Exponents (Scientific Notation)
1.
Write 1,200,000 in exponential form (i.e., in ”scientific notation”).
2.
Write 0.000054 in exponential form.
3.
Calculate the expressions below.
a.
(6.40 × 10 −1) + (1.1 × 10 −2)
b.
(3.20 × 10 −2) − (3.2 × 10 −3)
c.
(2.50 × 10 −3) − (3.0 × 10 −1)
d.
(2.016)
6.02 × 10 23
e.
(2.0 × 10 −4)(5.0 × 10 −4) 2
Fractions, Decimals, and Percentages
4.
Express 75% as a fraction.
5.
Express 75% as a decimal.
6.
A student obtains 68 of a possible 80 marks on a chemistry examination.
Express this grade as a percentage.
Algebra
7.
If x =
(y − 32)5
, find the value of x when y = 59.
9
8.
If a = b − 298c, find the value of c when a = 370 and b = 105.
9.
Find the value of x if 27x 3 = 4.8 × 10 −56 .
10. The formula for solving a quadratic equation of the type
ax 2 + bx + c = 0 is
− b  b 2 − 4ac
x=
2a
Find the two possible values for x if
x 2 + (1.8 × 10 −5x) − (1.80 × 10 −6) = 0
Averages
11. A certain small industrial firm pays 65.0% of its workers $7.50 per hour
and 25.0% of its workers $8.50 per hour. The remaining workers are
much more fortunate and earn $10.50 per hour. Calculate the average
hourly wage paid by the company.
Logarithms and Natural Logarithms
12. Determine the logarithm (to the base 10) of 0.1542.
13. Find the value of x if
a.
x = − log 10(2.5 × 10 −3)
b.
−3
x = log 10 2.5 × 10 −2
2.5 × 10


14. Find the value of x if
a.
− log 10 x = 11.45
b.
log 10 x = 107
15. If y = e −x, then log e y =
.
16. What is the relationship between loge y (or ln y) andlog 10 y?
Approximations and Assumptions
17. Given the equation (0.01 − x)x = 2.0 × 10 −8, and the assumption that x
is much smaller than 0.01, determine the (approximate) value of x
without setting up a quadratic equation.
Graphs
18. Al Berta makes widgets for The Exploitation Co. of Edmonton and is
paid a basic hourly wage of $B per hour, plus a bonus which depends on
the number of widgets he produces each hour. Some examples of Al’s
total hourly pay ($T) and the number of widgets produced per hour (n)
are given below.
Widgets/hour (n)
100
120
150
170
210
250
Total hourly pay ($T)
4.70
4.94
5.30
5.54
6.02
6.50
On the graph paper provided, plot a graph of Al’s total hourly pay
(y axis) against the number of widgets produced per hour (x axis).
From the graph determine:
a.
Al’s basic hourly wage (i.e., how much is he paid per hour even if he
does not produce any widgets).
b. the bonus paid by The Exploitation Co. for each widget that Al
produces.
c.
the number of widgets that Al must produce in order to earn
$3.80 per hour.
d. Al’s total hourly pay if he produces 220 widgets per hour.
19. Write an equation that shows the relationship between Al’s total hourly
wage and the number of widgets produced per hour
The Metric System
20. Convert 12.5 mL to litres and 0.025 kg to grams.
***END OF QUESTIONNAIRE**