PRE-CALCULUS B FINAL REVIEW NAME______
Work out problems in your notebook or on a separate piece of paper.
CHAPTER 5
Simplify each to one trig word or a number:
(1) (2)
(3) (4)
(5) (6)
(7) (8)
Find the exact value of each using a sum or difference formula:
(9) (10)
(11)
(a) (b) (c)
(12)
(a) (b) (c)
(13) Find the exact value of using a half -angle formula.
Solve each equation for :
(14) (15)
(16) (17)
Use a calculator to solve each equation correct to 4 decimal places for :
(18) (19)
CHAPTER SIX
(20) Solve the triangle: A =,a = 10, b = 14.
(angles to the nearest degree and sides to the nearest tenth)
(21) Solve the triangle: A =, b = 11, c = 15
(angles to the nearest degree and sides to the nearest tenth)
(22) Solve the triangle: a = 18, b = 14, c = 22
(angles to the nearest degree)
(23) Find the area of the triangle with A = , b = 19 miles, c = 7 miles
(answer to the nearest square unit)
(24) Find the area of the triangle with a = 8 yards, b = 12 yards, c = 15 yards.
(answer to the nearest square unit)
(25) Give the 3 other main polar coordinates for
(26) Write each polar coordinate as a rectangular coordinate. Exact answers.
(a) (b)
(27) Write each rectangular coordinate as a polar coordinate. Exact answers.
Keep r and positive. Use radians.
(a)(b)
(28) Write each rectangular equation in polar form. Solve each for r.
(a) 7x + 2y = 12(b) x2 + y2 = 49
(29) Write each polar equation in rectangular form. Simplify your answers.
(a) (b)
(30) Write the complex number -5 + 5 in polar form.
(31) Write the product of z1z2 if z1 = and z2 = .
Answer in polar form.
(32) Find and answer in rectangular form
(33) Find all of the complex cube roots of 27 and answer in rectangular form.
(34) If u = 5i + 7j and v = 10i – 3j, find:
(a) (b) 2u - 7v(c) u • v
(d) the angle, to the nearest tenth of a degree, between u and v
(e) the unit vector in the same direction as v
(35) If u = 5i – 10j, v = 5i + 10j, w = -4i - 2j, x = 8i + 4j
(a) Name the pairs of parallel vectors(b) Name the pairs of orthogonal vectors
(36) Let v be the vector from initial point P1 = (-2, 12) to terminal point P2 = (4, -7).
Write v in terms of i and j
(37) Two forces, F1 with magnitude 40 pounds and direction NE , and F2 with
magnitude 45 pounds and direction NE act on an object. Find the magnitude and the
direction angle of the resultant force. Express both answers to the nearest whole number.
(38) A person is pulling a wagon with a force of 42 pounds. How much work is done in moving the
wagon 58 feet if the wagon’s handle makes an angle of with the ground?
Answer to the nearest tenth.
CHAPTER 1.9, 9.1, 9.2, 9.3, 9.5
(39) Find the distance between (10, -2) and (7, 4)
(40) Find the midpoint of the line segment joining (1, 5) and (11, -12)
(41) A circle has center (-6, 5) and radius 9. Give the equation.
(42) Give the center and radius of the circle with equation .
(43) Find the vertex, focus and directrix of the parabola with the equation
(44) Find the equation of the parabola with vertex (3, -5) and directrix x = 10
(45) Find the center, vertices, co-vertices, and foci of the ellipse with the equation
(46) Find the standard equation of an ellipse if the major axis has endpoints (-5, 6) and (-5, -2) and
the minor axis has endpoints (-7, 2) and (-3, 2).
(47) Find the standard equation of an ellipse with equation 4x2 + 3y2 – 40x + 18y – 5 = 0
(48) Find the vertices, foci and asymptotes of the hyperbola with equation
(49) Eliminate the parameter t to find the rectangular equation for each:
(a) x = 3t – 10, y = t2(b) x = 2 - 7cost, y = 6 + 2sint
CHAPTER TEN
(50) Give the 1st three terms of the sequence with general term an = (-1)n(n + 4)
(51) Give the 1st three terms of the sequence with general term an =
(52) Give the 1st three terms of the sequence with recursion formula a1 = 8 and an = 5an-1– 2
(53) Find the indicated sum of
(54) Find the indicated sum of
(55) Express the sum using summation notation:
(56) Express the sum using summation notation: 75 + 85 + 95 + . . . 995
(57) Give the 1st 3 terms of the arithmetic sequence with a1 = 8 and d = -4
(58) Give the 1st 3 terms of the arithmetic sequence with a1 = 3 and an = an-1+ 9
(59) Find a40 of the arithmetic sequence with a1 = -50 and d = 17
(60) Give the formula for the general term of the arithmetic sequence 3, 11, 19, . . .
(61) Find the sum of the 1st 35 terms of the arithmetic sequence 3, 14, 25, . . .
(62) Find the sum of the even integers between 29 and 117.
(63) Give the 1st three terms of the geometric sequence with a1 = -20 and r =
(64) Give the 1st three terms of the geometric sequence with a1 = -10 and an= -2an-1
(65) Find a18 of the geometric sequence with a1 = and r = -4
(66) Give the formula for the general term of the geometric sequence 9, , , . . .
(67) Find the sum of the 1st 12 terms of the geometric sequence , 2, 16, . . .
(68) Find the sum of the infinite geometric series 2 + + + . . .
(69) Find the 7th term of the expansion of (x2 + 3y)15 and simplify your answer.
(70) Find the 6th term of the expansion of (4x – y)11 and simplify your answer.
(71) Amy has 12 pairs of different jeans, 15 different shirts and 8 different pairs of shoes.
How many different jeans-shirt-shoe outfits does she have to choose from?
(72) How many different ways can 12 people line up to get into the theater?
(73) If 20 swimmers compete in a race, in how many different ways can prizes be awarded for
1st, 2nd and 3rd?
(74) A secret code has 2 letters followed by 2 digits. The 1st letter has to be A or B, the 2nd letter
can be any letter, the 1st digit cannot be a 0 or 9 and the last digit has to be different from the
other digit. How many different secret codes can be made?
(75) If 22 students enter an essay contest, in how many ways can four “Certificate of Merit”
awards be given?
(76) How many different 5-card hands can be dealt using a standard deck of 52 cards?
(77) A test has 15 multiple choice questions with each question having A, B or C as the 3 choices
of answers. If a person selects one of these choices for each question, in how many ways can
the person answer all the questions?
(78) A school bus has 7 seats left for a field trip and 20 students want to go. How many different
groups of seven can be chosen to go on the bus?
(79) Twelve students volunteer to be in charge of the refreshment committee or the clean-up
committee for the next dance. In how many ways can 2 of the students be selected if each
one is put in charge of one of these committees?
(80) A card is drawn randomly from a standard deck of 52 cards. Find the probability of drawing
a 2 or a diamond.
(81) A card is drawn randomly from a standard deck of 52 cards. Find the probability of drawing
a card that is not an eight nor a picture card.
(82) Two dice are rolled. What is the probability that the sum will be 2 or 5?
(83) What is the probability of rolling a die and getting a 2 and then rolling it again and getting
an even number?
CHAPTER 8
Find the determinant of each matrix.Find the multiplicative inverse of each matrix
(84) (85). (86) (87)
Find the product of the matrices.
(88) (89)
(90). If the following system of equations was solved using Cramer’s Rule, a. write the determinant that would be used in the numerator for each variable. b. What determinant would be in the denominator? DON’T SOLVE.
4x + 3y – z = 30
3x – 2y +4z = 20
2x + 5y –6z = 18
CHAPTER 11
Find each limit.
(91) (92) (93)
(94) (95) (96)
The End!
If you did the entire review and UNDERSTAND how to do the problems you should get an A!!!!
ANSWERS:
(1) (2) (3) (4)
(5) 1(6) (7) (8)
(9) (10) (11a) (11b)
(11c) (12a) (12b) (12c) -3
(13) (14) (15) (16)
(17) (18) x = 1.2179, 5.0653(19) x = 1.8491, 4.9907
(20) B1 =, C1 =, c1 = 18.2 and B2 =, C2 =, c2 = 5.4
(21) a = 18.9, B =, C =(22) A = , B =, C =
(23) 56 sq miles(24) 48 sq yards(25) , ,
(26a) (26b) (27a) (27b)
(28a) (28b) (29a) x = 12(29b) x2 + y2 = 6x – 2y
(30) (31)
(32) (33)
(34a) (34b) -60i + 35j(34c) 29(34d)
(34e) i + j(35a) w, x(35b) u, w and u, x
(36) 6i – 19j (37)magnitude: 82 lbs.(38) 2207.8 foot-pounds
=
(39)
(40) (6, -3.5)(41) (x + 6)2 + (y – 5)2 = 81
(42) center: (6, -4) radius: 7(43) vertex: (-2, 6) focus: (-2, 10)
directrix: y = 2
(44) (y + 5)2 = -28(x – 3)(45) center: (7, -1) vertices: (2, -1), (12, -1)
co-vertices: (7, 2), (7, -4)
foci: (3, -1), (11, -1)
(46) (47)
(48) vertices: (6, 0), (-6, 0)(49a) (49b)
foci:
asymptotes:
(50) -5, 6, -7(51) (52) 8, 38, 188(53) 8
(54) 30(55) (56) (57) 8, 4, 0
(58) 3, 12, 21(59) 613(60) an = 8n – 5(61) 6650
(62) 3212(63) -20, -8, (64) -10, 20, -40(65) -8, 589,934,592
(66) an = 9(67) 2,454,267,026(68) 5(69) 3,648,645x18y6
(70) -1,892,352x6y5(71) 1440(72) 479,001,600(73) 6840
(74) 3744(75) 7315(76) 2,598,960(77) 14,348,907
(78) 77,520(79) 132(80) (81)
(82) (83)
84) 1185) –3086) 87) 88)
89)90)a. Dx =Dy = Dz =
90)b. 91) 92) –593) –194) 20
95) 96)