Questions and Answers of Financial Accounting Information For Decisions

The point A(-3, 2) and B(1, 4) are vertices of an isosceles triangle ABC, where angle B = 90°.a. Find the length of the line AB.b. Find the equation of the line BC.c. Find the coordinates of each of
Triangle PQR where P(1, 4), Q(-3, -4) and R(7, k) is right-angled at Q.a. Find the value of k.b. Find the area of triangle PQR.
Variables x and y are related so that, when y/x2 is plotted on the vertical axis and x3 is plotted on the horizontal axis, a straight-line graph passing through (2, 12) and (6, 4) is obtained.Express
The table shows experimental values of the variables x and y.a. Draw the graph of xy against x2.b. Use your graph to express y in terms of x.c. Find the value of x and the value of y for which xy =
A(- 1, 0), B(1, 6) and C(7, 4).Show that triangle ABC is a right-angled isosceles triangle.
A(- 1, - 5), B(5, - 2) and C(1, 1).ABCD is a trapezium.AB is parallel to DC and angle BAD is 90°.Find the coordinates of D.
P is the point (2, 5) and Q is the point (6, 0).A line l is drawn through P perpendicular to PQ to meet the y-axis at the point R.a. Find the equation of the line l.b. Find the coordinates of the
A is the point (-4, 0) and B is the point (2, 3), M is the midpoint of the line AB.Point C is such thata. Find the coordinates of M and C.b. Show that CM is perpendicular to AB.c. Find the area of
Variables x and y are related so that, when y2 is plotted on the vertical axis and 2x is plotted on the horizontal axis, a straight-line graph which passes through the point (8, 49) with gradient 3
The mass, m grams, of a radioactive substance is given by the formula m = m0 e-kt, where t is the time in days after the mass was first recorded and m0 and k are constants.The table below shows
Variables x and y are such that y = abx, where A and b are constants. The diagram shows the graph of ln y against x, passing through the points (2, 4) and (8, 10).Find the value of A and of b. Iny
The distance between two points P(10, 2b) and Q(b, - 5) is 5√10.Find the two possible values of b.
The midpoint of the line segment joining P(-2, 3) and Q(4, - 1) is M.The point C has coordinates (-1, -2).Show that CM is perpendicular to PQ.
Find the equation of the perpendicular bisector of the line segment joining the points.a. (1, 3) and (-3, 1)b. (-1, - 5) and (5, 3)c. (0, -9) and (5, - 2).
Angle ABC is 90° and M is the midpoint of the line AB.The point C lies on the y-axis.a. Find the coordinates of B and C.b. Find the area of triangle ABC. B М(6, 4) A(8, 3)
Variables x and y are related so that, when y/x is plotted on the vertical axis and x is plotted on the horizontal axis, a straight-line graph passing though the points (2, 4) and (5, - 2) is
The table shows experimental values of the variables x and y.The variables are known to be related by the equation y = kxn where k and n are constants.a. Draw the graph of lg y against lg x.b. Use
The diagram shows a trapezium ABCD with vertices A(11, 4), B(7, 7), C(-3, 2) and D.The side AD is parallel to BC and the side CD is perpendicular to BC.Find the area of the trapezium ABCD. В(7, 7)
The distance between two points P(6, -2) and Q(2a, a) is 5.Find the two possible values of a.
A(-2, 2), B(3, - 1) and C(9, - 4).a. Find the gradient of AB and the gradient of BC.b. Use your answer to part a to decide whether or not the points A, B and C are collinear.
The perpendicular bisector of the line joining A(-1, 4) and B(2, 2) intersects the x-axis at P and the y-axis at Q.a. Find the coordinates of P and of Q.b. Find the length of PQ.c. Find the area of
A is the point (-4, 5) and B is the point (5, 8).The perpendicular to the line AB at the point A crosses the y-axis at the point C.a. Find the coordinates of C.b. Find the area of triangle ABC.
Variables x and y are related so that, when ey is plotted on the vertical axis and x2 is plotted on the horizontal axis, a straight-line graph passing though the points (3, 4) and (8, 9) is
The table shows experimental values of the variables x and y.The variables are known to be related by the equation y = a × bx where a and b are constants.a. Draw the graph of lg y against
The table shows experimental values of two variables x and y.It is known that x and y are related by the equation y = a/√x + bx, where a and b are constants.a. Complete the following table.b. On a
Find the coordinates of the midpoint of the line segment joininga. (5, 2) and (7, 6)b. (4, 3) and (9, 11)c. (8, 6) and (-2, 10)d. (-1, 7) and (2, - 4)e. (-7, - 8) and (-2, 3)f. (2a, - 3b) and (4a,
The coordinates of 3 points are A(- 4, 4), B(k, - 2) and C(2k + 1, - 6).Find the value of k if A, and B and C are collinear.
The line l1 has equation 3x + 2y = 12.The line l2 has equation y = 2x – 1.The line l1 and l2 intersect at the point A.a. Find the coordinates of A.b. Find the equation of the line through A which
AB is parallel to DC and BC is perpendicular to AB.a. Find the coordinates of C.b. Find the area of trapezium ABCD. C D(3.5, 8) В(9, 3) A(1, 1)
Variables x and y are related so that, when lg y is plotted on the vertical axis and x is plotted on the horizontal axis, a straight-line graph passing though the points (6, 2) and (10, 8) is
The table shows experimental values of the variables x and y.The variables are known to be related by the equation y = a × enx where a and n are constants.a. Draw the graph of ln y against x.b. Use
The point A and B have coordinates (-2, 15) and (3, 5) respectively.The perpendicular to the line AB at the point A(-2, 15) crosses the y-axis at the point C.Find the area of triangle ABC.
The coordinates of the midpoint of the line segment joining P(-8, 2) and Q(a, b), are (5, - 3).Find the value of a and the value of b.
The vertices of triangle ABC are A(-k, - 2), B(k, - 4) and C(4, k – 2). Find the possible values of k if angle ABC is 90°.
The coordinates of three points are A(1, 5), B(9, 7) and C(k, - 6).M is the midpoint of AB and MC is perpendicular to AB.a. Find the coordinates of M.b. Find the value of k.
ABCD is a square.A is the point (-2, 0) and C is the point (6, 4).AC and BD are diagonals of the square, which intersect at M.a. Find the coordinates of M, B and D.b. Find the area of ABCD.
Variables x and y are related so that, when lg y is plotted on the vertical axis and lg x is plotted on the horizontal axis, a straight-line graph passing though the points (4, 8) and (8, 14) is
The table shows experimental values of the variables x and y.The variables are known to be related by the equation y = a × eax+b where a and b are constants.a. Draw the graph of ln y against x.b.
Variables x and y are such that, when ln y is plotted against ln x, a straight-line graph passing through the points (2, 5.8) and (6, 3.8) is obtained.a. Find the value of ln y when ln x = 0.b. Given
Three of the vertices of a parallelogram ABCD are A(-7, 6), B(-1, 8) and C97, 3).a. Find the midpoint of AC.b. Find the coordinates of D.
A is the point (-2, 0) and B is the point (2, 6).Find the point C on the x-axis such that angle ABC is 90°.
The coordinates of triangle ABC are A(2, - 1), B(3,7) and C(14, 5).P is the foot of the perpendicular from B to AC.a. Find the equation of BP.b. Find the coordinates of P.c. Find the length of AC and
The coordinates of 3 of the vertices of a parallelogram ABCD are A(-4, 3), B(5, - 5) and C(15, - 1).a. Find the coordinates of the points of intersections of the diagonals.b. Find the coordinates of
Variables x and y are related so that, when ln y is plotted on the vertical axis and ln x is plotted on the horizontal axis, a straight-line graph passing though the points (1, 2) and (4, 11) is
The table shows experimental values of the variables x and y.The variables are known to be related by the equation y = 10a × bx, where a and b are constants.a. Draw the graph of lg y against
The points A and B have coordinates (2, - 1) and (6, 5) respectively.i. Find the equation of the perpendicular bisector of AB, giving your answer in the form ax + by = c, where a, b and c are
The point P(2k, k) is equidistant from A(-2, 4) and B(7, - 5). Find the value of k.
The coordinates of triangle PQR are P(-3, - 2), Q(5, 10) and R(11, - 2).a. Find the equation of the perpendicular bisectors ofi. PQii. QR.b. Find the coordinates of the point which is equidistant
Variables x and y are related so that, when ln y is plotted on the vertical axis and ln x is plotted on the horizontal axis, a straight-line graph passing though the points (2.5, 7.7) and (3.7, 5.3)
The table shows experimental values of the variables x and y.The variables are known to be related by the equation y = a/x+b, where a and b are constants.a. Draw the graph of lg y against xy.b.
The curve y = xy + x2 – 4 intersects the line y = 3x – 1 at the points A and B. Find the equation of the perpendicular bisector of the line AB.
In triangle ABC, the midpoints of the sides AB, BC and AC are P92, 3), Q(3, 5) and R(-4, 4) respectively. Find the coordinates of A, B and C.
The table shows experimental values of the variables x and y.a. Draw the graph of ln y against x.b. Express y in terms of x.An alternate method for obtaining the relationship between x and y is to
Two points A and B have coordinates (-3, 2) and (9, 8) respectively.i. Find the coordinates of C, the point where the line AB cuts the y-axis.ii. Find the coordinates of D, the mid-point of AB.iii.
Change these angles to radians, in terms of π.a. 10°b. 20°c. 40°d. 50°e. 15°f. 120°g. 135°h. 225°i. 360°j. 720°k. 80°l. 300°m. 9°n. 75°o. 210°
Find, in terms of π, the arc length of a sector ofa. Radius 6 cm and angle π/4b. Radius 5 cm and angle 2π/5c. Radius 10 cm and angle 3π/8d. Radius 18 cm and angle 5π/6.
Find, in terms of π, the area of a sector ofa. Radius 6 cm and angle π/3b. Radius 15 cm and angle 3π/5c. Radius 10 cm and angle 7π/10d. Radius 9 cm and angle 5π/6.
The diagram shows a sector OPQ of a circle with centre O and radius x cm.Angle POQ is 0.8 radians. The point S lies on OQ such that OS = 5 cm.The point R lies on OP such that angle ORS is a right
Change these angles to degrees.a. π/2b. π/6c. π/12d. π/9e. 2π/3f. 4π/5g. 7π/10h. 5π/12i. 3π/20j. 9π/10k. 6π/5l. 3 πm. 7π/4n. 8π/3o. 9π/2
Find the arc length of a sector ofa. Radius 8 cm and angle 1.2 radiansb. radius 2.5 cm and angle 0.8 radians.
Find the area of a sector ofa. Radius 4 cm and angle 1.3 radiansb. Radius 3.8 cm and angle 0.6 radians.
The diagram shows a circle with centre O and a chord AB.The radius of the circle is 12 cm and angle AOB is 1.4 radians.a. Find the perimeter of the shaded region.b. Find the area of the shaded
Write each of these angles in radians correct to 3 sf.a. 32°b. 55°c. 84°d. 123°e. 247°
Find, in radians, the angle of a sector ofa. Radius 4 cm and arc length 5 cmb. Radius 9 cm and arc length 13.5 cm.
Find, in radians, the angle of a sector ofa. Radius 3 cm and area 5 cm2b. Radius 7 cm and area 30 cm2.
The diagram shows a square ABCD of side 16 cm. M is the mid-point of AB.The points E and F are on AD and BC respectively such that AE = BF = 6 cm.EF is an arc of the circle centre M, such that angle
Write each of these angles in degrees correct to 1 decimal place.a. 1.3 radb. 2.5 radc. 1.02 radd. 1.83 rade. 0.58 rad
Find the perimeter of each of these sectors.a.b.c. 1.1 rad 4 cm
POQ is the sector of a circle, centre O, radius 10 cm.The length of arc PQ is 8 cm. Finda. Angle POQ, in radiansb. The area of the sector POQ.
The diagram shows a right-angled triangle ABC and a sector CBDC of a circle with centre C and radius 12 cm. Angle ACB = 1 radian and ACD is a straight-line.a. Show that the length of AB is
Copy and complete the tables, giving your answers in terms of π.a.b. Degrees 45 90 135 180 225 270 315 360 Radians 2n
ABCD is a rectangle with AB = 6 cm and BC = 16 cm.O is the midpoint of BC.OAED is a sector of a circle, centre O. Finda. AOb. Angle AOD, in radiansc. The perimeter of the shaded region. E А D B'
A sector of a circle, radius rcm, has a perimeter of 150 cm. Find an expression, in terms of r, for the area of the sector.
The diagram shows two circles, centres A and B, each of radius 10 cm. The point B lies on the circumference of the circle with centre A. The two circles intersect at the points C and D. The point E
Use your calculator to finda. sin 1.3 radb. tan 0.8 radc. sin 1.2 radd. sin π/2e. cos π/3f. tan π/4.
Finda. The length of arc ABb. The length of chord ABc. The perimeter of the shaded segment. A B 2.3 rad 10 cm 10 cm
ABCD is rectangle with AB = 9 cm and BC = 18 cm.O is the midpoint of BC.OAED is a sector of a circle, centre O. Finda. AOb. Angle AOD, in radiansc. The area of the shaded region. E A B
The diagram shows a circle, centre O, radius 8 cm. The points P and Q lie on the circle. The lines PT and QT are tangents to the circle and angle POQ = 3π/4 radians.i. Find the length of PT.ii. Find
Anna is told the size of angle BAC in degrees and she is then asked to calculate the length of the line BC. She uses her calculator but forgets that her calculator is in radian mode. Luckily she
Triangle EFG is isosceles with EG = FG = 16 cm. GH is an arc of a circle, centre F, with angle HFG = 0.85 radians. Finda. The length of arc GHb. The length of EFc. The perimeter of the shaded region.
The circle has radius 12 cm and centre O.PQ is a tangent to the circle at the point P.QRO is a straight-line. Finda. Angle POQ in radiansb. The area of sector PORc. The area of the shaded region. 35
The diagram shows a circle, centre O, radius r cm. Points A, B and C are such that A and B lie on the circle and the tangents at A and B meet at C. Angle AOB = θ radians.i. Given that the area of
AOB is the sector of a circle, centre O, radius 8 cm.AC is a tangent to the circle at the point A.CBO is a straight-line and the area of sector AOB is 32 cm2.Finda. Angle AOB, in radiansb. The area
Triangle EFG is isosceles with EG = 9 cm.GH is an arc of a circle, centre F, with angleHFG = 0.6 radians, Finda. The area of sector of HFGb. The area of triangle EFGc. The area of the shaded region.
The diagram shows a circle, centre O, radius 12 cm.Angle AOB = θ radians.Arc AB = 9π cm.a. Show that θ = 3π/4.b. Find the area of the shaded region. 9t cm A В 12 cm 12 cm
AOD is a sector of a circle, centre O, radius 4 cm.BOC is a sector of a circle, centre O, radius 10 cm.The shaded region has a perimeter of 18 cm. Finda. Angle AOD, in radiansb. The area of the
AOB is a sector of a circle, centre O, with radius 9 cm.Angle COD = 0.5 radians and angle ODC is a right angle.OC = 5 cm. Finda. ODb. CDc. The perimeter of the shaded regiond. The area of the shaded
FOG is a sector of a circle, centre O, with angleFOG = 1.2 radians.EOH is a sector of a circle, centre O, with radius 5 cm.The shaded region has an area of 71.4 cm2.Find the perimeter of the shaded
The diagram shows a semi-circle, centre O, radius 10 cm.FH is the arc of a circle, centre E.Find the area ofa. Triangle EOFb. Sector FOGc. Sector FEHd. The shaded region. 2 rad E H G
The diagram shows a circle inscribed inside a square of side length 10 cm. A quarter circle of radius 10 cm is drawn with the vertex of the square as its centre. Find the shaded area.
Use the rule logb a = log10 a/log10 b to evaluate these correct to 3 sf.a. log2 10b. log3 33c. log5 8d. log7 0.0025
Use a calculator to evaluate correct to 3 sf.a. e2b. e1.5c. e0.2d. e-3
Convert from exponential from to logarithmic form.a. 103 = 1000b. 102 = 100c. 106 = 1000000d. 10x = 2e. 10x = 15f. 10x = 0.06
Convert from exponential form to logarithmic form.a. 43 = 64b. 25 = 32c. 53 = 125d. 62 = 36e. 2-5 = 1/32f. 3-4 = 1/81g. a2 = bh. xy = 4i. ab = c
At the start of an experiment the number of bacteria was 100.This number increases so that after t minutes the number of bacteria, N, is given by the formula N = 100 × 2t.a. Estimate the number of
Use a graphing software package to plot each of the following family of curves for k = 3, 2, 1, - 1, - 2 and – 3.a. y = ekxb. y = kexc. y = ex + kDescribe the properties of each family of curves.
Sketch the graphs of each of the following exponential functions. [Remember to show the axis crossing points and the asymptotes.]a. y = 2ex – 4b. y = 3ex + 6c. y = 5ex + 2d. y = 2e-x + 6e. y = 3e-x
The following functions are each defined for x ∈ R.Find f-1(x) for each function and state its domain.a. f(x) = ex + 4b. f(x) = ex – 2c. f(x) = 5ex – 1d. f(x) = 3e2x + 1e. f(x) = 5e2x + 3f.
a. Using the substitution y = 5x, show that the equation 52x+1 – 5x+1 + 2 = 2(5x) can be written in the form ay2 + by + 2 = 0, where a and b are constants to be found.b. Hence solve the equation
Write as a single logarithm.a. log2 5 + log2 3b. log3 12 – log3 2c. 3 log5 2 + log5 8d. 2 log7 4 – 3log7 2e. ½ log3 25 + log3 4f. 2 log7(1/4) + log7 9g. 1 + log4 3h. lg 5 – 2i. 3 – log4 10

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