Find three rational numbers \(\frac { 3 }{ 5 } \) and \(\frac { 7 }{ 8 } \)

4

(a)

Find your rational numbers between \(\frac { 1 }{ 5 } \) and \(\frac { 1 }{ 6 } \)  

4

(a)

Express \(0.15\overline { 9 } \) in \(\frac { p }{ q } \) , where p and q are integers and \(q\neq 0\)

4

(a)

(i) express 2.4 \(\overline { 248 } \) in the form of \(p\over q\) where \(p\over q\) is in its lowest form.
(ii) What is the value of p?
(iii) what is the value of q?
(iv) what name can be given to the number p?
(v) what name can be given to the number q?
(vi) Apala declares that p and q are co-prime. IS she correct? If so, which value of Apala is depicted by her declaration?
(vii) Which mathematical concept has been converted in this problem?
(viii) Write the formulae used in the solution.

4

(a)

Find the value of 'p' if \({ 5 }^{ p-3 }\times { 3 }^{ 2p-8 }=225\)

4

(a)

Find the values of a and b in \(\frac { 3-\sqrt { 5 } }{ 3+2\sqrt { 5 } } =a\sqrt { 5 } -\frac { b }{ 11 } \)

4

(a)

Write the various coefficients in the following polynomials:
1 - 2y + 3y⁶

4

(a)

Find the values of a and b so that (x+1) and (x-1) are factors of \(x^4+ax^3-3x^2+2x+b\)

4

(a)

Using suitable identify, find the value of \(\frac{87^3+13^3}{87^2-87\times13+13^3}\)

4

(a)

If \(x^2+\frac{1}{x^2}=23,\) then find the  value of  \(x^3+\frac{1}{x^3}\)

4

(a)

Divide 3x³-8x²+3x+2 by x²-3x+2 and verify the division algorithm.

4

(a)

In figure, ABCD is a rectangle with length 6 cm and breadth 3 cm.O is the mid point of AB.Find the coordinates of A, B C and D.

4

(a)

Draw the graph of the equations x = 3 and 4x = 3y in the same graph.Find the area of the triangle formed by these two lines and the x-axis

4

(a)

Draw the graph of the linear equation 3x+4y=6. Find the points where the line representing the equation 3x+4y=6 cuts the axes of x and y.

4

(a)

In figure, C is the mid-point of AB and Dis the mid-point of AC. Prove that AD = \(1\over2\)  AB.

4

(a)