Topic 6B Limits
From the last section, we can develop both average and instantaneous speeds using the
In fact, limits are fundamental to all of calculus. In this section, we will give a basic
definition of a limit, and show how it can be ap
Topic 6A Using motion to illustrate the concept of derivatives
While the topics of algebra, logarithms, and trigonometry are of fundamental importance
to the scientist, a wide variety of technical problems cant be solved using only these
The Seneca College Nursing program uses the Health Sciences Placement Network, known as HSPnet
to coordinate student placements. This is a province-wide placement system, which co-ordinates and
manages student placement requests. If you pl
1. Give the coordinates of the points graphed (each box represents 1 unit):
2. Plot the following points on a rectangular coordinate system.
3. Give the quadrant in whi
Topic 4E The Sine Wave as a Function of Time
A sine curve can be generated by rotating a
vector OP (called a phasor) using a constant
angular velocity (rad/s).
Compare the equation
y a sin(bx c) d
y a sin( t ) d
Ex 1) Write the equation for a s
Topic 6F Derivative of a Function Raised to a Power (Chain Rule)
To determine which rule to apply, you must correctly identify the function to be solved.
y (1 2 x)3
- is a power function
- must expand to take derivative
where u is a
Topic 5A: Fundamental Identities
sin csc 1
x2 + y2 = 1
cos2 sin 2 1
cos2 sin 2 1
cos2 sin 2 1 sin
Change to an expression conta
Topic 8A Motion of a Point
1. Rectilinear (straight line) motion
s f t
The first derivative
represents displacement at a given time t.
v f t
represents the instantaneous velocity or
change of displacement with respect to time.
The second der
Chapter Test, pp. 360361 Solutions to Odd Number Problems
A single die can roll a prime in three ways: 2, 3, or 5.
P(one prime) =
P(10 primes) =
Review of Key Concepts, pp. 357359 Solutions to Odd Number Problems
P(not black) = 1 P(black)
3. Answers may vary.
a) P(all classes cancelled) = low
b) P(at least one severe snow
Review of Prerequisite Skills pp. 302-303 Solutions to Odd Number Problems
1. To express a decimal as a percent, multiply by 100. You can achieve this by moving
the decimal point two places to the right.
a) 0.35 = 35%
Section 6.6, pp. 353356 Solutions to Odd Number Problems
a) Not a probability vector; the components do not add to 1.
b) A probability vector; the components add to 1 and all lie between 0 and 1.
c) Not a probability vect
Section 6.5, pp. 340343 Solutions to Odd Number Problems
a) Non-mutually exclusive; a wool sock may be grey.
b) Non-mutually exclusive; a student on the honour roll may have brown eyes.
c) Mutually exclusive; the numbe
Section 6.4, pp. 334335 Solutions to Odd Number Problems
a) Dependent; staying up late may affect performance on the examination.
b) Independent; eating chocolate is unlikely to affect performance at checkers.
Section 6.3, pp. 324326 Solutions to Odd Number Problems
1. The three possible scenarios are F1F2 versus M1M2, F1M1 versus F2M2, and
F1M2 versus F2M1
P(two females are partners) =
3. a )
P(not 2G) = 1
Section 6.2, pp. 318319 Solutions to Odd Number Problems
1. a) Odds against good weather = 2:3
P(good weather) =
3. a) P(sum=12)=
. The odds in favour of rolling 12 with two dice are 1:35.
Section 6.1, pp. 312313 Solutions to Odd Number Problems
P( x ) =
P( x ) =
P(at least one head)= 1 P (three tails)
d) There are two composite numbers, 4 and 6, among the faces of a d
Review of Key Concepts, pp. 296297 Solutions to Odd Number Problems
a) R2, R3, R5, R6, R7, R8
b) R7, R8 c) R5, R8 d) all regions
T = colour TV, C = computer, D = dishwasher. Let the population be 100%.
a) T only, C on
Section 5.3, pp. 286288 Solutions to Odd Number Problems
1. For each coin, you can choose to include it or choose not to include it. Assuming
that you will include at least one coin,
number of sums = 24 1
3. a) n = 22
Section 5.1, pp. 270272 Solutions to Odd Number Problems
1. A = cfw_apple, orange, pear
B = cfw_apple, banana
A B = cfw_apple
A B = cfw_apple, orange, pear, banana
iii) S = cfw_apple, orange, pear, banana
iv) S B = cfw_app
Chapter Test, p. 261 Solutions to Odd Number Problems
1. a) n = 24
c) For each coin toss, there are two possible outcomes: heads or tails, as indicated
on each branch of the tree diagram.
3. a) i) n = 33
ii) n = 3 + 32 + 33
Section 4.5, pp. 256259 Solutions to Odd Number Problems
495 + d = 825
d = 330
f + 825 = 2112
f = 1287
b + 495 = 1287
b = 792
e + 1287 = 3003
e = 1716
a + 792 = 1716
a = 924
h = 3003 + 2
Section 4.3, pp. 245246 Solutions to Odd Number Problems
1. a) the two as, the two ms, and the two ts
b) the two green notebooks and the four white notebooks
c) the 50 chicken sandwiches, the 100 hamburgers, and the 70 plates of Fre