All ACT Math Resources
Example Questions
Example Question #251 : Coordinate Plane
What is the distance between (7, 13) and (1, 5)?
12
10
None of the answers are correct
7
5
10
The distance formula is given by d = square root [(x2 – x1)2 + (y2 – y1)2]. Let point 2 be (7,13) and point 1 be (1,5). Substitute the values and solve.
Example Question #251 : Algebra
What is the slope of this line?
The slope is found using the formula .
We know that the line contains the points (3,0) and (0,6). Using these points in the above equation allows us to calculate the slope.
Example Question #252 : Algebra
What is the amplitude of the function if the marks on the y-axis are 1 and -1, respectively?
π
1
0.5
2π
3π
1
The amplitude is half the measure from a trough to a peak.
Example Question #253 : Algebra
What is the midpoint between and ?
None of the answers are correct
The x-coordinate for the midpoint is given by taking the arithmetic average (mean) of the x-coordinates of the two end points. So the x-coordinate of the midpoint is given by
The same procedure is used for the y-coordinates. So the y-coordinate of the midpoint is given by
Thus the midpoint is given by the ordered pair
Example Question #4 : How To Graph A Line
If the graph has an equation of , what is the value of ?
is the -intercept and equals . can be solved for by substituting in the equation for , which yields
Example Question #3 : How To Graph A Line
The equation represents a line. This line does NOT pass through which of the four quadrants?
Cannot be determined
II
IV
III
I
III
Plug in for to find a point on the line:
Thus, is a point on the line.
Plug in for to find a second point on the line:
is another point on the line.
Now we know that the line passes through the points and .
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
Example Question #1 : Graphing Linear Functions
Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. Give the equation of that line in slope-intercept form.
First, we need to find the slope of the above line.
The slope of a line. given two points can be calculated using the slope formula
Set :
The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be . Since we want this line to have the same -intercept as the first line, which is the point , we can substitute and in the slope-intercept form:
Example Question #2 : Graphing Functions
Refer to the above diagram. If the red line passes through the point , what is the value of ?
One way to answer this is to first find the equation of the line.
The slope of a line. given two points can be calculated using the slope formula
Set :
The line has slope 3 and -intercept , so we can substitute in the slope-intercept form:
Now substitute 4 for and for and solve for :
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