Download Calculus w/Applications Prerequisite Packet

Calculus w/Applications Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
The problems in this packet are designed to help you review topics from previous math
courses that are important to your success in Calculus with Applications.
It is important that you take time during summer break to review the math concepts you learned this past
school year. In order to ensure that you are appropriately placed in, and prepared for Calculus with
Applications, you may be required to take a course pre-assessment when you return to school next year.
It is YOUR responsibility to prepare for the course pre-assessment!
The specific math concepts that will be assessed are listed on the front page of this summer packet. To
prepare for the course pre-assessment, you are encouraged to complete this summer math packet. Please
note, this summer math packet will not be collected or graded. Instead, the course pre-assessment will be
used to measure your knowledge of the prerequisite skills.
If you have any questions, please feel free to email the resource teacher, [email protected]
Concepts To Be Assessed
on the Calculus with Applications Course Pre-assessment.
Students should be able to:
 Solve linear, quadratic, cubic, exponential, logarithmic, radical, rational, trigonometric,
piecewise equations.
 Simplify and evaluate algebraic expressions, rational expressions and complex fractions.
 Graph and identify properties of linear, quadratic, cubic, exponential, logarithmic,
radical, rational, trigonometric, and piecewise functions.
 Simplify and evaluate trigonometric expressions and identities.
 Apply rules of function notation, function composition and inverse functions.
 Write the equation of a linear function in slope-intercept and point-slope form.
 Use summation notation to express and determine the value of the sum of a sequence.
Calculus w/Applications Prerequisite Packet
Updated 6/2014
Paint Branch High School Math Department
Name _____________________________________Date ___________________ Pd _______
1. Simplify.
a)
x4
2
x  3x  4
b)
x3  8
x2
c)
5 x
x 2  25
a) sin 2 x + cos 2x = _____________________________
2. Trigonometric Pythagorean Identities:
b) 1 + tan2x = _____________________________
c) cot2x + 1 = _____________________________
3. Simplify each expression. Write answers with positive exponents where applicable:
a)
1
1

xh x
2
3
2
2
b) x
10
x5
c)
5
12 x 3 y 2
18 xy 1
3
1
100
d) (5a 3 )(4a 2 )
e) (4a 3 ) 2
f) log
g) ln e 7
h) log 1 8
i) x 2 ( x  x 2  x 2 )
2
3
5
Calculus w/Applications Prerequisite Packet
Updated 6/2014
Paint Branch High School Math Department
4. Given: f(x) = {(3, 5), (2, 4), (1, 7)}, g ( x)  x  3 and h(x) = x 2  5 , determine:
a) h(g(x))
b) g(h(-2))
c) f -1(x)
d) g-1(x) by switching _____ and then solving for
_____. (Fill in the blanks and find the inverse.)
5
5. Expand and simplify:
 (3n  6)
n2
6. Without a calculator, determine the exact value of each expression:
a)
sin
e) cos

2

3
b) sin
3
4
c) cos 
f) tan
7
4
g) tan
2
3
d) cos
h) tan
7
6

2
Calculus w/Applications Prerequisite Packet
Updated 6/2014
Paint Branch High School Math Department
7. Using EITHER the slope/intercept (y = mx + b) or the point slope y  y1  m( x  x1 )) form of a line,
write an equation for the lines described: SHOW ALL WORK
a) with slope -2, containing the point (3, 4)
b) containing the points (1, -3) and (-5, 2)
c) with slope 0, containing the point (4, 2)
d) parallel to 2x – 3y = 7 and passes through (5,1)
e) perpendicular to the line in problem #7 a, containing the point (3, 4)
Calculus w/Applications Prerequisite Packet
Updated 6/2014
Paint Branch High School Math Department
8. For each function, make a neat sketch, putting numbers on each axis. Determine the Domain and
Range for each function. Also, for parts d, e, f and g , write the equations of the asymptotes
a) y = sin x
d) y 
x4
x 1
b) y  x 3  2 x 2  3x
c) y  x 2  6 x  1
e) y = ln x
f) y  e x
Calculus w/Applications Prerequisite Packet
Updated 6/2014
g) y 
Paint Branch High School Math Department
1
x
h) y 
j) y  x  3  2
x2  4
x2
k) y  x  4
i) y  3 x
l)
x 2 if x < 0
y = x + 2 if 0 < x < 3
4 if x > 3
9. If f(x) = x2 -2x, determine
a) f(x + h)
b)
f(x + h) – f(x)
c)
f ( x  h)  f ( x )
h
Calculus w/Applications Prerequisite Packet
Updated 6/2014
Paint Branch High School Math Department
10. Solve for x, where x is a real number. Show the work that leads to your solution:
a) 2 x 2  5x  3
b) ( x  5) 2  9
c) (x + 3)(x – 3) > 0
d) log x + log(x – 3) = 1
e) x  3 < 7
f) ln x = 2t – 3
g) 12 x 2  3x
h) 27 2 x  9 x3
i) e3x = 5