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 re-consider doing calculus at university.

 

1. Solve the inequality

|3x - 7| < 4

2. Simplify

\frac{\frac{1}{x - 1} + \frac{1}{5}}{x + 2}

3. Find all values of x for which

(x^2 + 2)(x - 4) - (2x^2 + 4)(\frac{1}{2}x) = 0

4. Find the points (a, b) on the graph of 2x + 3y = 6 that are

1. intercepts
2. have x = -3
3. have y = -2

5. Find the equation of the line with slope 5 that passes through the point on the graph of  y = x^3  with x-coordinate 2

6. Find the equation of the line through the point (-1, 3) that is parallel to the line 4x – 7y + 6 = 0

7. Find the equation of the line through the point (-1, 3) that is perpendicular to the line 4x – 7y + 6 = 0

8. If   \sin(\theta) = x/5   and   -\pi/2 \leq \theta \leq \pi/2 ,  express   \cos(\theta)   in terms of x

9. Sketch the graph of 2x – 3y = 6

10. Sketch the graph of

y = \frac{1}{1 + x}