ACT Math Genius Quiz – Lite

LITE

A cricket is at the origin of the XY plane (0,0) and makes a sequence of jumps. Each jump has a length of 5, and after each jump, the cricket is always at a point whose coordinates are both integers; thus there are 12 possible locations for the cricket after the first hop. What is the smallest number of jumps the grasshopper would need to get to the point (7,7) on the coordinate plane?

The solution set of which of the following equations is the set of all real numbers that are 10 units from -7?

For all positive \(x\), which of the following is equal to \(4+\frac{x}{x+4}-\frac{8}{2x+8}\)?

In the complex numbers, where \(i^{2}=-1\), \(\frac{3-2i}{4+3i}=?\)

When \(log_{2}x=-5\), what is \(x\)?

How long, in centimeters, is 1 side of a square whose perimeter is equal to the circumference of a circle with a diameter of 12 centimeters?

Which of the following equations determines the above ellipse shown in the standard \((x,y)\) coordinate plane?

Which of the following equations determines the graph of a circle with a radius of 10 units?

In the triangle below, which of the following expressions represents the length of \(\overline{BC}\) ?

The graph of \(y=sin(ax)\) is graphed below. What is the value of \(a\)?