Questions and Answers of Financial Accounting Information For Decisions

A team of 5 members is to be chosen from 5 men and 3 women.Find the number of different teams that can be chosena. If there are no restrictionsb. That consists of 3 men and 2 womenc. That consists of
a. A 6-character password is to be chosen from the following 9 characters.Each character may be used only once in any password.Find the number of different 6-character password that may be chosen
A committee of 5 people is to be chosen from 6 women and 7 men.Find the number of different committees that can be chosena. If there are no restrictionsb. If there are more men than women.
A committee of 6 people is to be chosen from 6 men and 7 women.The committee must contain at least 1 man.Find the number of different committees that can be formed.
A school committee of 5 people is to be selected from a group of 5 teachers and 7 students.Find the number of different ways that the committee can be selected ifa. There are no restrictionsb. There
In a group of 15 entertainers, there are 6 singers, 5 guitarists and 4 comedians.A show is to be given by 6 of these entertainers.In the show there must be at least 1 guitarist and 1 comedian.There
Solve the following equations.i. 4 sin 2x + 5 cos 2x = 0 for 0° ≤ x ≤ 180°.ii. cot2 y + 3 cosec y = 3 for 0° ≤ y ≤ 360°iii. cos(z + π/4) = - ½ for 0 ≤ z ≤ 2π radians, giving each
Prove each of these identities.a. sin x/ tan x = cos xb. cos x sin x/ tan x = 1 – sin2 xc. 1 – sin2 x/cos x = cos xd.e. (sin x + cos x)2 = 1 + 2 sin x cos xf. tan2 x – sin2 x = tan2 x sin2
Solve each of these equations for 0° ≤ x ≤ 360°.a. cot x = 0.3b. sec x = 4c. cosec x = -2d. 3 sec x – 5 = 0
Prove each of these identities.a. tan x + cot x = sec x cosec xb. sin x + cos x cot x = cosec xc. cosec x – sin x = cos x cot xd. sec x cosec x – cot x = tan x
a. Sketch the curve y = 3 cos 2x – 1 for 0° ≤ x ≤ 180°.b. i. State the amplitude of 1 – 4 sin 2x.ii. State the period of 5 tan 3x + 1.
Given that tan θ = 2/3 and that θ is acute, find the exact values ofa. sin θb. cos θc. sin2 θd. sin2 θ + cos2 θe. 2 + sin θ/3 – cos θ.
Draw a diagram showing the quadrant is which the rotating line OP lies for each of the following angles. In each question indicate clearly the direction of rotation and find the acute angle that the
Express the following as trigonometric ratios of acute angles.a. sin 220°b. cos 325°c. tan 140°d. cos(-25°)e. tan 600°f. sin 4π/5g. tan 7π/4h. cos(-11π/6)i. tan 2π/3j. sin 9π/4
a. The following function are defined for 0° ≤ x ≤ 360°.For each function, write down the amplitude, the period and the coordinates of the maximum and minimum points.i. f(x) = 7 cos xii. f(x) =
Sketch the graphs of each of the following functions, for 0° ≤ x ≤ 360°, and state the range of each function.a. f(x) = |tan x|b. f(x) = | cos 2x |c. f(x) = |3 sin x| d. f(x) = |sin ½
Solve each of these equations for 0° ≤ x ≤ 360°.a. sin x = 0.3b. cos x = 0.2c. tan x = 2d. sin x = - 0.6e. tan x = - 1.4f. sin x = - 0.8g. 4 sin x – 3 = 0h. 2 cos x + 1 = 0
Prove each of these identities.a. cos2 x – sin2 x = 2 cos2 x – 1b. cos2 x – sin2 x = 1 – 2 sin2 xc. cos4 x + sin2 x cos2 x = cos2 xd. 2(1 + cos x) – (1 + cos x)2 = sin2 xe. 2 – (sin x +
Solve each of these equations for 0 ≤ x ≤ 2π.a. cosec x = 5b. cot x = 0.8c. sec x = - 4d. 2 cot c + 3 = 0
Prove each of these identities.a. (1 + sec x) (cosec x – cot x) = tan xb. (1 + sec x)(1 – cos x) = sin x tan xc. tan2 x – sec2 x + 2 = cosec2 x – cot2 xd. (cot x + tan x) (cot x – tan x) =
a. Solve 2 cos 3x = cot 3x for 0° ≤ x ≤ 90°.b. Solve sec(y + π/2) = - 2 for 0 ≤ y ≤ π radians.
Given that sin θ √2/5 and that θ is acute, find the exact values ofa. cos θb. tan θc. 1 – sin2 θd. sin θ + cos θe. cos θ – sin θ/tan θ.
State the quadrant that OP lies in when the angle that OP makes with positive x-axis isa. 110°b. 300°c. -160°d. 245°e. 500°f. π/4g. 11π/6h. - 5π/6i. 13π/6j. 9π/4
Given that cos θ = 2/5 and that 270° ≤ θ ≤ 360°, find the value ofa. tan θb. sin θ.
a. The following functions are defined for 0 ≤ x ≤ 2π.For each function, write down the amplitude, the period and the coordinates of the maximum and minimum points.i. f(x) = 4 sin xii. f(x) =
a. Sketch the graph of y = 2 sin x – 1 for 0° ≤ x ≤ 180°.b. Sketch the graph of y = |2 sin x – 1| for 0° ≤ x ≤ 180°.c. Write down the number of solutions of the equation |2 sin x –
Solve each of these equations for 0° ≤ x ≤ 2π.a. cos x 0.5b. tan x = 0.2c. sin x = 2d. tan x = - 3e. sin x = - 0.75f. cos x = - 0.55g. 4 sin x = 1h. 5 sin x + 2 = 0
Prove each of these identities.a.b.c.d. cos x - sin? x = cos x + sin x Cos x - sinx
Solve each of these equations for 0° ≤ x ≤ 180°.a. sec 2x = 1.6b. cosec 2x = 5c. cot 2x = - 1d. 5 cosec 2x = - 7
Prove each of these identities.a. a/tan x + cot x = sin x cos xb. sin2 x + cos2 x/cos2 x = sec2 xc. sin2 x cos x + cos3 x/sin x = cot xd. sin2 x + cos2 x/cos2 x = sec2 xe. 1 + tan2 x/ tan x = sec x
a. Prove that sec x cosec x – cot x = tan x.b. Use the result from part a to solve the equation sec x cosec x = 3 cot x for 0° < x < 360°.
Given that cos θ = 1/7 and that θ is acute, find the exact values ofa. sin θb. tan θc. tan θ cos θd. sin2 θ + cos2 θe. cos θ – tan θ/1 – cos2 θ.
Give that tan θ = - √3 and that 90° ≤ θ ≤ 180°, find the value ofa. sin θb. cos θ
The graph of y = a + b sin cx, for 0 ≤ x ≤ π, is shown above.Write down the value of a, the value of b and value of c. 7 6- 4- 3- 2- 1- TC 2
a. Sketch the graph of y = 2 + 5 cos x for 0° ≤ x ≤ 180°.b. Sketch the graph of y = |2 + 5 cos x| for 0° ≤ x ≤ 180°.c. Write down the number of solutions of the equation |2 + 5 cos x| = 1
Solve each of these equations for 0° ≤ x ≤ 180°.a. sin 2x = 0.8b. cos 2x = -0.6c. tan 2x = 2d. sin 2x = - 0.6e. 5 cos 2x = 4f. 7 sin 2x = -2g. 1 + 3 tan 2x = 0h. 2 – 3 sin 2x = 0
Solve each of these equations for the given domains.a. sec(x – 30°) = 3 for 0° ≤ x ≤ 360°b. cosec (2x + 45°) = - 5 for 0° ≤ x ≤ 180°c. cot(x + π/3) = 2 for 0 < x < 2πd. 3
Prove each of these identities.a.b.c.d.e.f. sin x COS X = sec x cOsec x cos x COS X sin x
Show that 1 + sin θ/cos θ + cos θ/1 + sin θ = 2sec θ.
Find the exact value of each of the following.a. tan 45° cos 60°b. tan2 60°c. tan 30°/cos 30°d. sin 45° + cos 30°e. cos2 30°/ cos 45° + cos 60°f. tan 45° - sin 30°/1 + sin2 60°
Given that sin θ = 5/13 and that θ is obtuse, find the value ofa. cos θb. tan θ.
Part of the graph of y = a sin bx + c is shown above.Write down the value of a, the value of b and the value of c. y 8- 7- 6- 5- 4 3- 2 1 45 90 135 180 *
a. Sketch the graph of y = 2 + 3 cos x for 0° ≤ x ≤ 180°.b. Sketch the graph of y = |2 + 3 cos x| for 0° ≤ x ≤ 180°.c. Write down the number of solutions of the equation |2 + 3 sin 2x| =
Solve each of these equations for the given domains.a. cos(x = - 30°) = - 0.5 for 0° ≤ x ≤ 360°.b. 6 sin(2x + 45°) = - 5 for 0° ≤ x ≤ 180°.c. 2 cos(2x/3) + √3 = 0 for 0° ≤ x ≤
Solve each of these equation for 0° ≤ x ≤ 360°.a. sec2 x = 4b. 9 cot2 x = 4c. 16 cot2 1/2x = 9
Show that (3 + 2 sin x)2 + (3 – 2 sin x)2 + 8 cos2 x has constant value for all x and state this value.
a. Solve the equation 2 cosec x + 7/cos x = 0 for 0° ≤ x ≤ 360°.b. Solve the equation 7 sin(2y – 1) = 5 for 0 ≤ y ≤ 5 radians.
Find the exact the value of each of the following.a.b. sin2 π/4c.d.e.f. sin cos- 3 4,
Given that tan θ = 2/3 and that θ is reflex find the value ofa. sin θb. cos θ.
The graph of y = a + b cos cx, for 0° ≤ x ≤ 360°, is shown above.Write down the value of a, the value of b and the value of c. y. 4- 3- 2- 1- 60 120 180 240 300 360 A O 5 321
a. On the same grid, sketch the graphs of y = |tan x| and y = cos x for 0° ≤ x ≤ 360°.b. State the number of roots of the equation |tan x| = cos x for 0° ≤ x ≤ 360°.
Solve each of these equations for 0° ≤ x ≤ 360°.a. 4 sin x = cos xb. 3 sin x + 4 cos x = 0c. 5 sin x – 3 cos x = 0d. 5 cos 2x – 4 sin 2x = 0
Solve each of these equations for 0° ≤ x ≤ 360°.a. 3 tan2 x – sec x – 1 = 0b. 4 tan2 x + 8 sec x = 1c. 2 sec2 x = 5 tan x + 5d. 2 cot2 x – 5 cosec x – 1 = 0e. 6 cos x + 6 sec x = 13f.
a. Express 5 sin2 x – 2 cos2 x in the form a + b sin2 x.b. State the range of the function f(x) = 5 sin2 x – 2 cos2 x for 0 ≤ x ≤ 2π.
On a copy of the axes below sketch, for 0 ≤ x ≤ 2π, the graph ofa. y = cos x – 1b. y = sin 2x.c. State the number of solutions of the equation cos x – sin 2x = 1, for 0 ≤ x ≤ 2π. 2- 0-
Given that tan A = 4/3 and cos B = - 1/√3, where A and B are in the same quadrant, find the value ofa. sin Ab. cos Ac. sin Bd. tan B.
a. The following functions are defined for 0° ≤ x ≤ 360°.For each function, write down the period and the equations of the asymptotes.i. f(x) = tan 2xii. f(x) = 3 tan 1/2xiii. f(x) = 2 tan 3x +
a. On the same grid, sketch the graphs of y = |sin 2x| and y = tan x for 0° ≤ x ≤ 2π.b. State the number of roots of the equation |sin ex| = tan x for 0° ≤ x ≤ 2π.
Solve 4 sin(2x – 0.4) – 5 cos(2x – 0.4) = 0 for 0 ≤ x ≤ π.
a. Express sin2 θ + 4 cos θ + 2 in the form a – (cos θ – b)2.b. Hence state the maximum and minimum values of sin2 θ + 4 cos θ + 2.
Prove that (1 + sin θ/cos θ)2 + (1 – sin θ/cos θ)2 = 2 + 4 tan2 θ.
Given that sin A = - 12/13 and cos B = 3/5, where A and B in the same quadrant, find the value ofa. cos Ab. Tan Ac. sin Bd. tan B.
a. The following functions are defined for 0 ≤ x ≤ 2π.For each function, write down the period and the equations of the asymptotes.i. f(x) = tan 4xii. f(x) = 2 tan 3xiii. f(x) = 5 tan 2x – 3b.
a. On the same grid, sketch the graphs of y = |0.5 + sin x| and y = cos x for 0° ≤ x ≤ 360°.b. State the number of roots of the equation |0.5 + sin x| = cos x for 0° ≤ x ≤ 360°.
Solve each of these equations for 0° ≤ x ≤ 360°.a. sin x tan(x - 30°) = 0.b. 5 tan2 x – 4 tan x = 0c. 3 cos2 x = cos xd. sin2 x + sin x cos x = 0e. 5 sin x cos x = cos xf. sin x tan x = sin x
a. Given that 15 cos2 θ + 2 sin2 θ = 7, show that tan2 θ = 8/5.b. Solve 15 cos2 θ + 2 sin2 θ = 7 for 0 ≤ θ ≤ π radians.
Part of the graph of y = A tan Bx + C is shown above.The graph passes through the point P(π/4, 4).Find the value of A, the value of B and the value of C. 3- 元 3元 2元 2 2.
a. On the same grid, sketch the graphs of y = |1 + 4 cos x| and y = 2 + cos x for 0° ≤ x ≤ 360°.b. State the number of roots of the equation |1 + 4 cos x| = 2 + cos x for 0° ≤ x ≤ 360°.
Solve each of these equations for 0° ≤ x ≤ 360°.a. 4 sin2 x = 1b. 25 tan2 x = 9
Solve each of these equations for 0° ≤ x ≤ 360°.a. tan2 x + 2 tan x – 3 = 0b. 2 sin2 x + sin x – 1 = 0c. 3 cos2 x – 2 cos x – 1 = 0d. 2 sin2 x – cos x – 1 = 0e. 3 cos2 x – 3 = sin
a. The diagram shows a sketch of the curve y = a sin(bx) + c for 0° ≤ x ≤ 180°. Find the values of a, b and c.b. Given that f(x) = 5 cos 3x + 1, for all x, statei. The period of f,ii. The
F(x) = a + b sin cxThe maximum value of f is 13, the minimum value of f is 5 and the period is 60°.Find the value of a, the value of b and the value of c.
The equation |3 cos x – 2| = k, has 2 roots for the interval 0° ≤ x ≤ 2π. Find the possible value of k.
F(x) sin x for 0 ≤ x ≤ π/2 g(x) = 2x – 1 for x ∈ RSolve gf(x) = 0.5.
a. Solve 4 sin x = cosec x for 0° ≤ x ≤ 360°.b. Solve tan2 3y – 2sec 3y – 2 = 0 for 0° ≤ y ≤ 180°.c. Solve tan(z – π/3) = √3 for 0 ≤ z ≤ 2π radians.
F(x) = A + 3 cos Bx for 0° ≤ x ≤ 360°.The maximum value of f is 5 and the period is 72°.a. Write down the value of A and the value of B.b. Write down the amplitude of f.c. Sketch the graph of
The diagram shows the graph of f(x) = |a + b cos cx|, where a, b and c are positive integers.Find the value of a, the value of b and the value of c. f(x) 5- 4- 3- 2- 1- 90 180 270 360 x
Show that √sec2θ–1 + √cosec2θ–1 = sec θ cosec θ.
F(x) = A + B sin Cx for 0° 2264 x ≤ 360°.The amplitude of f is 3, the period is 90° and the minimum value of f is -2.a. Write down the value of A, the value of B and the value of C.b. Sketch the
a. On the same grid, sketch the graphs of y = sin x and y = 1 + sin 2x for 0° ≤ x ≤ 360°.b. State the number of roots of the equation sin 2x – sin x + 1 = 0 for 0° ≤ x ≤ 360°
a. On the same grid, sketch the graphs of y = sin x and y = 1 + cos 2x for 0° ≤ x ≤ 360°.b. State the number of roots of the equation sin x = 1 + cos 2x for 0° ≤ x ≤ 360°.
a. On the same grid, sketch the graphs of y = 3 cos 2x and y = 2 + sin x for 0° ≤ x ≤ 360°.b. State the number of roots of the equation 3 cos 2x = 2 + sin x for 0° ≤ x ≤ 360°.
Find the gradient of the line AB for each of the following pairs of points.a. A(1, 2) B(3, - 2)b. A(4, 3) B(5, 0)c. A(- 4, 4) B(7, 4)d. A(1, - 9) B(4, 1)e. A(- 4, - 3) B(5,
Find the equation of the line witha. Gradient 3 and passing through the point (6, 5)b. Gradient – 4 and passing through the point (2, -1)c. Gradient – ½ and passing through the point (8, - 3).
Find the area of these triangles.a. A(-2, 3), B(0, -4), C(5, 6)b. P(-3, 1), !(5, - 3), R(2, 4)
Convert each of these non-linear equations into the form Y = mX + c, where a and b are constants. State clearly what the variables X and Y and the constants m and c represent.a. y = ax2 + bb. y = ax
The graphs show part of a straight line obtained by plotting y against some function of x. For each graph, express y in terms of x.a.b.c.d.e.f. (3, 6)
The table shows experimental values of the variables x and y.a. Copy and complete the following table.b. Draw the graph of xy against x.c. Express y in terms of x.d. Find the value of x and the value
The point P lies on the line joining A(-2, 3) and B(10, 19) such that AP: PB = 1:3.a. Show that the x-coordinate of P is 1 and find the y-coordinate of P.b. Find the equation of the line through P
Find the length of the line segment joininga. (2, 0) and (5, 0)b. (-7, 4) and (- 7, 8)c. (2, 1) and (8, 9)d. (-3, 1) and (2, 13)e. (5, - 2) and (2, -6)f. (4, 4) and (- 20, - 3)g. (6, - 5) and (1,
Write down the gradient of lines perpendicular to a line with gradienta. 3b. – ½c. 2/5d. 1/¼e. -2 ½
Find the equation of the line passing througha. (3, 2) and (5, 7)b. (-1, 6) and (5, - 3)c. (5, - 2) and (- 7, 4).
Find the area of these quadrilaterals.a. A(1, 8), B(-4, 5), C(-2, -3), D(4, -2)b. P(2, 7), Q(-5, 6), R(-3, - 4), S(7, 2)
Convert each of these non-linear equations into the form Y = mX + c, where a and b are constants. State clearly what the variables X and Y and the constants m and c represent.a. y = 10ax+bb. y =
For each of the following relationsi. Express y in terms of xii. Find the value of y when x = 2.a.b.c.d.e.f. (5, 6) (1, 2) gt
The table shows experimental values of the variables x and y.a. Copy and complete the following table.b. Draw the graph of 1/y against 1/x.c. Express y in terms of x.d. Find the value of x when y =
The table shows values of variables V and P.a. By plotting a suitable straight-line graph, show that V and P are related by the equation P = kVn, where k and n are constants.Use your graph to findb.
Calculate the lengths of the sides of the triangle PQR.Use your answers to determine whether or not the triangle is right-angled.a. P(3, 11), Q(5, 7) R(11, 10)b. P(- 7, 8), Q(-1, 4), R(5, 12)c. P(-
Two vertices of a rectangle ABCD are A(3, - 5) and B(6, - 3),a. Find the gradient of CD.b. Find the gradient of BC.
Find the equation of the linea. Parallel to the line y = 2x + 4, passing through the point (6, 2)b. Parallel to the line x + 2y = 5, passing through the point (2, - 5)c. Perpendicular to the line 2x

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