Summer Assignment for Calculus Students

SUMMER ASSIGNMENT FOR CALCULUS STUDENTS

Name: ______

SHOW WORK on a separate paper please.

(A) Factor and check

1) x2─ 5x ─ 84 2) x2 + 21x ─ 100

3) x2─ 19x + 88 4) x2 + 17x +72

5) 49 ─ x2 6) x2 + 7x

7) x3 + x2─ 56x 8) 3x3 ─ 48xy2

9) 6x3 + 9x2 +10x + 15 10) 8x3 + 4x2 ─ 10x ─ 5

11) x4 ─ 14x2 + 45 12) + x.25 ─ 90

13) + + 12

(B)Solve

14) 2(3x + 6) ─ (5x ─ 2) = 4(x + 3)─ 16 15) x2 + 23x = 50

16) x2 = 7.3x 17) x2 + 20 = ─ 8x

18) 3x2 ─ 7x = 9 19) x ─ = ─ 1

20) = 21) +2 = x ─ 3

22) ─ 2 23) = 27

24) 6x-1 + 4 = 25) =

26) 8cosθ =4 ; 0θ 27) sin θ ─ 5 = ─ 4; 0θ

(C) Solve for y

28) xy + y = 4 ─ x 29) = 4x

30) = x + 2 31) F = G

D) EXACT VALUES ONLY (no decimals)

32) sin 33) cos 34) tan

35) cos (─ ) 36) cot 37) 2cos

E) Find all the missing sides and angles using only trigonometry.

38) A c = 16, , B = 2

C B

39) B a = 6, C = , A = 4

C A

(F) Change degrees to radians or vice-versa.

40) 4 41) 42)

43) 7 44) 45)

(G) Simplify: No negative exponents in answers

46) 47)

48) 5 (4) 49)

50) 51)

52) 6• 4 53)

54)

(H) Write an equation of the line that meets the given conditions.

This is a VERY important skill for Calculus.

Either y = mx + b or y ─ y1 = m(x ─ x1) is ok.

55) Slope is 4 and goes through (6,-2)

56) Contains (2, 8) and (5,20)

57) Contains (-3, 9) and is // to y = 7x + π

58) Goes through (1, 12) and is perpendicular to y = -3x ─ 4.2

59)Contains (5, 0) and is parallel to the line that goes through (1, 9) and (-1, 13)

60) Contains (3, 0) and is normal to the line that goes through (0, 2) and (3, 6)

(I)Solve:

61) 5x + 2y = 24

4x +3y = 15

62) x + y = 10

─ = 20