Gateway Tests
Gateway tests are tests designed to determine the appropriate placement for
students entering university, specifically if they are ready to embark on
calculus university courses. They are intended to help the student, as opposed
to something that would affect him or her negatively.
Below is a sample of such a test. If you score less than 8 out of 10, you
should seriously reconsider doing calculus at university.
 Solve the inequality 3x 7 < 4.
 Simplify .
 Find all values of x for which
is zero.
 Find the points (a,b) on the graph of 2x+3y =6
that are (i) intercepts, (ii) have x = 3, (iii) have y=2.
 Find the equation of the line with slope 5 that passes through the point on
the graph of
with xcoordinate 2.
 Find the equation of the line through the point (1,3) that is parallel to
the line 4x  7y +6 = 0.
 Find the equation of the line through the point (1,3) that is
perpendicular to the line 4x  7y + 6 = 0.
 If
and ,
express
in terms of x.
 Sketch the graph of 2x 3y = 6.
 Sketch the graph of
.
