ordinates of P and Q. (1,4)
b) Show that PQ= (1/3)BC
21) A(-3,4) B(3,-1) and C(-2,4) are the vertices of a triangle ABC. Find the length of line segment AP, where point P lies in side BC, such that BP: PC = 2:3.
Day- 4 (17/5/24)
1) 2x²+ 3x-20= 0
2) 4x² - 12x + 9= 0.
3) 3x² -8x + 2= 0.
4) 2x + 2/x +5= 0
5) x + 96/x = 22.
6) x(2x +5) -3= 0
7) x(3x + 1/2) - 6 = 0
8) 3x(3x - 8)+ 16= 0
9) 4(x +2)(x +1)= 15.
10) One root of x² - 3x - c= 0 is -2, find the value of c and the other root.
11) One root of 2x²- 3(5x + c)= 0 is 3/2, find the value of c and other root.
Solve the following equations using formula
Give your answer correct to 2 decimal places.
1) x²+ 4x + 2 = 0.
2) 5x²- 3x- 7= 0.
3) x - 10/x = -7.
4) 2x + 5 = 9/x.
5) 3x(2x -7)= 4.
6) 2(x -1)(x -5)= 5.
7) 5(x +1)²+ 10(x +1)+ 3= 0.
8) (x -1)² -6(x -1)= 11.
9) Find the values of k for which the given equation has real and equal roots:
a) 12x²+ 4kx +3= 0.
b) kx² - 2 √5 x + 4= 0.
c) 4x²- 3kx + 1 = 0.
d) (k+1) x² - 2(k -1)x + 1 = 0.
10) Find the values of k for which the given equation has real roots.
a) 2x² - 5x- k = 0.
b) kx²+ 6x +1 = 0.
Day - 3 (12/5/24)
Type -1
1) 2x²+ 2= 5x.
2) x²+ 9x - 52= 0
3) 6x²+ 5x - 4= 0.
4) 3x²+ 14x +8= 0
5) 7x²= 8 - 10x.
6) x(x +1)+ (x +2)(x +3)= 42.
7) 6x(3x -7)= 7(7- 3x).
8) 3(x²- 4)= 5x.
9) √3 x²+ 10x + 7 √3 = 0.
10) x²+ 2 √2 x - 6= 0
Type - 2
1) (x +3)/(x +2)= (3x -7)/(2x -3).
2) (x +2)/(x +3)= (2x -3)/(3x -7).
3) (5x +1)/(7x +5)= (3x +1)/(7x +1).
4) (3x -7)/(2x -5)= (x +1)/(x -1).
5) (x +1)/(x - 2)+ (x +11)/(x +3)= 4.
6) x/(x +1)+ (x +1)/x = 34/15, x≠ 0, x≠ -1
7) 6/(x +1 )+ 5/(2x +1)= 3
8) 4/(x -1)- 5/(x +2)= 3/x.
9) 5/(x -2)- 4/x = 3//(x +6).
10) (x +2)/6 - 1/(x +2)= 1/6.
11) x⁴- 10x² + 9= 0
12) x⁴- 25x² + 25= 0
13) 11/(5x -4) - 10/(4 - 5x)= 1
Type -3
1) Find the value of p in the following:
a) If (k+2)= 0 and 4k²+ kp²+ 82= 0.
b) If (2k -1)= 0 and k²+ 8kp²+ 2p= 0.
Type - 4
For each of the following solution set, find the quadric equation:
a) x= 2,3
b) x= 3, -4
c) x = 2, 2
d) x= 1/2, 1/3
Miscellaneous
1) Solve: x - 10/x = 9, if x= (a, b), then find
a) a+ b
b) ab
2) Find solution set of 2x² - 5 x - 3= 0, where x= (α, β). if the above quadratic equation is identical equal to ac²+ bx + c= 0, find a, b and c. Hence show that
a) α+ β = -b/a
b) α β = c/a
3) Find the solution set of 2x - 5/x = 3, x= (α, β). If the above quadratic equation is identical equal to ax² + bx + c= 0, find a, b and c. Hence show that
a) α + β = -b/a
b) α β = c/a
Day -2 7/5/24
1) 4 sin²60° + 3 tan²30° - 8 sin45° cos45°
2) 4 sin45° cos45° - sin²30° + tan²60°
3) 4/tan²60° + 1/cos²30° - sin²45°.
4) 4 cos²60° + 4 tan²45° - sin²30°
5) (cos90° + sinn²30° - sin45°)(sin0° + cos60°sin45°)
6) (sin90° + sin²45° cos45° - tan30°)(4sin²30° + cos60° + 1/tan60°)
7) Given cosA = 1/3, A is an acute angle, find tan²A.
8) Given 7 tanA = 24, A is an acute angle, find tan²A.
9) Given 5 tanA = 4, find the value of (5 sinA - 3 cosA)/(5sinA + 2 cosA)
10) Given 5 sinA = 3, A is an acute angle, find (cosA - 1/tanA)/2/tanA.
Day -1 5/5/24
1) If 2 cosx = 3/5, find the value of tanx + sin²x. (2)
2) Solve graphically: 2x + 3y = -5; 2y + 3x = 0. (3)
3) The midpoint of the line joining A(2, p) and B(q, 4) is (3,5). Find the numerical value of p and q. (1)
4) Find the value of 3 cos45 cosec30+ 2 cos60 cosec 30. (2)
5) Show 1/(sinx + cosx) + 1/(sinx - cosx)= 2 sinx/(2sin²x -1). (3)
6) P(2,4), Q(3,3) and R(7,5) are the vertices of a ∆PQR. Find
a) The coordinates of the centroid G of ∆PQR. (2)
7) Solve: x/(x +1) + (x +1)/x = 34/15. (2)
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