Questions and Answers of Financial Accounting Information For Decisions

At 15:00 hours, a submarine departs from point A and travels a distance of 120 km to a point B.The position vector, r km, of the submarine relative to an origin O, t hours after 15:00 is given bya.
OA(vector) = a and OB(vector) = b.OA: AE = 1: 3 and AB: BC = 1: 2.OB = BDa. Find, in terms of a and/or b,i. OE(vector)ii. OD(vector)iii. OC(vector).b. Find, in terms of a and/or b,a. CE(vector)ii.
Relative to an origin O, the position vector of A isAnd the position vector of B isa. Find:i. |OA(vector)|ii. |OB(vector)|iii. |AB(vector)|.The point A, B and C lie on a straight line such that
P = 7i – 2j and q = I + µj.Find λ and µ such that λp + q = 36i – 13j.
The figure shows points A, B and C with position vectors a, b and c respectively, relative to an origin O. The point P lies on AB such that AP: AB = 3: 4. The point Q lies on OC such that OQ:QC = 2:
At 12:00 hours, a boat sails from a point P.The position vector, r km, of the boat relative to an origin O, t hours after 12:00 is given bya. Write down the position vector of the point P.b. Write
O, A, B and C are four points such thatOA(vector) = 7a – 5b, OB(vector) = 2a + 5b and OC(vector) = 2a + 13b.a. Findi. AC(vector)ii. AB(vector).b. Use your answers to part a to explain why B lies on
Relative to an origin O, the position vector of A isAnd the position vectors of B isa. Find AB(vector).The points A, B and C lie on a straight line such that AC(vector) = 2AB(vector).b. Find the
P = 9i + 12j, q = 3i – 3j and r = 7i + jFinda. |p + q|b. |p + q + r|.
The position vectors of points A and B relative to an origin O are a and b respectively. The point P is such that OP(vectors) = µOA(vectors). The point Q is such that OQ(vectors) = λOB(vectors).
At 12:00 hours, a tanker sails from a point P with position vector (5i + 12j) km relative to an origin O. The tanker sails south-east with a speed of 12√2 km h-1.a. Find the velocity vector of the
OA(vector) = a, OB(vector) = b and O is the origin.OX = λOA(vector) and OY(vector) = µOB(vector).a. i. Find Bx in terms of λ, a and b.ii. Find AY(vector) in terms of µ, a and b.b. 5
Relative to an origin O, the position vector of A is 4i – 2j and the position vector of B is λi + 2j.The unit vector in the direction of AB(vector) is 0.3i + 0.4j. Find the value of λ.
P = 8i – 6j, q = -2i + 3j and r = 10iFinda. 2qb. 2p + qc. 1/2p – 3rd. 1/2r – p – q.
Relative to an origin O, points A, B and C have position vectorsRespectively. All distance are measured in kilometers. A man drives at a constant speed directly from A to B in 20 minutes.i. Calculate
At 12:00 hours, a ship leaves a point Q with position vector (10i + 38j) km relative to an origin O. The ship to an origin O. The ship travels with velocity (6i – 8j) km h-1.a. Find the speed of
OA(vector) = a, OB(vector) = b, BX(vector) = 3/5 BA(vector) ANDOY(vector) = 5/7 OA(vector).OP(vector) = λOX(vector) AND BP(vector) = µBY(vector).a. Find OP(vector) in terms of λ, a and b.b.
Relative to an origin O, the position vector of P is – 2i – 4j and the position vector of Q is 8i + 20j.a. Find PQ(vector).b. Find ||PQ(vector)|.c. Find the unit vector in the direction of
Find the unit vector in the direction of each of these vectors.a. 6i + 8jb. 5i + 12jc. -4i – 3jd. 8i – 15je. 3i + 3j
a. The four points O, A, B and C are such that OA(vectors) = 5a, OB(vectors) = 15b, OC(vectors) = 24b = 3a. Show that B lies on the line AC.b. Relative to an origin O, the position vector of the
A particle starts at a point P with position vector (-20i + 60j)m relative to an origin O.The particle travels with velocity (12i 16j) ms-1.a. Find the speed of the particle.b. Find the position
OA(vector) = a, OB(vector) = b.M is the midpoint of AB and OY(vector) = ¾ OA(vector).OX(vector) = λOM(vector) and BX(vector) = µBY(vector).a. Find in terms of a and b,i. AB(vector)ii.
Relative to an origin O, the position vector of A is -7i – 7j and the position vector of B is 9i + 5j.The point C lies on AB such that AC(vector) = 3 CB(vector).a. Find AB(vector).b. Find the unit
The vector OA(vector) has a magnitude of 25 units and is parallel to the vector -3i + 4j.The vector OB(vector) has a magnitude of 26 units and is parallel to the vector 12i + 5j.Find:a. OA(vector)b.
The position vectors of the points A and B relative to an origin O are -2i + 17j and 6i + 2j respectively.i. Find the vector AB(vectors).ii. Find the unit vector in the direction of AB(vectors).iii.
The vector PQ(Vector) has a magnitude of 39 units is parallel to the vector 12j – 5j.Find PQ(Vector).
a. A car travels north-east with a speed of 18√2 km h-1. Find the velocity vector of the car.b. A boat sails on a bearing of 030° with a speed of 20 km h-1. Find the velocity vector of the boat.c.
OA(vector) = a, OB(vector) = b.B is the midpoint of OD and AC(vector) = 2/3 OA(vector).AX(vector) = λAD(vector) and BX(vector) = µBC(vector).a. Find OX(vector) in terms of λ, a and b.b. Find
The vector AB(Vector) has magnitude of 20 units and is parallel to the vector 4i + 3j.Find AB(Vector).
Relative to an origin O, the position vectors of the points A and B are I – 4j and 7i + 20j respectively. The point C lies on AB and is such that AC(vectors) = 2/3 AB(vectors). Find the position
A helicopter flies from a point P with position vector (50i + 100j) km to a point Q.The helicopter flies with a constant velocity of (30i – 40j) km h-1 and takes 2.5 hours to complete the journey.
OP(vector) = a, PY(vector) = 2b, and OQ(vector) = 3b.OX(vector) = λOY(vector) and QX(vector) = µQP(vector).a. Find OX(vector) in terms of λ, a and b.b. Find OX(vector) in terms of µ, a
a. O is the origin, P is the point (1, 5) andb. O is the origin, E is the point (-3, 4) andc. O is the origin, M is the point (4, -2) andFind the position vector of N. PQ = ;) 3 Find OQ.
Find the magnitude of each of these vectors.a. -2ib. 4i + 3jc. 5i – 12jd. -8i – 6je. 7i + 24jf. 15i – 8jg. -4i + 4jh. 5i – 10j
In the diagram OA(vectors) = a, OB(vectors) = b and AP(vectors) = 2/5 AB(vectors).a. Given that PX(vectors) = µOP(vectors), where µ is a constant, express OX(vectors) in terms of µ, a and b.b.
A car travels from a point A with position vector (60i – 40j) km to a point B with position vector (-50i + 18j) km.The car travels with constant velocity and takes 5 hours to complete to
AB(vector) = 5a, DC(vector) = 3a and CB(vector) = b.AX(vector) = λAC(vector) and DX(vector) = µDB(vector).a. Find in terms of a and b,i. AD(vector),ii. DB(vector).b. Find in terms of
Find AB(Vector), in the form ai + bj, for each of the following.a. A(4, 7) and B(3, 4)b. A(0, 6) and B(2, - 4)c. A (3, -3) and B(6, - 2)d. A(7, 0) and B(-5, 3)e. A(-4, -2) and B(-3, 5)f. A(5, -6) and
Write each vector in the form ai + bj.a. AB(Vector)b. AC(Vector)c. AD(Vector)d. AE(Vector)e. BE(Vector)f. DE(Vector)g. EA(Vector)h. DB(Vector)i. DC(Vector) A E D B
Relative to an origin O, the position vectors of the points A and B are 2i – 3j and 11i + 42j respectively.a. Write down an expression AB(vectors).The point C lies on Ab such that AC(vectors) = 1/3
a. Displacement = (21i + 54j) m, time taken = 6 second. Find the velocity.b. Velocity = (5i – 6j)ms-1, time taken = 6 seconds. Find the displacement.c. Velocity = (-4i + 4j) kmh-1, displacement =
OA(vector) = a, OB(vector) = b.R is the midpoint of OA and OP(vector) = 3 OB(vector).AQ(vector) = λAB(vector) and RQ(vector) = µ RP(vector).a. Find OQ(vector) in terms of λ, a and b.b.
A curve has equation y = 4x3 + 3x2 – 6x – 1.a. Show that dy/dx = 0 when x = - 1 and when x = 0.5.b. Find the value of d2y/dx2 when x = - 1 and when x = 0.5.
Find the coordinates of the point on the curve y = 2x2 – x – 1 at which the gradient is 7.
The curve y = 2x3 + ax2 – 12x + 7 has a maximum point at x = -2. Find the value of a.
A cuboid has a total surface area of 400 cm2 and a volume of V cm3.The dimensions of the cuboid are 4x cm by x cm by h cm.a. Express h in terms of V and x.b. Show that V = 160x – 160/5 x3.c. Find
Find the gradient of the curve y = (2x – 5)4 at the point (3, 1).
Find the gradient of the curve y = (x + 2) (x – 5)2 at the points where the curve meets the x-axis.
A sector of a circle of radius r cm has an angle θ radians, where θ < π. The perimeter of the sector is 30 cm.a. Show that the area, A cm2, of the sector is given by A = 15r – r2.b. Given
Find the gradient of the curve y = 7x – 2/2x + 3 at the point where the curve crosses the y-axis.
The normal to the curve y = x3 – 2x + 1 at the point (2, 5) intersects the y-axis at the point P.Find the coordinates of P.
A curve has equation y = (x + 1) (2x – 3)4.Find, in terms of p, the approximate change in y as x increases from 2 to 2 + p, where p is small.
Variables x and y are connected by the equation y = 2x/x2 + 3.Given that x increases at a rate of 2 units per second, find the rate of change of y when x = 1.
A curve has equation y = 2x3 – 15x2 + 24s + 6. Copy and complete the table to show whether dy/dx and d2y/dx2 are positive (+), negative (-) or zero (0) for given values of x. 1 3 4 dy dx d'y
Find the gradient of the curve y = x-4/x at the point where the curve crosses the x-axis.
The curve y = x3 + ax + b has a stationary point at (1, 3).a. Find the value of a and the value of b.b. Determine the nature of the stationary point (1, 3).c. Find the coordinates of the other
A piece of wire, of length 60 cm, is bent to form a sector of a circle with radius r cm and sector angle θ radians. The total area enclosed by the shape is A cm2.a. Express θ in terms of r.b. Show
Find the gradient of the curve y = 8/(x – 2)2 at the point where the curve crosses the y-axis.
Find the x-coordinates of the points on the curve y = (2x – 3)3 (x + 2)4 where the gradient is zero.
a. Given that y = (1/4 x – 5)8, find dy/dx.b. Hence find the approximate change in y as x increases from 12 to 12 + p, where p is small.
Differentiate with respect to x:a. √x/2x + 1b. x/√1- 2xc. x2/√x2+2d. 5√x/3+x
Find the equation of the tangent and the normal to the curve y = x – 1/√x + 4 at the point where the curve intersects the y-axis.
A curve has equation y = (x - 2) √2x + 1.Find, in terms of p, the approximate change in y as x increases from 4 to 4 + p, where p is small.
Variables x and y are connected by the equation y = 2x – 5/x - 1.Given that x increases at a rate of 0.02 units per second, find the rate of change of y when y = 1.
A curve has equation y = 2x3 + 3x2 – 36x + 5. Find the range of values of x for which both dy/dx and d2y/dx2 are both positive.
Find the gradient of the curve y = x3 – 2x2 + 5x – 3 at the point where the curve crosses the y-axis.
The curve y = x2 + a/x + b has a stationary point at (1, - 1).a. Find the value of a and the value of b.b. Determine the nature of the stationary point (1, - 1).
The diagram shows a window made from a rectangle with base 2r m and height h m and a semicircle of radius r m. The perimeter of the window is 6 m and the surface area is A m2.a. Express h in terms of
Find the gradient of the curve y = x + 4/x – 5 at the points where the curve crosses the x-axis.
Find the x-coordinate of the point on the curve y = (x + 3) √4 – x where the gradient is zero.
Find the equation of the normal to the curve y = x2 + 8/x – 2 at the point on the curve where x = 4.
Find the gradient of the curve y = x-2/√x + 5 at the point (-4, -6).
The tangents to the curve y = x2 – 5x + 4, at the points (1, 0) and (3, - 2), meet at the point Q.Find the coordinates of Q.
The periodic time, T seconds, for a pendulum of length Lcm is T = 2π √L/10.Find the approximate increase in T as L increases from 40 to 41.
Variables x and y are connected by the equation 1/y = 1/8 – 2/x.Given that x increases at a rate of 0.01 units per second, find the rate of change of y when x = 8.
Given that y = x2 – 2x + 5, show that 4 d2y/dx2 + (x – 1) dy/dx = 2y.
The curve y = 2x2 + 7x – 4 and the line y = 5 meet at the point P and Q. Find the gradient of the curve at the point P and at the point Q.
The curve y = ax + b/x2 has a stationary point at (1, - 12).a. Find the value of a and the value of b.b. Determine the nature of the stationary point (- 1, - 12).
ABCD is rectangle with base length 2p units, and area A units2. The points A and B lie on the x-axis and the points C and D lie on the curve y = 4 – x2.a. Express BC in terms of p.b. Show that A =
Find the coordinates of the point on the curve y = √(x2 – 6x + 13) where the gradient is 0.
a. Find the equation of the tangent to the curve y = x3 + 2x2 – 3x + 4 at the point where the curve crosses the y-axis.b. Find the coordinates of the point where the tangent meets the curve again.
Find the coordinates of the point on the curve y = 2(x – 5)/√x+1 where the gradient is 5/4.
The tangent to the curve y = 3x2 – 10x – 8 at the point P is parallel to the line y = 2x – 5.Find the equation of the tangent at P.
The volume of the solid cuboid is 360 cm3 and the surface area is A cm2.a. Express y in terms of x.b. Show that A = 4x2 + 1080/x.c. Find, in terms of p, the approximate change in A as x increases
A square has sides of length x cm and area A cm2.The area is increasing at a constant rate of 0.2 cm2s-1.Find the rate of increase of x when A = 16.
Given that y = 8√x, show that 4x2 d2y/dx2 + 4x dy/dx = y.
The curve y = ax2 + bx has gradient 8 when x = 2 and has gradient – 10 when x = - 1.Find the value of a and the value of b.
The curve y = 2x3 – 3x2 + ax + b has a stationary point at the point (3, - 77).a. Find the value of a and the value of b.b. Find the coordinates of the second stationary point on the curve.c.
A solid cylinder has radius r cm and height h cm. The volume of this cylinder is 250π cm3 and the surface area is A cm2.a. Express h in terms of r.b. Show that A = 2πr2 + 500π/r.c. Find dA/dr and
The curve y = a/√bx + 1 passes through the point (1, 4) and has gradient – 3/2 at this point.Find the value of a and the value of b.
The normal to the curve y = x3 + 6x2 – 34x + 44 at the point P(2, 8) cuts the x-axis at A and the y-axis at B. Show that the mid-point of the line AB lies on the line 4y = x + 9.
The line 5x – 5y = 2 intersects the curve x2y – 5x + y + 2 = 0 at three points.a. Find the coordinates of the points of intersection.b. Find the gradient of the curve at each of the points of
A curve has equation y = x3 – x + 6.a. Find the equation of the tangent to this curve at the point P(-1, 6). The tangent at the point Q is parallel to the tangent at P.b. Find the coordinates of
A cube has sides of length x cm and area V cm3.The volume is increasing at a rate of 2 cm3s-1.Find the rate of increase of x when V = 512.
The gradient of the curve y = ax + b/x at the point (-1, -3) is – 7.Find the value of a and the value of b.
The diagram shows a solid formed by joining a hemisphere of radius r cm to a cylinder of radius r cm and height h cm. The surface area of the solid is 288π cm2 and the volume is V cm3.a. Express h
Given that f(x) = x2 – 648/√x, find the value of x for which f”(x) = 0.
A curve has equation y = 4 + (x – 1)4.The normal at the point P(1, 4) and the normal at the point Q(2, 5) intersects at the point R.Find the coordinates of R.
A sphere has radius r cm and volume V cm3.The radius is increasing at a rate of 1/π cm s-1.Find the rate of increase of the volume when V = 972π.
Find the coordinates of the points on this curve y = x3/3 – 5x2/2 + 6x – 1 where the gradient is 2.

Showing 200 - 300 of 1440