Thread: Maths Assignment ...Help me Please !!!!!

Hi, here is my maths assignment any help would be great,im so confused with this!!!


1. Let A = { 4, 5, 6, 7 } and B = {11, 12, 13, 14, 15,1 6 } and

let us define binary relations S and T as follows:


(a) For all (x, y) є A x B, (x, y) є S ↔x divides y (3 marks)

(b) For all (x, y) є A x B, (x, y) є T ↔ 2x > y(3 marks)


By drawing mapping diagrams for each relation determine:
(i) the type of mapping
(ii) which of the above relations if any between A and B forms a
function.





2. Let R be the relation between { 5, 6, 7 } and given by { 8, 9, 10, 11 }

R = { (5, 8), (5, 10), (6, 9), (6, 10), (7, 11) }


Let S be the relation between { 8, 9, 10, 11 } and given by { 5, 6, 7 }

S = { (8, 6), (8, 5), (9, 5), (9, 7), (10, 7) }


Calculate: (a) (i) R-1 (1 mark)
(ii) S-1 (1 mark)
(iii) S º R (2 marks)


(b) Verify that (S º R)-1 = R-1 ° S-1 (3 marks)






3. The functions f and g are defined by

f: x → x2 + 7 , x є R

g: x → 3x + 3 , x є R

h: x → 1 , x ≠ 0, x є R
x


(a) Find the inverses of functions f, g and h (3 marks)

(b) Hence find:
(i) fo g (x) (ii) h-1og (x) (2 marks)

(c) Evaluate:
(i) f (3) (ii) fo g (3) (2 marks)




4. The function f is defined by f(x) = x + 2 , x є R
3

(a) Find f-1(x) (1 mark)


(b) Given that g(x) = x2, x є R, find an expression for f-1og (x) (1 mark)


(c) Solve the equation f-1og(x) = 25 (3 marks)




5. (a) Evaluate the following:
(i) 38 (ii) 25-1/2 (2 marks)


(b) Simplify the following leaving your answers in index form.
(i) e6. e2 (ii) 818
84 (2 marks)


6. (a) Convert the number 345 into:
(i) binary
(ii) hexadecimal numbers (4 marks)
(b) Convert the following numbers to decimal numbers:
(i) 1111112 (ii) 2978 (4 marks)





7. (a) Draw by hand on graph paper, the graphs of
y = 2e-x and y = x + 1 for -2 ≤ x ≤ 2
(3 marks)
(b) Hence solve the equation 2e-x - x = 1
(2 marks)







8. (a) Simplify the following expressions into a single logarithmic term.

(i) log 7 + log 6 – log 3
(ii) log 5t - log 3t
(4 marks)


(b) Solve the following equations, giving your answers to 2 decimal places:

(i) 10x = 17 (ii) ln (1 + 3x) = 2.25

(4 marks)

(Total Marks = 50)

Originally Posted by chris89108

Hi, here is my maths assignment any help would be great,im so confused with this!!!


1. Let A = { 4, 5, 6, 7 } and B = {11, 12, 13, 14, 15,1 6 } and

let us define binary relations S and T as follows:


(a) For all (x, y) є A x B, (x, y) є S ↔x divides y (3 marks)

(b) For all (x, y) є A x B, (x, y) є T ↔ 2x > y(3 marks)


By drawing mapping diagrams for each relation determine:
(i) the type of mapping
(ii) which of the above relations if any between A and B forms a
function.





2. Let R be the relation between { 5, 6, 7 } and given by { 8, 9, 10, 11 }

R = { (5, 8), (5, 10), (6, 9), (6, 10), (7, 11) }


Let S be the relation between { 8, 9, 10, 11 } and given by { 5, 6, 7 }

S = { (8, 6), (8, 5), (9, 5), (9, 7), (10, 7) }


Calculate: (a) (i) R-1 (1 mark)
(ii) S-1 (1 mark)
(iii) S º R (2 marks)


(b) Verify that (S º R)-1 = R-1 ° S-1 (3 marks)






3. The functions f and g are defined by

f: x → x2 + 7 , x є R

g: x → 3x + 3 , x є R

h: x → 1 , x ≠ 0, x є R
x


(a) Find the inverses of functions f, g and h (3 marks)

(b) Hence find:
(i) fo g (x) (ii) h-1og (x) (2 marks)

(c) Evaluate:
(i) f (3) (ii) fo g (3) (2 marks)




4. The function f is defined by f(x) = x + 2 , x є R
3

(a) Find f-1(x) (1 mark)


(b) Given that g(x) = x2, x є R, find an expression for f-1og (x) (1 mark)


(c) Solve the equation f-1og(x) = 25 (3 marks)




5. (a) Evaluate the following:
(i) 38 (ii) 25-1/2 (2 marks)


(b) Simplify the following leaving your answers in index form.
(i) e6. e2 (ii) 818
84 (2 marks)


6. (a) Convert the number 345 into:
(i) binary
(ii) hexadecimal numbers (4 marks)
(b) Convert the following numbers to decimal numbers:
(i) 1111112 (ii) 2978 (4 marks)





7. (a) Draw by hand on graph paper, the graphs of
y = 2e-x and y = x + 1 for -2 ≤ x ≤ 2
(3 marks)
(b) Hence solve the equation 2e-x - x = 1
(2 marks)







8. (a) Simplify the following expressions into a single logarithmic term.

(i) log 7 + log 6 – log 3
(ii) log 5t - log 3t
(4 marks)


(b) Solve the following equations, giving your answers to 2 decimal places:

(i) 10x = 17 (ii) ln (1 + 3x) = 2.25

(4 marks)

(Total Marks = 50)

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