Most of the material we covered since the first mid term is
similar to what we did up to the first midterm,
but the methods are different .
It is also essential to be familiar with linear and
quadratic expressions , and the associated formulas.
As always, please show all your work in order to receive full credit.
Main Skills to Review:
1. Be able to find a linear formula from an English description. Phrases to
watch for:
“…is a linear function of…”or “…has a straight line graph…”
“Items sell for $p each” (interpret: TR is linear with slope p )
“It costs you $c to make each Item” (interpret: TC is linear with slope c)
”for each increase in order size by one item, you reduce the price by $d per
item”
. (interpret: price p(q) is linear with slope –d) (see WS 3 and 12)
“has a constant rate of change c ” (read: “linear function, with slope c”)
2. Given a formula for distance D(t), find formulas for ATS(t), and for AS over
an interval of
specified length (WS 11)
3. Given a formula for price per item (in terms of q), you should be able to
find a formula for TR(q).
4. Given a formula for TR(q), you should be able to find formulas for AR(q) and
MR(q). Vice versa,
given AR(q), know how to find TR(q).
5. Given a formula for TC(q), you should be able to find FC and formulas for
VC(q), AC(q),
AVC(q), and MC(q). Vice versa, given one of: FC and VC(q), or AC(q), or FC and
AVC(q), know
how to find TC(q).
6. Understand that BEP is
i. The smallest value of AC(q)
(so, if AC is a quadratic in q, then BEP is the “y”-coordinate of the
vertex)
ii. the “y”-coordinate of the point where AC and MC intersect.
7. Understand that SDP is:
i. smallest value of AVC(q)
(so, if AVC is a quadratic in q, …)
ii. the “y”-coordinate of the point where AVC and MC intersect.
8. If you have formulas for MR and MC and you want to find the quantity that
maximizes the profit,
set MR=MC and solve for q. (If you get two positive quantities , remember that
the profit is
maximized at the transition from MR>MC to MR<MC.) Round up to next whole number
of units .
9. Know when and how to use the vertex formula .
Some typical questions:
• Find the time/quantity at which <some quadratic function> is
largest/smallest/highest/ lowest /maximized/minimized.
Give the “x”- coordinate of the vertex .
(if you’re maximizing the profit, round off to the nearest whole number
quantity)
• Find the largest/smallest/highest/lowest/maximal/minimal value of <some
quadratic
function>
Give the “y”-coordinate of the vertex.
• Find the largest interval on which <some quadratic function> is
increasing/decreasing.
10. Know when and how to apply the quadratic formula (to solve quadratic
equations in standard
form: ax2+bx+c=0).
11. Know how to obtain the formula for profit given formulas for price per item
and for average cost
(WS14).
12. Understand the area-under-the-graph rectangle function, how to find its
formula, and how to
interpret it in a specific example. For instance:
• If the function is price per item, then taking areas of rectangles under it
gives what function??
• If the function is average cost, then taking areas of rectangles under it
gives what function??
• If the function is average revenue, then taking areas of rectangles under it
gives what
function??
• Etc (can you think of other examples? What’s the pattern?)
13. Know how to compute the average trip speed and the total distance traveled
from a given linear
formula of the instantaneous speed (WS 16)
