# MATH 1009 TOPICS TO BE COVERED ON THE DIAGNOSTIC

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```					               MATH 1009: TOPICS TO BE COVERED ON THE DIAGNOSTIC TEST

1) Functions (Definition, Basic Manipulations, Domain, and Range)
3) Equation of a Line
4) Solving Equations with One or Two Unknowns, including Word Problems
5) Order of Operations
6) Factoring
7) Exponents and Logarithms, including e and ln
8) Inequalities
9) Absolute Value
10) Sequences and Series

NOTE: Questions may simultaneously cover more than one of the topics above.

PRACTICE TEST
(The actual diagnostic test will be multiple choice)

1) List the following numbers in numerical order, starting with the smallest:

1
, − 10 , − − 6 , − 4 , 0.25, − π
5

− 14
2) Evaluate the expression: − 7 −                     − 3(8 − 6) .
2(2 − 3)

− 35 x −1 y ( x 2 y )
3) Simplify the expression:                            . Express the result with positive exponents only.
5 xy −1

7 2 81
4) Simplify the expression:                  .
3 2 49

5) Expand the expression: 2n(5 – n)(6n + 5).

27 s 3 t 2 − 18s 4 t + 9 s 2 t
6) Simplify the expression:                                     .
9s 2 t

3 x 3 − 7 x 2 + 11x − 3
7) Evaluate                            .
3x − 1

8) Solve the following equation for t: 3t – 2(7 – t) = 5(2t + 1).

9) Two computer software programs cost \$190 in total. If one costs \$72 more than the other, what is the
cost of the more expensive program?

10) If f ( x) = 3x 2 − 2 x + 4, find f(x + 3).

2
11) What is the domain of y =                    ?
x+4
2
12) What is the range of y =                 ?
x+4

13) Find the equation of the line with slope 2.5 that passes through the point (10, 5).

14) If 12x + 9y = 14, and 6x = 7y – 16, what is the numerical value of x?

15) Suppose that Wayne has spent \$18000 in total on two investments. Investment 1 has an annual
interest rate of 5.5%, while Investment 2 has an annual interest rate of 3%. If Wayne receives a total
of \$700 in interest at the end of the year, compute the amounts that he contributed to each of the two
investments.

6T 2 − NT − N 2 8T 2 − 2 NT − N 2
16) Simplify                     ÷                 .
2V 2 − 9V − 35   V 2 − 6V − 7

2 1 1
17) Simplify      + + .
3 2 7

x y
−
y x
18) Simplify      .
y
1+
x

1   1  1
19) Solve the following equation for x in terms of a, b, and c:          =   + .
a x+b c

20) If 2 x 2 − 7 x + 6 = 3 , what are the values of − 6 x + 2 ?

3 6− 2
21) Rationalize the denominator of                      and simplify the result.
6+ 2

 a 3b 5       
22) Using the rules for logarithms, expand the expression ln  1 / 2
c
.

              

23) If ln (e 2 x +5 ) = 5 x + 9 , solve for x.

2x
24) Solve the inequality 5 −          ≥6.
3

25) Find the 7th term in the geometric sequence 125, -25, 5, … .

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