11th Maths Weekly Test-2( Basic Algebra )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-2( Basic Algebra )-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Solve 3x - 5 ≤ x + 1 for x.

If log₂x+log₄x+log₈x=\(\frac{11}{6}\), find x

Find the logarithm of 1728 to the base 2\(\sqrt{3}\)

Find the value of \(\frac { 2-\sqrt { 3 } }{ \sqrt { 3 } } \) when \(\sqrt { 3 } \) =1.732

Find the complete set of values of a for which the quadratic x² - ax + a + 2 = 0 has equal roots.

Write f(x) = x²+ 5x + 4 in completed square form.

Prove \(log\frac { { a }^{ 2 } }{ bc } +log\frac { b^{ 2 } }{ ca } +log\frac { c^{ 2 } }{ ab } =0\)

If a and b are both rational numbers,find the values of a and b if \(\frac { 3+\sqrt { 7 } }{ 3-\sqrt { 7 } } =a+b\sqrt { 7 } \)

If a³+b³=ab(8-3a-3b),show that log \(\left( \frac { a+b }{ 2 } \right) =\frac { 1 }{ 3 } \) (log a +log b)

If log₁₀ (a²-4a+5) = 0 then show that a = 2

Part - B

Generic 5 - Answer All Question

Resolve the following rational expressions into partial fractions.
\({{x^2+x+1}\over{x^2-5x+6}}\)

Solve for x⁴-7x³+8x²+8x-8=0 .Given 3-\(\sqrt { 5 } \) is a root

Solve: \(\sqrt{x+5}+\sqrt{x+21}=\sqrt{6x+40}\)

If α and β are the roots of the equation 3x²-4x+1 =0,form the equation whose roots are \(\frac { { \alpha }^{ 2 } }{ \beta } \)and \(\frac { { \beta }^{ 2 } }{ \alpha } \)

If x=2 is one root x³+2x²-5x-6=0 then find the other roots of the equation

Solve the equation (ax+b)²+(bx-a)²=2(a²+b²)

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11th Maths Weekly Test-2( Basic Algebra )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-2( Basic Algebra )-Aug 2020

Part - A

Generic 2 - Answer All Question

Solve 3x - 5 ≤ x + 1 for x.

If log2x+log4x+log8x=\(\frac{11}{6}\), find x

Find the logarithm of 1728 to the base 2\(\sqrt{3}\)

Find the value of \(\frac { 2-\sqrt { 3 } }{ \sqrt { 3 } } \) when \(\sqrt { 3 } \) =1.732

Find the complete set of values of a for which the quadratic x2 - ax + a + 2 = 0 has equal roots.

Write f(x) = x2 + 5x + 4 in completed square form.

Prove \(log\frac { { a }^{ 2 } }{ bc } +log\frac { b^{ 2 } }{ ca } +log\frac { c^{ 2 } }{ ab } =0\)

If a and b are both rational numbers,find the values of a and b if \(\frac { 3+\sqrt { 7 } }{ 3-\sqrt { 7 } } =a+b\sqrt { 7 } \)

If a3+b3=ab(8-3a-3b),show that log \(\left( \frac { a+b }{ 2 } \right) =\frac { 1 }{ 3 } \) (log a +log b)

If log10 (a2-4a+5) = 0 then show that a = 2

Part - B

Generic 5 - Answer All Question

Resolve the following rational expressions into partial fractions. \({{x^2+x+1}\over{x^2-5x+6}}\)

Solve for x4-7x3+8x2+8x-8=0 .Given 3-\(\sqrt { 5 } \) is a root

Solve: \(\sqrt{x+5}+\sqrt{x+21}=\sqrt{6x+40}\)

If α and β are the roots of the equation 3x2-4x+1 =0,form the equation whose roots are \(\frac { { \alpha }^{ 2 } }{ \beta } \)and \(\frac { { \beta }^{ 2 } }{ \alpha } \)

If x=2 is one root x3+2x2-5x-6=0 then find the other roots of the equation

Solve the equation (ax+b)2+(bx-a)2=2(a2+b2)

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If log₂x+log₄x+log₈x=\(\frac{11}{6}\), find x

Find the complete set of values of a for which the quadratic x² - ax + a + 2 = 0 has equal roots.

Write f(x) = x²+ 5x + 4 in completed square form.

If a³+b³=ab(8-3a-3b),show that log \(\left( \frac { a+b }{ 2 } \right) =\frac { 1 }{ 3 } \) (log a +log b)

If log₁₀ (a²-4a+5) = 0 then show that a = 2

Resolve the following rational expressions into partial fractions.
\({{x^2+x+1}\over{x^2-5x+6}}\)

Solve for x⁴-7x³+8x²+8x-8=0 .Given 3-\(\sqrt { 5 } \) is a root

If α and β are the roots of the equation 3x²-4x+1 =0,form the equation whose roots are \(\frac { { \alpha }^{ 2 } }{ \beta } \)and \(\frac { { \beta }^{ 2 } }{ \alpha } \)

If x=2 is one root x³+2x²-5x-6=0 then find the other roots of the equation

Solve the equation (ax+b)²+(bx-a)²=2(a²+b²)