Questions and Answers of Financial Accounting Information For Decisions

Solve the following equations.Express roots in the form a ± b √c, where necessary.a. x3 + 5x2 – 4x – 2 = 0b. x3 + 8x2 + 12x – 9 =0c. x3 + 2x2 – 7x – 2 = 0d. 2x3 + 3x2 – 17x + 12 = 0
x – 2 is a factor of x3 + ax2 + bx – 4.Express b in terms of a.
Simplify.a.b.c.d. 3x – 3x2 - 4x + 4 x - 1
Simplify each of the following.a. (2x – 3) (x + 2) + (x + 1) (x – 1)b. (3x + 1) (x2 + 5x + 2) – (x2 – 4x + 2) (x +3)c. (2x3 + x – 1) (x2 + 3x – 4) – (x + 2) (x3 – x2 + 5x + 2)
a. The remainder when the expression x3 + 9x2 + bx + c is divided by x – 2 is twice the remainder when the expression is divided by x – 1. Show that c = 24.b. Given that x + 8 is a factor of x3 +
F(x) = x3 + ax2 + bx – 5F(x) has a factor of x – 1 and leaves a remainder of 3 when divided by x + 2. Find the value of a and of b.
Solve the following equations.a. x3 – 3x2 – 33x + 35 = 0b. x3 – 6x2 + 11x – 6 = 0c. 3x3 + 17x2 + 18x – 8 = 0d. 2x3 + 3x2 – 17x + 12 = 0e. 2x3 – 3x2 – 11x + 6 = 0f. 2x3 + 7x2 – 5x
Find the value of a in each of the following.a. x + 1 is a factor of 6x3 + 27x2 + x + 8.b. x + 7 is a factor of x3 – 5x2 – 6x + a.c. 2x + 3 is a factor of 4x3 + ax2 + 29x + 30.
Simplify each of the following.a. (3x3 + 8x2 + 3x – 2) ÷ (x + 2)b. (6x3 + 11x2 – 3x – 2) ÷ (3x + 1)c. (3x3 – 11x2 + 20) ÷ (x – 2)d. (3x3 – 21x2 + 4x – 28) ÷ (x – 7)
Find the following products.a. (2x – 1) (4x3 + x + 2)b. (x3 + 2x2 – 1) (3x + 2)c. 3x2 + 2x – 5) (x3 + x2 + 4)d. (x + 2)2 (3x3 + x – 1)e. (x2 – 5x + 2)2f. (3x – 1)3
The function f(x) = ax3 + 4x2 + bx – 2, where a and b are constants, is such that 2x – 1 is a factor. Given that the remainder when f(x) is divided by x – 2 is twice the remainder when f(x) is
a. When x3 + x2 + ax – 2 is divided by x – 1, the remainder is 5. Find the value of a.b. When 2x3 – 6x2 + 7x + b is divided by x + 2, the remainder is 3. Find the value of b.c. When 2x3 + x2 +
Factorise these cubic expressions completely.a. x3 + 2x2 – 3x – 10b. x3 + 4x2 – 4x – 16c. 2x3 – 9x2 – 18xd. x3 – 8x2 + 5x + 14e. 2x3 – 13x2 + 17x + 12f. 3x3 + 2x2 – 19x + 6g. 4x3
Use the factor theorem to show:a. x – 4 is a factor of x3 – 3x2 – 6x + 8b. x + 1 is a factor of x3 – 3x – 2c. x – 2 is a factor of 5x3 – 17x2 + 28d. 3x + a is a factor of 6x3 + 11x2 –
Simplify each of the following.a. (x3 + 3x2 – 46x – 48) ÷ (x + 1)b. (x3 – x2 – 3x + 2) ÷ (x – 2)c. (x3 – 20x2 + 100x – 125) ÷ (x – 7)d. (x3 – 3x – 2) ÷ (x – 2)e. (x3 – 3x2
If P(x) = 3x4 + 2x2 – 1 and Q(x) = 2x3 + x2 + 1, find an expression fora. P(x) + Q(x)b. 3P(x) + Q(x)c. P(x) – 2Q(x)d. P(x) Q(x)
a. Show that x – 2 is a factor of 3x3 – 14x2 + 32.b. Hence factorise 3x3 – 14x2 + 32 completely.
Find the remainder whena. x3 + 2x2 – x + 3 is divided by x – 1b. x3 – 6x2 + 11x – 7 is divided by x – 2c. x3 – 3x2 – 33x + 30 is divided by x + 2d. 2x3 – x2 – 18x + 11 is divided by
a. Given that find the value of a and the value of b.b. Given that find the value of c and the value of d. V6 – 4 V2 = va - Vb, %3D
The diagram shows two parallelograms that are similar. The base and height, in centimeters, of each parallelogram is shown. Given that x, the height of the smaller parallelogram, is p+q√3/6, find
a. Solve the equation 3y = 8 + 3/y.b. Use your answer to part a to solve the equation 3x2 = 8 + 3x 2.
The blue circle has radius 2 and the green circle has radius 1. AB is common tangent and al three circles touch each other. Find the radiuse of the saller circle. A B
1. Find the exact value of V2 +V3- V2-V3.
Given thatFind the value of a, b, and c.
a. Solve the equation 4y2 = 15 + 7y.b. Use your answer to part a to solve the equation 4(9x) = 15 + 7(3x).
Find the value of cos θ. Write your answer in the form a+b√7/c, where a, b and c are integers. A (2 + 7) ст 3cm B- 5cm
A cuboid has a square base.The sides of the square are of length (1 + √2) cm.The height of the cuboid is (5 - √2) cm.Find the volume of the cuboid.Express your answer in the form a + b√2, where
The diagram shows a triangle ABC in which angle A = 90°.Sides AB and AC are √5 – 2 and √5 + 1 respectively.Find tan B in the form a + b√5, where a and b are integers. V5 - 2 A V5 - 1 B,
a. Solve the equation 2y2 - 7y - 4 = 0.b. Use your answer to part a to solve the equation 2(2x)2 - 7(2x) - 4 = 0.
a. Find the value of tan x. Write your answer in the form a+b√2/c, where a, b and c are integers.b. Find the area of the triangle. Write your answer in the form p+q√2/2, where p, q and r are
a. Find the value of AG2.b. Find the value of tan x. Write your answer in the form a√6/b, where a and b are integers.c. Find the area of the triangle. Write your answer in the form p√6/q, where p
a. i. Show that 3√5 - 3√2 is a square root of 53 – 12√10.ii. State the other square roots of 53 - 12√10.b. ExpressIn the form a + b√6, where a and b are integers to be found. 6V3 + 7V2 4
Find the positive root of the equation (4 - √2) x2 - (1 + 2√2) x - 1 = 0. Write your answer in the form a+b√2/c, where a, b and c are integers.
Solve each of the following pairs of simultaneous equations.a. 4x ÷ 2y = 1632x × 9y = 27b. 27x = 9(3y)2x ÷ 8y = 1c. 125* + 5' = 25 11-y 23* x (8/ = 32
Simplify (1 + x)3/2 - (1 + x)1/2.
A right circular cylinder has a volume of (25 + 14√3)π cm3 and a base radius of (2 + √3) cm. Find its height in the form (a + b√3) cm, where a and b are integers.
A rectangle has sides of length (2 + √8) cm and (7 - √2) cm.Find the area of the rectangle.Express your answer in the form a + b√2, where a and b are integers.
This design is made from 1 blue circle, 4 orange circle and 16 green circles. Th circles touch each other. Given that the radius of each green circle is 1 unit, find the exact radius of a.
Express (4√5 – 2)2/√5 – 1 in the form p√5 + q, where p and q are integers.
The roots of the equations x2 - 2√6 x + 5 = 0 are p and q, where p > q. Write p/q in the form a+b√6/c, where a, ab and c are integers.
Solve each of the following equations.a.b. 22x × 5x = 80000c. 3오x x 2* =_ 18
A cuboid has a square base of length (2 + √5) cm.The volume of the cuboid is (16 + 7√5 cm3.Find the height of the cuboid.Express your answer in the form a + b√5, where a and b are integers.
Given thatfind the value of x and the value of y. か-4 a² b*, a (a*)2 ー= 5- x
Expand and simplify.a. (2 + √5)2b. (5 - √3)2c. (4 + 5√3)2d. (√2 + √3)2
The number in the rectangle on the side of the triangle is the sum of the numbers at the adjacent vertices.Find the value of x, the value of y and the value of z. 13 +V2 17 - 10 V2 20 - 3 V2
Without using calculator, express 6(1 + √3)-2 in the form a + b√3, where a and b are integers to be found.
Solve these equations.a.b.c.d.e.f. V2x+7 Vx+ 3 +1
Solve each of the following equations.a.b.c.d. 272x 32x+1 35- x+3
The area of a rectangle is (8 + √10) cm2.The length of one side is (√5 + √2) cm.Find the length of the other side in the form a√5 + b√2, where a and b are integers.
Given thatfind the value of x and the value of y. 4 a5 6 3 1 2 a 5 63 2 = a* b ',
Expand and simplify.a. √2(3 + √2)b. √3(2√3 + √12)c. √2(5 - 2√2)d. √3(√27 + 5)e. √3(√3 - 1)f. √5(2√5 + √20)g. (√2 + 1) (√2 - 1)h. (√3 + 5) (√3 - 1)i. (2 +
Simplify.a. 5√3 + √48b. √12 + 3c. √20 + 3√5d. √75 + 2√3e. √32 - 2√8f. √125 + √80g. √45 - √5h. √20 - 5√5i. √175 - √28 + √63j. √50 + √72 - √118k. √200 -
a. Find the exact length of AB.b. Find the exact perimeter of the triangle. A 7 cm В 4cm
Integers a and b are such that (a + 3√5)2 + a - b√5 = 51. Find the possible values of a and the corresponding values of b.
Solve these equations.a.b.c.d.e.f.g.h.i. √x = 2x - 6j. k. 2x-1 x
Solve each of the following equations.a. 23x × 4x+1 = 64b. 23x+1 × 8x-1 = 128c. (22-x) (42x+3) = 8d. 3x+1 × 92-x = 1/27
Write as a single faction.a.b.c. 1 1 V3 + 1 V3 – 1
Which of the mappings in Exercise 1.1 are functions?x → x + 1 x ∈ R
Give thatfind the value of a and the value of b. 32 X Vy 3.
Simplify.a. √8b. √12c. √20d. √28e. √50f. √72g. √18h. √32i. √80j. √90k. √63l. √99m. √44n. √125o. √117p. √200q. √75r. √3000s. √20/2t. √27/3u. √500/5v. √20 ×
The first 4 terms of a sequence area. Write down the 6th term of this sequence.b. Find the sum of the first 5 terms of this sequence.c. Write down an expression for the nth term of this sequence. 2+3
Simplify.a. √112/√28b. √52/√26c. √12/√3d. √17/√68e. √12/√108f. √15/√3g. √54/√6h. √4/√25i. √5/√81j. √81/2√11k. 9√20/3√5l. √120/√24
Simplify.a. A + Bb. A - Cc. 2A + 3Bd. 5A + 2B - C A 3 V5 + 7V3 B 2V5 - 3V3 C 2V3 - 15
Solve the simultaneous equations,4x/256y = 102432x × 9y = 243
Solve these simultaneous equations.a. 3x - y = 5√22x + y = 5b. x + y = 5√6x + 2y = 12c. 3x + y = 64x + 3y = 8 - 5√5d. 2x + y = 115x - 3y = 11√7e. x + √2 y = 5 + 4√2x + y = 8
Rationalise the denominators and simplify.a.b.c. d.e.f.g.h.i.j. 1+ V2
Simplify each of the following.a.b.c.d. -2
Simplify.a. √18 × √2b. √2 × √72c. √5 × √6d. (√5)2e. (√13)2f. (√5)3g. 3√2 × 5√3h. 7√5 × 2√7
Simplify.a.b.c.d. 3 V5 +7V5
Solve 2x2-5x = 1/64.
Solve these equations.a.b.c. V12 x- V5 x = V3 %3D
Rationalise the denominators.a. 1/√5b. 3/√2c. 9/√3d. √2/√6e. 4/√5f. 12/√3g. 4/√12h. 10/√8i. 3/√8j. √2/√32k. √3/√15l. √12/√156m. 5/2√2n. 7/2√3o. 1 + √5/√5p.
Solve each of the following equations.a. 52x = 57x - 1b. 42x+1 = 43x-2c. 7x2 = 76-xd. 32x2 = 39x+5
Simplify each of the following.a. (x5)3b. x7 × x9c. x5 ÷ x8d. e.f. (x-3)5g. h.i. 3x2 y × 5x4 y3j. k.l. V10
Determine whether each of these mappings is one-one, many-one or one-many.x → x3 x ∈ R
The function g is defined as g(x) = x2 + 2 for x ≥ 0. Write down the range of g.
f(x) = (x + 2)2 - 1 for x ∈ RFind f2 (3).
Solve a. |x2 - 1| = 3b. |x2 + 1| = 10c. |4 - x2| = 2 - xd. |x2 - 5x| = 3xe. |x2 - 4| = x + 2f. |x2 - 3| = x + 3g. |2x2 + 1| = 3xh. |2x2 - 3x| = 4 - xi. |x2 - 7x + 6| = 6 - x
Draw the graphs of each of the following functions.a. y = |x| + 1b. y = |x| - 3c. y = 2 - |x|d. y = |x - 3| + 1e. y = |2x + 6| - 3
f(x) = (2x - 3)2 + 1 for x ≥ 1 1/2. Find an expression for f-1(x).
g(x) = 2x for x ∈ ROn the same axes, sketch the graphs of y = g(x) and y = g-1(x), showing the coordinates of any points where the curves meet the coordinate axes.
A function f is such that f(x) = 3x2 - 1 for - 10 ≤ x ≤ 8.a. Find the range of f.b. Write down a suitable domain for f for which f-1 exists.
Determine whether each of these mappings is one-one, many-one or one-many.x → 2x x ∈ R
The function f is defined by f(x) = x2 - 4 for x ∈ R. Find the range of f.
On a copy of the grid, draw the graph of the inverse of the function f. 6- 4- 2- f -6 -4 -2 2 4 6 * -2 -4- -6-
Solve the equation |4x - 5| = 21.
Determine whether each of these mappings is one-one, many-one or one-many.x → x + 1 x ∈ R
f: x → 2x + 3 for x ∈ Rg: x → x2 - 1 for x ∈ RFind fg(2).
Solvea. |3x - 2| = 10b. |2x + 9| = 5c. |6 - 5x| = 2d.e.f.g.h.i. |2x - 5| = x x - 1 6. 4
Sketch the graphs of each of the following functions showing the coordinates of the points where the graph meets the axes.a. y = |x + 1|b. y = |2x - 3|c. y = |5 - x|d. e. y = |10 - 2x|f. x + 3 2
f(x) = (x + 5)2 - 7 for x ≥ 5. Find an expression for f-1(x).
On a copy of the grid, draw the graph of the inverse of the function g. 6- 4- -6 -4 -2 0 4 6 x -2- 4- -6 2.
a. Sketch the graph of y = |3 + 5x|, showing the coordinates of the points where your graph meets the coordinate axes.b. Solve the equation |3 + 5x| = 2.
Determine whether each of these mappings is one-one, many-one or one-many.x → x2 + 5 x ∈ R
Find the range for each of these functions.a. f(X) = x - 5, -2 ≤ x ≤ 7b. f(x) = 3x + 2, 0 ≤ x ≤ 5c. f(x) = 7 - 2x, - 1 ≤ x
f(x) = x2 - 1 for x ∈ Rg(x) = 2x + 3 for x ∈ RFind the value of gf(5).
Solvea.b.c.d. |3x - 5| = x + 2e. x + |x - 5| = 8f. 9 - |1 - x| = 2x 2x – 5 = 8 x + 3
a. Complete the table of values for y = |x - 2| = 3.b. Draw the graph of y = |x - 2| + 3 for -2 ≤ x ≤ 4. -2 -1 0. 1 4 y 6. 4
f(x) = 6/x+2 for x ≥ 0. Find an expression for f-1(x).
f(x) = x2 + 3, x ≥ 0.On the same axes, sketch the graphs of y = f(x) and y = f-1(x), showing the coordinates of any points where the curves meet the coordinate axes.

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