2000009406
Level:
A
For \(x\), \(a\), \(b \in \mathbb{R}\), \(x>0\), simplify the expression \( \sqrt{\frac{x^{a-b}}{x^{b-a}}}\).
\(x^{a-b}\)
\(x^{-\frac12}\)
\(1\)
\(-1\)
A
2000009405
Level:
A
The expression \( \frac{6^3\cdot 50^2}{2^3 \cdot 3^3 \cdot 10^2}\) equals:
\(25\)
\(5\)
\(1.25\)
\(\frac1{125}\)
2000009404
Level:
A
The expression \( \frac{31 \cdot 10^3 \cdot 0.001}{10^4 \cdot 10^{-2}}\) equals:
\(0.31\)
\(3.1\)
\(3100\)
\(310\)
2000009402
Level:
A
The expression \( \left(2\left(4\left(6\cdot 8^0\right)^1\right)^{-1}\right)^2\) equals:
\(\frac1{144}\)
\(\frac1{1152}\)
\(6\)
\(0\)
2000009401
Level:
A
The expression \( 5^{12} +5^{11}+5^{10}-6\cdot 5^{10}\) equals:
\(5^{12}\)
\(5^{-27}\)
\(19\cdot 5^{10}\)
\(-15^{23}\)
2010009306
Level:
A
Given the linear function \(f(x) = -2x + 1\),
evaluate
\[
f(a) + f(a-1).
\]
\(- 4a +4\)
\(- 4a +3\)
\(4\)
\(- 4a +2\)
2010009305
Level:
A
Consider the linear function \(f(x) = -3x + 9\).
Find the intersection point of the graph of
\(f\) with
\(y\)-axis.
\([0;9]\)
\([9;0]\)
\([0;3]\)
\([3;0]\)
2010009304
Level:
A
Consider the linear function \(f(x)= -\frac{2}
{5}x + 3\).
Find the intersection point of the graph of
\(f\) with
\(x\)-axis.
\(\left[\frac{15}2;0\right]\)
\(\left[-\frac{15}2;0\right]\)
\([0;3]\)
\([13;0]\)
2010009303
Level:
A
Let the function \(g\)
be defined as a linear function with graph passing through the points
\(A = [-3;2]\) and
\(B = [-2;4]\). Find an analytic
expression for the function \(g\).
\(g(x)= 2x + 8\)
\(g(x)= \frac12 x -4\)
\(g(x)= -\frac74 x + \frac12\)
\(g(x)= 2x -4\)
2010009302
Level:
A
Given the linear function \(f(x) = -5x + 3\),
evaluate \(f(-2) + f(2)\).
\( 6\)
\( -14\)
\( 0\)
\( -20\)