L1 Mathematical Reasoning
Question Bank
Find the value of $x$ if $2^{x-3} = 32$.
Find the co-ordinates of the y-intercept for the exponential graph $y = 4(3^{2x-1}) + 7$.
Find the coordinates of the y-intercept for the exponential graph $y = (\frac{1}{2})^{x-3} - 5$.
The diagram below shows the graphs of $y = (1.2)^x$ and $y = \frac{1}{2}x + 1$.
Use the graph to estimate the solutions to the equation $1.2^x = \frac{1}{2}x + 1$.
Simplify the following expression:
$ \frac{\displaystyle 5^{4m-2}}{\displaystyle 5^{m+4}} $
Simplify the following expression:
$ 3^{p+1} \times 9^{2p-5} $
Simplify the following expression:
$ 2^{a+2} \times 4^{2a-1} \times 2^{-3a} $
Solve the equation $9^{2x-1} = 27^{x+4}$.
Find the value of $x$ by solving the equation $8^{x+3} = 16^{x-1}$.
Solve for $x$ in the equation $25^{2x} = (\frac{1}{125})^{x-5}$.
Make $y$ the subject of the formula $\frac{8^{x+2}}{4^x} = 2^{5y-1}$.
Make $y$ the subject of the formula $25^{x-1} \times 5^{3x+1} = 125^{y+2}$.
Find the values of $x$ by solving the equation $9^{x^2} \times 3^{5x} = \frac{1}{9}$.
Given the equation $6^{2x} + 6^{2x} + 6^{2x} + 6^{2x} + 6^{2x} + 6^{2x} = 6^y$, find an expression for $y$ in terms of $x$.