AP Calculus Review Worksheet This packet is a review of the entering objectives for AP Calculus and is due on the first day back to school. It is to be done neatly and on a separate sheet of paper. Have a great summer! I. Simplifying Rational Expressions
THEOREM 2.1.2
If A is an n x n triangular matrix (upper triangular, lower triangular, or
diagonal), then det(A) is the product of the entries on the main diagonal of
the matrix.
Works for 2x2 and 3x3 matrices only
THEOREM 2.2.1 Let A be a square matrix. I
UNCERTAINTY AND LAB MEASUREMENTS
ALL measurements posses some level in uncertainty in their value. When you make a measurement ( x ) , you must estimate the ABSOLUTE UNCERTAINTY ( x ) in your measurement. This error in measurement is based on how well yo
SIGNIFICANT FIGURES Significant Figures: Many of the numbers in science are the result of MEASUREMENTS and therefore are subject to some degree of EXPERIMENTAL UNCERTAINTY. A rough indication of the uncertainty is implied by the number of digits used. EXA
AP CALCULUS
PRECALCULUS SUPPLEMENTARY VIII
Problems: 1) a)
e x e x 3 =. 2 4 1 x Hint: Note that e = x . Let u = e x and then e solve for u.
Solve for x:
x y = 1 . Using the definition of each a b hyperbolic trigonometric function given in part b), show t
AP CALCULUS
PRECALCULUS SUPPLEMENTARY VII Problems: 1) If 4 x 2 12 x + k is a perfect square, find the value of k.
a 2 2 2) Show that ( log a ) ( log b) = log( ab) log . b
3) If the coefficient of x 2 in the expansion ( x a ) 3x 2 x + 2 is 2 , then what
AP CALCULUS
PRECALCULUS SUPPLEMENTARY VI Problems: 1) From a rectangular piece of cardboard having dimensions a = 3 cm and b = 7 cm , an open box is to be made by cutting out an identical square with side length x from each corner and turning up the sides
AP CALCULUS
PRECALCULUS SUPPLEMENTARY V Problems: 1) Solve the following linear system:
713x + 637 y = 4839 637 x + 713 y = 4611
Hint: You can solve the system using the traditional methods from grade 10 (i.e. elimination, substitution, graphing) however
AP CALCULUS
PRECALCULUS SUPPLEMENTARY IV Problems: 1) Solve the following linear system:
a + b + c + d = 10 b+c+d +e = 9 c+d +e+a = 8 d +e+a +b = 7 e+a +b+c = 6
Hint: Add all the equations simultaneously and back substitute the result into each respective
AP CALCULUS
PRECALCULUS SUPPLEMENTARY III Problems: 1) Simplify: A) 1 x +1 B) x 1 C)
x2 1 x2 + 1 x2 2x + 1 x2 + 2x + 1
( x + 1) 3 ( x 2 + 1)( x 1) ( x 1) 3 ( x 2 + 1)( x 1)
x 1 x +1
D) E)
2) Let line l 1 pass through the points (11) and ( 2,0) and let lin
AP CALCULUS
PRECALCULUS SUPPLEMENTARY II
Problems: 1) A bus travels the first 4.0 km of its route in 15 minutes. How many hours will it take to travel the next 48.3 km if it continues at the same speed? A) 181.1 B) 12.9 C) 3.0 D) 2.5 E) 2.0 2) An antibiot
AP CALCULUS
SUPPLEMENTARY RELATED RATES PROBLEMS:
2 1) If a snowball melts so that its surface area decreases at a rate of 2 cm min , find the rate at which the diameter changes when the snowball has radius 5 cm .
2) Boyles Law states that when a sample o
AP CALCULUS
SUMMER WORKSHOP III Problems: 1) (2004 Nova Scotia Math League, Game 2: Team Question) The parabola y = x 2 meets the parabola
y = x 2 +6 x 4 at two points, P and Q. Find the equation of the line passing through P and Q.
2) (2004 Nova Scotia M
Physics worksheet #1
Vectors, kinematics, dynamics, work and energy
Question #1:
What is the magnitude of the vector 3A - B in the figure above? (a) 3 (b) 4 (c) 5 (d) 2 (e) 6
Question #2: When a car's kinetic energy increases 9 times, what happens with
Physics worksheet #2
Electricity, DC circuits, magnetism
Question #1:
Three point charges of charge +Q are placed as shown above. At what point will a negative charge experience a force toward the bottom of the page?
(a) A (b) B (c) C (d) D (e) E
Questi
NAME_ SPH3U3/6 WORK, POWER & ENERGY TEST A
MULTIPLE CHOICE: Place your answer on the LEGAL SIZE paper.
1) (1K) An object with mass m and speed v 0
directed to the right strikes a wall and rebounds with speed v 0 directed to the left. The change in the obj
NAME_ SPH3U3/6 SIMPLE MACHINES QUIZ A
FULL SOLUTION: Answer all questions with COMPLETE STATEMENTS on the LEGAL SIZE paper provided. 1) A mover wishes to load a truck with a piano that has a mass of 400 kg. The height above the ground (h) of the trucks lo
NAME: SOLUTIONS SPH3U3/6 KINEMATICS TEST B
MULTIPLE CHOICE: Place your answer on the LEGAL SIZE paper. 1) (1K) Karen travels a 10.0 km path to and from school every school day. If there are 39 school weeks, how many meters does Karen travel? Assume that t
NAME_ SPH3U3/6 KINEMATICS TEST B
MULTIPLE CHOICE: Place your answer on the LEGAL SIZE paper. 1) (1K) Karen travels a 10.0 km path to and from school every school day. If there are 39 school weeks, how many meters does Karen travel? Assume that there are f
NAME: SOLUTIONS SPH3U3/6 KINEMATICS TEST A
MULTIPLE CHOICE: Place your answer on the LEGAL SIZE paper. 1) (1K) The length, width and height of a box is 2.0 cm 8.12 cm 0.013 m respectively. The volume of the box with the correct number of significant figur
NAME_ SPH3U3/6 KINEMATICS TEST A
MULTIPLE CHOICE: Place your answer on the LEGAL SIZE paper. 1) (1K) The length, width and height of a box is 2.0 cm 8.12 cm 0.013 m respectively. The volume of the box with the correct number of significant figures is A) B
NAME_ SPH3U3/6 DYNAMICS TEST A
MULTIPLE CHOICE: Place your answer on the LEGAL SIZE paper. 1) (1K) When a parachutist jumps from an airplane, he eventually reaches a constant velocity called the terminal velocity. This means that A) the acceleration is eq
FLUID MECHANICS PROBLEMS II SOLUTIONS
1) B; The pressure experienced by the diver is the sum of the atmospheric pressure and the pressure exerted by the
weight of the water. Hence, P = 1 0 1 . 3 1 0 P = 1 .9 9 1 0
5 3
P a + 1 0 0 0 k g 3 9 .8 m 2 ( 1 0 m
FLUID MECHANICS PROBLEMS I SOLUTIONS
1) a) The buoyant force provides the upwards thrust that essentially reduces the weight of the object. Hence, F B = ( 3 .0 1 .4 ) N F B = 1 .6 N .
b) F
B
= w a te r V
(
)(
w a te r
)( g )
1 . 6 N = 1 0
3
kg
V m 3
(
NAME_ SPH3U3/6 FLUID MECHANICS TEST B
FULL SOLUTION: Answer all problems with COMPLETE STATEMENTS on the LEGAL SIZE paper provided.
1) A solid concrete block of volume V weighs 67.6 N in air and when completely
immersed in water the right). a) (1K, 1C) Wh
NAME_ SPH3U3/6 FLUID MECHANICS TEST A
FULL SOLUTION: Answer all problems with COMPLETE STATEMENTS on the LEGAL SIZE paper provided. kg which is 30 cm thick floating in 1) (3K, 1C) What is the minimum area of a block of ice i c e = 9 1 7 m 3 kg sea water s
AP CALCULUS
SUMMER WORKSHOP II Problems: 1) Solve for x: a) b) c) d) e) f) g) h) i)
x 4 17 x 2 + 16 = 0
6) a) Show that ( cos x )( cos 2 x )( cos 4 x )( sin x ) =
1 sin 8 x 8
b) Find the exact values of
2 4 cos cos cos 7 7 7 2 4 cos cos cos 9 9 9
x 3 + 5x
AP CALCULUS
SUMMER WORKSHOP I Problems: 1) Consider the points A( 2,3) , B( 5,6) , C( 2,3) and D( k ,2) . Find the value of k so that a) AB is parallel to CD b) AC is perpendicular to BD 2) Find the perimeter of the triangle formed by the coordinate axes
OPERATIONS WITH VECTORS
1) Let u = ( 9,2) and v = ( 3,9) . Find u v . A) 45 B) 23 C) (12,11) D)
4) In which of the following diagrams do the vectors satisfy a + b + c = 0 ? A) B) C)
( 27,18)
E) 132 2) Let u = ( 9,0,1) and v = ( 9,9,9) . Find u v . A
NAME_
MCV4U0 OPERATIONS WITH VECTORS TEST A
ANSWER ALL QUESTIONS on LEGAL SIZE PAPER. MULTIPLE CHOICE: Choose the ONE BEST answer to each question. 1) (1K) Let u = 2 j and v = 2 i + 4 j . What is
u v
4)
(1K) Which of the following statements is INCORRE