Questions and Answers of Financial Accounting Information For Decisions

A piece of wire, of length 50 cm, is cut into two pieces. One piece is bent to make a square of side x cm and the other is bent to make circle of radius r cm. The total area enclosed by the two
A rectangular sheet of metal measures 60 cm by 45 cm. A scoop is made by cutting out squares, of side x cm, from two corners of the sheet and folding the remainder as shown.a. Show that volume, V cm3
A curve has equation y = (2 - √x)4.The normal at the point P(1, 1) and the normal at the point Q(9, 1) intersect at the point R.a. Find the coordinates of R.b. Find the area of triangle PQR.
A solid metal cuboid has dimensions x cm by x cm by 5x cm.The cuboid is heated and the volume increases at a rate of 0.5 cm3s-1.Find the rate of increase of x when x = 4.
The curve y = 1/3 x3 – 2x2 – 8x + 5 and the line y = x + 5 meet at the points A, B and C.a. Find the coordinates of the points A, B and C.b. Find the gradient of the curve at the points A, B and
The diagram shows a solid cylinder of radius r cm and height 2h cm cut from a solid sphere of radius 5 cm. The volume of the cylinder is V cm3.a. Express r in terms of h.b. Show that V = 2πh(25 –
The diagram shows an empty container in the form of an open triangular prism. The triangular faces are equilateral with a side of x cm and the length of each rectangular face is y cm. The container
A curve has equation y = √x(x – 2)3. The tangent at the point P(3, √3) and the normal at the point Q(9, 1) intersect at the point R.a. Show that the equation of the tangent at the point P(3,
A cone has base radius r cm and a fixed height 18 cm.The radius of the base is increasing at a rate of 0.1 cm s-1.Find the rate of change of the volume when r = 10.
Y = 4x3 + 3x2 – 6x – 1a. Find dy/dx.b. Find the range of values of x for which dy/dx ≥ 0.
The diagram shows a hollow cone with base radius 12 cm and height 24 cm. A solid cylinder stands on the base of the cone and the upper edge touches the inside of the cone. The cylinder has base
The equation of a curve is y = x2/x + 2.The tangent to the curve at the point where x = - 3 meets the y-axis at M.The normal to the curve at the point where x = - 3 meets the x-axis at N.Find the
Water is poured into the conical container at a rate of 5 cm3 s-1.After t seconds, the volume of water in the container, V cm3 is given by V = 1/12 πh3, where h cm is the height of the water in the
Y = x3 + x2 – 16x – 16a. Find dy/dx.b. Find the range of values of x for which dy/dx ≤ 0.
The diagram shows a right circular cone of base radius r cm and height h cm cut from a solid sphere 10 cm. The volume of the cone is V cm3.a. Express r in terms of h.b. Show that V = 1/3πh2 (20 –
The equation of a curve is y = x-3/x+2.The curve intersects the x-axis at the point P.The normal to the curve at P meets the y-axis at the Point Q.Find the area of the triangle POQ, where O is the
Water is poured into the hemispherical bowl at a rate of 4π cm3 s-1.After t seconds, the volume of water in the bow, V cm3, is given by V = 8πh2 – 1/3 πh3, where h cm is the height of the water
A curve has equation y = x5 – 5x3 + 25x2 + 145x + 10. Show that the gradient of the curve is never negative.
Variables x and y are connected by the equation y = 2x3 – 3x.Find the approximate change in y as x increases from 2 to 2.01.
Variables x and y are connected by the equation y = x2 – 5x.Given that x increases at a rate of 0.05 units per second, find the rate of change of y when x = 4.
Find d2y/dx2 for each of the following functions.a. y = 5x2 – 7x + 3b. y = 2x3 + 3x2 – 1c. y = 4 – 3/x2d. y = (4x + 1)5e. y = √2x + 1f. y = 4/√x + 3
Differentiate with respect to x.a. x4b. x9c. x-3d. x-6e. 1/xf. 1/x5g. √xh. √x5i. x1/5j. x1/3k. 3√x2l. 1/√xm. xn. x3/2o. 3√x5p. x2 × x4q. x2 × xr. x4/x2s. x/√xt. x√x/x3
Find the coordinates of the stationary points on each of the following curves and determine the nature of each of the stationary points.a. y = x2 – 12x + 8b. y = (5 + x) (1 – x)c. y = x3 – 12x
The sum of two numbers x and y is 8.a. Express y in terms of x.b. i. Given that P = xy, write down an expression for P in terms of x.ii. Find the maximum value of P.c. i. Given that S = x2 + y2,
Differentiate with respect to x.a. (x + 2)9b. (3x – 1)7c. (1 – 5x)6d. (1/2x – 7)4e. (2x + 1)6/3f. 2(x – 4)6g. 6(5 – x)5h. ½(2x + 5)8i. (x2 + 2)4j. (1 – 2x2)7k. (x2 – 3x)5l. (x2 + 2/x)4
Use the product rule to differentiate each of the following with respect to x.a. x(x + 4)b. 2x(3x + 5)c. x(x + 2)3d. x2(x – 1)3e. x√x – 5f. (x + 2) √xg. x2√x + 3h. √x(3 – x2)3i. (2x +
Find the coordinates of the stationary point on the curve y = x2 + 16/x.
Use the quotient rule to differentiate each of the following with respect to x:a. 1 + 2x/5x – 2b. 3x + 2/x + 4c. x – 1/3x + 4d. 5x – 2/3 – 8xe. x2/5x – 2f. x/x2 – 1g. 5/3x – 1h. x +
Find the equation of the tangent to the curve at the given value of x.a. y = x4 – 3 at x = 1b. y = x2 + 3x + 2 at x = -2c. y = 2x3 + 5x2 – 1 at x = 1d. y = 5 + 2/x at x = -2e. y = (x -3) (2x –
Variables x and y are connected by the equation y = 5x2 – 8/x3.Find the approximate change in y as x increases from 1 to 1.02.
Variables x and y are connected by the equation y = x + √x – 5.Given that x increases at a rate of 0.01 units per second, find the rate of change of y when x = 9.
Find d2y/dx2 for each of the following functions.a. y = x(x – 4)3b. y = 4x – 1/x2c. y = x +1/x-3d. y = x+2/x2 -1e. y = x2/x – 5f. y = 2x+5/3x -1
Differentiate with respect to x.a. 2x3 – 5x + 4b. 8x5 – 3x2 – 2c. 7 – 2x3 + 4xd. 3x2 + 2/x – 1/x2e. 2x – 1/x – 1/√xf. x + 5/√xg. x2 – 3/xh. 5x2 - √x/xi. x2 – x – 1/√xj.
Find the coordinates of the stationary points on each of the following curves and determine the nature of each of the stationary points.a. y = √x + f/√xb. y = x2 – 2/xc. y = 4/x + √xd. y =
The diagram shows a rectangular garden with a fence on three of its sides and a wall on its fourth side. The total length of the fence is 100 m and the area enclosed is Am2.a. Show that A = 1/2x(100
Differentiate with respect to x.a. 1/(x + 4)b. 3/(2x – 1)c. 5/(2 – 3x)d. 16/(2x2 – 5)e. 4/(x2 – 2x)f. 1/(x – 1)5g. 2/(5x + 1)3h. 1/2(3x – 2)4
Find the gradient of the curve y = x2 √x + 2 at the point (2, 8).
Given that y = x2/2 + x2, show that dy/dx = kx/(2 + x)2, where k is a constant to be found.
Find the gradient of the curve y = x + 3/x – 1 at the point (2, 5).
Find the equation of the normal to the curve at the given value of x.a. y = x2 + 5x at x = - 1b. y = 3x2 – 4x + 1 at x = 2c. y = 5x4 – 7x2 + 2x at x = - 1d. y = 4 – 2/x2 at x = - 2e. y = 2x(x
Variables x and y are connected by the equation y = x2y = 400.Find, in terms of p, the approximate change in y as x increases from 10 to 10 + p, where p is small.
Variables x and y are connected by the equation y = (x – 3) (x + 5)3.Given that x increases at a rate of 0.02 units per second, find the rate of change of y when x = - 4.
Given that f(x) = x3 – 7x2 + 2x + 1, finda. f(1)b. f’(1)c. f”(1).
Find the value of dy/dx at the given point on the curve.a. y = 3x2 – 4 at the point (1, - 1)b. y = 4 – 2x2 at the point (- 1, 2)c. y = 2 + 8/x at the point (-2, 2)d. y = 5x3 – 2x2
The equation of a curve is y = 2x + 5/x+1.Find dy/dx and hence explain why the curve has no turning points.
The volume of the solid cuboid is 576 cm3 and the surface area is A cm2.a. Express y in terms of x.b. Show that A = 4x2 + 1728/x.c. Find the maximum value of A and state the dimensions of the cuboid
Differentiate with respect to x.a.b.c.d.e.f.g.h. x+2
Find the gradient of the curve y = (x – 1)3 (x + 3)2 at the point where x = 2.
Given that curve has equation y = 1/x + 2√x, where x > 0, finda. dy/dx,b. d2y/dx2.Hence or otherwise, findc. The coordinates and nature of the stationary point on the curve.
Find the coordinates of the points on the curve y = x2/2x – 1 where dy/dx = 0.
Find the equation of the tangent and the normal to the curve y = 5x – 3/x at the point where x = 1.
Variables x and y are connected by the equation y = (1/3x – 2)6.Find, in terms of p, the approximate change in y as x increases from 9 to 9 + p, where p is small.
Variables x and y are connected by the equation y = 5/2x – 1.Given that y increases at a rate of 0. 1 unit per second, find the rate of change of x when x = - 2.
A test consists of 10 different questions.4 of the questions are on trigonometry and 6 questions are on algebra.Students are asked to answer 8 questions.a. Find the number of ways in which students
Identify whether the following sequences are geometric. If they are geometric, write down the common ratio and the eighth term.a. 1, 2, 4, 6, …b. -1, 4, -16, 64, …c. 81, 27, 9, 3, …d. 2/11,
Find the sum to infinity of each of the following geometric series.a.b.c.d. – 162 + 108 – 72 + 48 - … 1 1 3+1+ニ+ニ+
The firs term of a progression is 8 and the second term is 12. Find the sum of the first six terms given that the progression isa. Arithmeticb. Geometric.
a. Find the first four terms in the expansion of (2 + x)6 in ascending powers of x.b. Hence find the coefficient of x3 in the expansion of (1 + 3x) (1 – x) (2 + x)6.
Write down the sixth and seventh rows of Pascal’s triangle.
The first term in an arithmetic progression is a and the common difference is d.Write down expressions, in terms of a and d, for the fifth term and the 14th term.
Write the following rows of Pascal’s triangle using combination notation.a. row 3b. Row 4c. Row 5
The first term in a geometric progression is a and the common ratio is r. Write down expressions, in terms of a and r, for the ninth term and the 20th term.
The first term of a geometric progression is 10 and the second term is 8. Find the sum to infinity.
The first term of a progression is 25 and the second term is 20.a. Given that the progression is geometric, find the sum to infinity.b. Given that the progression is arithmetic, find the number of
a. Find the first 3 terms, in descending powers of x, in the expansion of (x + 2/x2)6.b. Hence find the term independent of x in the expansion of (2 – 4/x3) (x + 2/x2)6.
Use Pascal’s triangle to find the expansions ofa. (1 + x)3b. (1 – x)4c. (P + q)4d. (2 + x)3e. (x + y)5f. (y + 4)3g. (a – b)3h. (2x + y)4i. (x – (2y)3j. (3x – 4)4k. (x + 2/x)3l. (x2 –
Use the binomial theorem to find the expansions ofa. (1 + x)4b. (1 – x)5c. (1 + 2x)4d. (3 + x)3e. (x + y)4f. (2 – x)5g. (a – sb)4h. (2x + 3y)4i. (1/2x – 3)4j. (1 – x/10)5k. (x – 3/x)5l.
Find the sum of each of these arithmetic series.a. 2 + 9 + 16 + … (15 terms)b. 20 + 11 + 2 … (20 terms)c. 8.5 + 10 + 11.5 + … (30 terms)d. – 2x – 5x – 8x - … (40 terms)
The third term of a geometric progression is 108 and the sixth term is -32. Find the common ratio and the first term.
The firs term of a geometric progression is 300 and the fourth term is -2 2/5. Find the common ratio and the sum to infinity.
The first, second and third terms of a geometric progression are the first, fifth and 11th terms respectively of an arithmetic progression. Given that the first term in each progression n is 48 and
Find the coefficient of x3 in the expansions ofa. (x + 4)4b. (1 + x)5c. (3 – x)4d. (3 + 2x)3e. (x – 2)5f. (2x + 5)4g. (4x – 3)3h. (3 – ½ x)4
The coefficient of x2 in the expansion of (1 + x/5)n, where n is a positive integers is 3/5.a. Find the value of n.b. Using this value of n, find the term independent of x in the expansion of(1 +
Find the term in x3 for each of the following expansions.a. (2 + x)5b. (5 + x)8c. (1 + 2x)6d. (3 + 2x)5e. (1 – x)6f. (2 – x)9g. (10 – 3x)7h. (4 – 5x)15.
Find the number of terms and the sum of each of these arithmetic series.a. 23 + 27 + 31 … + 159b. 28 + 11 – 6 - … 210
The first term of a geometric progression is 75 and the third term is 27. Find the two possible values for the fourth term.
The first four terms of a geometric progression are 1, 0.82, 0.84 and 0.86. Find the sum to infinity.
A geometric progression has six terms. The first term is 486 and the common ratio is 2/3. An arithmetic progression has 35 and common difference 3/2. The sum of all the terms in the geometric
a. Find the coefficient of x3 in the expansion of (1 – x/2)12.b. Find the coefficient of x3 in the expansion of (1 + 4x) (1 – x/2)12.
(4 + x)5 + (4 – x)5 = A + Bx2 + Cx4Find the value of A, the value of B and the value of C.
Use the binomial theorem to find the first three terms in each of these expansions.a. (1 + x)10b. (1 + 2x)8c. (1 – 3x)7d. (3 + 2x)6e. (3 – x)9f. (2 + 1/2x)8g. (5 – x2)9h. (4x – 5y)10.
The first term of an arithmetic progression is 2 and the sum of the first 12 terms is 618.Find the common difference.
The second term of a geometric progression is 12 and the fourth term is 27. Given that all the terms are positive, find the common ratio and the first term.
a. Write the recurring decimal 0.42 as the sum of a geometric progression.b. Use your answer to part a to show that 0.42 can be written as 14/33.
The first, second and third terms of a geometric progression are the first, fifth and eighth terms respectively of an arithmetic progression. Given that the first term in each progression is 200 and
a. Find, in ascending powers of x, the first 3 terms in the expansion of (2 – 5x)6, giving your answer in the form a + bx + cx2, where a, b and c are integers.b. Find the coefficient of x in the
Expand (1 + 2x) (1 + 3x)4.
a. Write down, in ascending powers of x, the first 4 terms in the expansion of (1 + 2x)6.b. Find the coefficient of x3 in the expansions of (1 – x/3) (1 + 2x)6.
In an arithmetic progression, the first term is – 13, the 20th term is 82 and the last term is 112.a. Find the common difference and the number of terms.b. Find the sum of the terms in this
The sixth and 13th terms of a geometric progression are 5/2 and 320 respectively. Find the common ratio, the first term and the 10th term of this progression.
The first term of a geometric progression is – 120 and the sum to infinity is – 72. Find the common ratio and the sum of the first three terms.
The first term of an arithmetic progression is 12 and the sum of the first 16 terms is 282.a. Find the common difference of this progression.The first, fifth and nth term of this arithmetic
The coefficient of x in the expansion of (2 ax)3 is 96.Find the value of the constant a.
i. Write down, in ascending powers of x, the first 3 terms in the expansion of (3 + 2x)6. Give each term in its simplest form.ii. Hence find the coefficient of x2 in the expansion of (2 – x) (3 +
a. Write down, in ascending powers of x, the first 4 terms in the expansion of (1 + x/2)13.b. Find the coefficient of x3 in the expansions of (1 + 3x) (1 + x/2)13.
The first two terms in an arithmetic progression are 57 and 46. The last term is –207. Find the sum of all the terms in this progression.
The sum of the second and third terms in a geometric progression is 30. The second term is 9 less than the first term. Given that all the terms in the progression are positive, find the first term.
The second term of a geometric progression is 6.5 and the sum to infinity is 26. Find the common ratio and the first term.
The first two terms of a geometric progression are 80 and 64 respectively.The first three terms of this geometric progression are also the first, 11th and nth terms respectively of an arithmetic
i. Find the first 4 terms in the expansion of (2 + x2)6 in ascending powers of x.ii. Find the term independent of x in the expansion of (2 + x2)6 (1 – 3/x2)2.

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