**Note: This is not a test! It will have no effect on
your grade. Its sole purpose is to help diagnose**

your weakness, if any, in the math , which is needed in this course (not just for
the lab).

Your instructor will be happy to help you.

**Part 1. Angles and Triangles**

1. |
θ = ________________ |

2. |
ø
= _________ θ= ________ |

3. |
x = _________________ |

4. |
x = _________________ |

**Part 2. Trigonometry **

5.

sin θ = 0.60

x = ______________

y = ______________

6. If sin 35° = cos θ, then θ = _____________

7. If sin θ = 0.80, then cos θ = _____________ and tan θ =
_____________

8.

Mark all angles that are equal to the angle θ .

How many did you mark (including the one

that was already marked)? _____________

9. For what values of θ, if any, is the following
expression true ?

sin^{2} θ + cos^{2} θ = 2.0

θ = ____________________________

**Part 3. Scientific Notation**

In scientific work, it is convenient to express numbers as
the product of a number between 1

and 10 multiplied by an appropriate power of 10. Thus 0.00050 becomes 5.0*10^{-4},
and 1,800,000

is written as 1.8*10^{6}. This way of writing numbers is called scientific (or
powers of ten) notation.

Carry out the operations indicated and express the results in scientific
notation.

10. 2 * 0.000015 = _________________________________

11. (0.00002)^{3} = ______________________________

12. (7.1 * 10^{5}) + (2.2 * 10^{4}) =
_______________________________

13. (4*10^{8}) * (9*10^{9}) = _______________________

14. (3*10^{7}) * (6*10^{-12}) = ________________________

**Part 4. Algebra **

15. Given that
write an expression, which contains only l on the left-hand side.

l = ___________________

16. 3x - 5 = 13 x = __________________

17. a^{2} + a^{2} + 2a^{2} = _________________

18. The radius of a circle is R . Write an expression for
the area of the circle. ______________

Write an expression for the circumference of the circle. ______________________

19. The radius of a cylinder is R and its height is h.

Write an expression for the volume of the cylinder. _________________________

**Part 5. The Straight Line Graph **

If the relation between x and y is given by:** y = mx + b
,**

then it may be pictured by a straight line on the y (vertical axis) versus x
(horizontal axis) graph.

The parameter b, called the y-intercept, represents the value of y for x = 0.
The parameter m is

equal to the slope of the straight line and is also equal to the tangent of the
angle that the line makes

with the x-axis.

Sometimes it is not possible to read the value of b
directly from the graph. In that case, b

has to be calculated. First, find the slope m and then select any point on the
straight line and read x

and y values for that point. Substituting m , x, and y into the straight-line
equation, you will be able

to calculate the value of the y- intercept b (b = y - mx).

20. From the graph below , find the slope m and the
y-intercept b.

m = ____________________ b = _____________________

21. From the graph below , find the slope m and the
y- intercept b .

m = ____________________ b = _____________________