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MTH 150 Prerequisite Skills Name: _______________________ Initial Skills Packet Welcome to Calculus! Calculus is a lively, dynamic and interesting subject that touches nearly every discipline. Calculus influences the technical (engineering, biology, chemistry, physics, medicine, computer science, etc.) as well as the not-sotechnical (business, education, psychology, etc.) Unfortunately, learning Calculus in the traditional sense is simply impossible without a thorough grasp of both Algebra and Trigonometry. What follows are some sample problems that you should be able to do BEFORE entering Calculus. It is important to understand that these problems do not serve as the only problems that must be mastered. Rather, it should give you an idea of the types of things you should have internalized at the completion of a solid Algebra and Trigonometry sequence. Completing this Sample Packet with 60-70% accuracy is important (the other 3040% will probably “come back” as you learn Calculus). Remember that this is just a sample. The actual exam you take next time will be much shorter in length but will test the same basic core material. No calculators are allowed on the exam. Do your work on a separate sheet of paper and provide answers in the spaces given. ARITHMETIC/NUMERICAL REASONING 1 2 4 1. Simplify . 2 3 5 2. Is __________________ 8 103 a large or small number? (Circle one) 2 105 LARGE SMALL 3. Fill in the blanks below with the narrowest estimate possible. Use whole numbers (positive or negative) that are one unit apart. Example: ______ < 4 < ______ 5 7 (a) ______ < cos < ______ 10 (b) ______ < log 4 30 < ______ (c) ______ < e 1 < ______ Solution: 0 4 1 5 ELEMENTARY ALGEBRA 1 2x 4. Express as a single fraction. x 1 x 3 __________________ 5. Find the exact solution(s) to 2 x2 8x 7 6. ____________ 6. Find the equation of the line passing through 1, 2 and 4, 5 . ____________ 7. Write 2x 5 without negative exponents. ____________ 8. Factor the following expressions. If prime, so state. (a) 3x2 3x x 1 (a) ____________________ (b) x3 x2 x 1 (b) ____________________ (c) 2 x2 3x 4 (c) ____________________ (d) x 2 25 (d) ____________________ (e) x 2 25 (e) ____________________ (f) 3x4 5x2 2 (f) ____________________ (g) 8 y 3 27 (g) ____________________ ADVANCED ALGEBRA & FUNCTIONS 9. Given that f x 2 x 2 5x 6 and g x x 4 , find and/or simplify the following: (a) f 1 (a) ____________ (b) g 10 (b) ____________ (c) f x h (c) ____________ (d) g a b (d) ____________ (e) f g x (e) ____________ (f) g f x (f) ____________ 10. Simplify xh x so that no radicals appear in the numerator of the fraction. h ____________________ 11. Simplify the complex rational expression 1x . h 1 xh ____________________ TRIGONOMETRY 12. Evaluate (a) sin 4 (a) ______________ (b) tan 6 (b) ______________ (c) cos 3 (c) ______________ 3 13. Evaluate (a) tan 1 3 (a) ______________ 2 (b) arcsin sin 3 (b) ______________ 2 (c) sin arcsin 3 (c) ______________ MISCELLANEOUS 14. State as TRUE or FALSE. Assume all expressions denote real numbers. (a) ____________ x2 y 2 x y (b) ____________ sin 2 cos2 1 for any angle . (c) ____________ ln A B ln A ln B (d) ____________ ln A p p ln A (e) ____________ sin 100 sin for any angle . (f) ____________ ab a b (g) ____________ arcsin sin x x for any number x . (h) ____________ Given any number x , x 2 x . (i) ____________ e A B e AeB (j) ____________ (k) ____________ x m n xm x y n x y (l) ____________ x1/ 2 x (m) ____________ A function may have two x-intercepts. (n) ____________ A function may have two y-intercepts. (o) ____________ For any function f , f 3 2 f 3 f 2