Solutions for Given Expressions and Equations

Part – A
Solution 1: Given the expression , where U and S are speed and distance
respectively. Note that both speed and distance are depends on time t, so S and U are
dependent variables and time t is independent variable.
Solution 2a): Given that the ratio of x to the sum of x and 5 is 6. So the algebraic
expression is
Now
Simplify further,
Hence
Solution 2b): Given that doubling the result 4 less than x is 6 so the algebraic expression
is
Now,
Hence
Solution 2c): Given that 6 more than half of x is 6 so the algebraic expression is
Now,
Hence
Solution 3a): Given the expression .
Now,
Hence,
Solution 3b): Given the expression .
Now,

Simplify further,
Hence,
Solution 4a): Given the expression .
Now,
Use formula we get,
Solution 4b): Given the expression .
Now use factorization method
Hence
Solution 5: Consider the expression -------- (1)
Now,
Simplify further,
Hence
Solution 6: Given that the expression

Rearranging the above expression, we get
Squaring the both sides of above equation and simplify we get,
Hence equation y as function of x is
Now, substitute in above equation and simplify
Simplify further,
Hence, when
Solution 7a): Given the points . We need to find an equation that
passes through these three points. Suppose that the expression in terms of x and y will be
------ (1)
Our firs aim is to find the unknown a, b and c.
Since equation (1) passes through point , that is at
Use these values in equation (1), we get
Again equation (1) passes through point that is at
Use these values in equation (1), we get
Since so -------- (2)
Again equation (1) passes through point that is at
Use these values in equation (1), we get
Since so ------- (3)
Equation (2) and (3) gives . Substitute the values of a, b and c in equation
(1), we get the required expression