Winter 2010
Math 2A
Course Code 44240
Midterm 2
Wednesday, March 3rd, zOtO
Ner,rr:
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Student ID number:
Email address:
Inslructions:
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This exam consists of 8 problems and is out of 63 points.
Neither a calculator nor notes is allowed.
Yo
Math 2B : Midterm # 2 Sample
This exam consists of 5 questions and 90 total points. The point value of each problem is indicated. Read
directions for each problem carefully. Please show all work needed to arrive at your solutions. Clearly indicate
your fi
Decimals
mc-TY-decimals-2009-1
In this unit we shall look at the meaning of decimals, and how they are related to fractions. We
shall then look at rounding to given numbers of decimal places or signicant gures. Finally we
shall take a brief look at irrati
Differentiation by
taking logarithms
mc-TY-ditakelogs-2009-1
In this unit we look at how we can use logarithms to simplify certain functions before we dierentiate them.
In order to master the techniques explained here it is vital that you undertake plenty
Trigonometric
Identities
mc-TY-trigids-2009-1
In this unit we are going to look at trigonometric identities and how to use them to solve
trigonometric equations.
In order to master the techniques explained here it is vital that you undertake plenty of pra
Conic sections
mc-TY-conics-2009-1
In this unit we study the conic sections. These are the curves obtained when a cone is cut by
a plane. We nd the equations of one of these curves, the parabola, by using an alternative
description in terms of points whos
Cubic equations
mc-TY-cubicequations-2009-1
A cubic equation has the form
ax3 + bx2 + cx + d = 0
where a = 0
All cubic equations have either one real root, or three real roots. In this unit we explore why this
is so.
Then we look at how cubic equations ca
Cosecant, Secant &
Cotangent
mc-TY-cosecseccot-2009-1
In this unit we explain what is meant by the three trigonometric ratios cosecant, secant and
cotangent. We see how they can appear in trigonometric identities and in the solution of
trigonometrical equ
Differentiation of xn.
mc-TY-dixtothen-2009-1
In this unit we derive the result, from rst principles, that if y = xn then
dy
= nxn1 .
dx
The result is then illustrated with several examples.
In order to master the techniques explained here it is vital tha
The double angle
formulae
mc-TY-doubleangle-2009-1
This unit looks at trigonometric formulae known as the double angle formulae. They are called
this because they involve trigonometric functions of double angles, i.e. sin 2A, cos 2A and tan 2A.
In order t
Expanding and
removing brackets
mc-TY-expandingbrackets-2009-1
In this unit we see how to expand an expression containing brackets. By this we mean to rewrite
the expression in an equivalent form without any brackets in. Fluency with this sort of algebrai
Exponential and
logarithm functions
mc-TY-explogfns-2009-1
Exponential functions and logarithm functions are important in both theory and practice. In this
unit we look at the graphs of exponential and logarithm functions, and see how they are related.
In
Fractions: multiplying
and dividing
mc-TY-fracmult-2009-1
In this unit we shall see how to multiply fractions. We shall also see how to divide fractions by
turning the second fraction upside down.
In order to master the techniques explained here it is vit
Fractions: adding and
subtracting
mc-TY-fracadd-2009-1
In this unit we shall see how to add and subtract fractions. We shall also see how to add and
subtract mixed fractions by turning them into improper fractions.
In order to master the techniques explai
Factorising quadratics
mc-TY-factorisingquadratics-2009-1
An essential skill in many applications is the ability to factorise quadratic expressions. In this unit
you will see that this can be thought of as reversing the process used to remove or multiply-
Fractions basic ideas
mc-TY-fracbasic-2009-1
In this unit we shall look at the basic concept of fractions what they are, what they look like,
why we have them and how we use them. We shall also look at dierent ways of writing down
the same fraction.
In or
Differentiation from
rst principles
mc-TY-rstppls-2009-1
In order to master the techniques explained here it is vital that you undertake plenty of practice
exercises so that they become second nature.
After reading this text, and/or viewing the video tuto
The sum of an innite
series
mc-TY-convergence-2009-1
In this unit we see how nite and innite series are obtained from nite and innite sequences.
We explain how the partial sums of an innite series form a new sequence, and that the limit
of this new sequen
Completing the square
mc-TY-completingsquare2-2009-1
In this unit we consider how quadratic expressions can be written in an equivalent form using
the technique known as completing the square. This technique has applications in a number of
areas, but we w
Trigonometric
equations
mc-TY-trigeqn-2009-1
In this unit we consider the solution of trigonometric equations. The strategy we adopt is to nd
one solution using knowledge of commonly occuring angles, and then use the symmetries in the
graphs of the trigon
Volumes of solids of
revolution
mc-TY-volumes-2009-1
We sometimes need to calculate the volume of a solid which can be obtained by rotating a curve
about the x-axis. There is a straightforward technique which enables this to be done, using
integration.
In
Trigonometric ratios
of an angle of any size
mc-TY-trigratiosanysize-2009-1
Knowledge of the trigonometrical ratios sine, cosine and tangent, is vital in very many elds of
engineering, mathematics and physics. This unit explains how the sine, cosine and t
Trigonometrical ratios
in a right-angled
triangle
mc-TY-trigratios-2009-1
Knowledge of the trigonometrical ratios sine, cosine and tangent, is vital in very many elds of
engineering, mathematics and physics. This unit introduces them and provides examples
The vector product
mc-TY-vectorprod-2009-1
One of the ways in which two vectors can be combined is known as the vector product. When
we calculate the vector product of two vectors the result, as the name suggests, is a vector.
In this unit you will learn
The addition formulae
mc-TY-addnformulae-2009-1
There are six so-called addition formulae often needed in the solution of trigonometric problems.
In this unit we start with one and derive a second from that. Then we take another one as given,
and derive a
Integrating
algebraic fractions 1
mc-TY-algfrac1-2009-1
Sometimes the integral of an algebraic fraction can be found by rst expressing the algebraic
fraction as the sum of its partial fractions. In this unit we will illustrate this idea. We will see
that
Integrating
algebraic fractions 2
mc-TY-algfrac2-2009-1
Sometimes the integral of an algebraic fraction can be found by rst expressing the algebraic
fraction as the sum of its partial fractions. In this unit we look at the case where the denominator
of th
Arithmetic and
geometric progressions
mcTY-apgp-2009-1
This unit introduces sequences and series, and gives some simple examples of each. It also
explores particular types of sequence known as arithmetic progressions (APs) and geometric
progressions (GPs)
The Chain Rule
mc-TY-chain-2009-1
A special rule, the chain rule, exists for dierentiating a function of another function. This unit
illustrates this rule.
In order to master the techniques explained here it is vital that you undertake plenty of practice
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