Calculus w/applications Prerequisite Packet Paint Branch High School Math Department

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1 Updated 6/014 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 have learned this school year. In order to ensure that you are appropriately placed in, and prepared for, the net math course in the sequence of study, you will be required to take a course pre-assessment when you return to school net year. This assessment will be given within the first three days of school. It will be GRADED FOR ACCURACY and count towards your first quarter grade. It is YOUR responsibility to prepare for the course pre-assessment! The specific math concepts that will be assessed are listed below. To prepare for the course pre-assessment, you are encouraged to complete the summer math packet for the course you are taking net year. However, you also have other options. You may choose to review using online tetbook resources or those found in the public library. You may choose to watch video tutorials or even take online practice quizzes throughout the summer. How you choose to prepare for the course pre-assessment is completely up to you! 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 required prerequisite skills Concepts To Be Assessed on the Calculus with Applications Course Pre-assessment. Students should be able to: Solve linear, quadratic, cubic, eponential, logarithmic, radical, rational, trigonometric, piecewise equations. Simplify and evaluate algebraic epressions, rational epressions and comple fractions. Graph and identify properties of linear, quadratic, cubic, eponential, logarithmic, radical, rational, trigonometric, and piecewise functions. Simplify and evaluate trigonometric epressions 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 epress and determine the value of the sum of a sequence.

2 Updated 6/014 Name Date Pd 1. Simplify. a) 4 4 b) 8 c) 5 5. Trigonometric Pythagorean Identities: a) sin + cos = b) 1 + tan = c) cot + 1 =. Simplify each epression. Write answers with positive eponents where applicable: a) 1 1 h b) 10 5 c) 1 y 18y 1 d) ( 5a )(4a ) e) ( 4a ) f) 5 1 log 100 g) 7 ln e h) log 1 8 i) 5 ( )

3 Updated 6/ Given: f() = {(, 5), (, 4), (1, 7)}, g ( ) and h() = 5, determine: a) h(g()) b) g(h(-)) c) f -1 () d) g -1 () by switching and then solving for. (Fill in the blanks and find the inverse.) 5. Epand and simplify: 5 n (n 6) 6. Without a calculator, determine the eact value of each epression: a) sin b) sin c) cos d) 4 7 cos 6 e) cos f) 7 tan g) 4 tan h) tan

4 Updated 6/ Using EITHER the slope/intercept (y = m + b) or the point slope y y1 m( 1)) form of a line, write an equation for the lines described: SHOW ALL WORK a) with slope -, containing the point (, 4) b) containing the points (1, -) and (-5, ) c) with slope 0, containing the point (4, ) d) parallel to y = 7 and passes through (5,1) e) perpendicular to the line in problem #7 a, containing the point (, 4)

5 Updated 6/ For each function, make a neat sketch, putting numbers on each ais. 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 b) y c) y 6 1 d) 4 y e) y = ln f) 1 y e

6 Updated 6/014 g) 1 y h) 4 y i) y j) y k) y 4 l) if < 0 y = + if 0 < < 4 if > 9. If f() = -, determine a) f( + h) b) f( + h) f() c) f ( h) f ( ) h

7 Updated 6/ Solve for, where is a real number. Show the work that leads to your solution: a) 5 b) ( 5) 9 c) ( + )( ) > 0 d) log + log( ) = 1 e) < 7 f) ln = t g) 1 h) 7 9 i) e = 5