23) Problem: Explain how to determine whether a parenthesis or a square bracket is used when graphing an inequality on a number line.
Solution: a. Parenthesis: indicate a range of values, open interval, I think of parenthesis as being the parent that is more open to given their child toys and bending the rules.
b. Brackets: has limits between two numbers, closed interval, I think of brackets as the stern parent who enforces the rules to the highest degree.
24)Problem: The threepart inequality a < x < b means “a is less than x, and x is less than b.” Which one of the following inequalities is not satisfied by some real number x?
A. 3 < x < 5B. 0 < x < 4
C. 3 < x < 2D. 7 < x < 10
Solution: D, because 10 is less than 7 and x is greater than 7 which also means that x is also greater than 10.
66)Problem: If f(3) = 9.7, identify a point on the graph of f.
Solution: (3,9.7), f(3) is f(x) which means that 3 is the xvalue and 9.7 is the yvalue.
67)Problem: If the point (7,8) lies on the graph of f, then f(___) = ____.
Solution: f(7) = 8, this problem is the reverse of the problem before, you plug in the xvalue (7) into x in f(x) and then plug in the yvalue (8) in for the y.
70)Problem: Use the graph of y = f(x) to find each function value: a. f(2), b. f(0), c. f(1), and d. f(4).
73)Problem: Explain each term in your own words.
a. Relation
b. Function
c. Domain of a function
d. Range of a function
e. Independent variable
f. Dependent variable
Solution: a. Relation: one set of ordered pairs
b. Function: relates an input to an output
c. Domain of a function: the...
...MDM 4U Chapter 5 Test
K ( ) T ( / ) A( / ) C( / )
Short Answer
1. For a calculus quiz, the teacher will choose 11 questions from the 15 in a set of review exercises. How many different sets of questions could the teacher choose? K6
2. All 16 people at a function shake hands with everyone else at the function. Use combinations to find the total number of handshakes. T 6
3. How many different sums of money can you make with three pennies, a nickel, a dime, and two quarters?K5
4. How many different sums of money can you make with four pennies, two nickels, and six quarters? A6
5. Susan’s company has just won an important new contract. She will have to assign a project team of at least 4 of her 11 staff members to this contract in order to complete it on time. If no more than 5 staff members can be spared from other work, how many different project teams could Susan form for the new contract? T8
6. A new theme park will have five roller coasters, six water rides, and eight suspension rides. How many different combinations of rides could you try at this park? K7
7. Write the first three terms of the expansion of (2x – y)7. C 5
8. Expand (x + 3y)5. K 6
Problem
9. There are 10 councillors and 12 planning department staff available to serve on a budget committee for the new city council. If the committee will consist of 3 councillors and either 1 or 2 planning staff, how many...
...PROFICIENCY TEST STUDY GUIDE
With sample test questionsMATHEMATICS / ALGEBRA 
Key Words and Converting Words to EquationsFractions Adding, subtracting, multiplying, dividing Simplifying Writing decimals as fractions StatisticsReading Tables and ChartsExponentsPreAlgebra and Algebra Special notation for multiplication and division with variable Algebra word problems Order of operations Simplifying expressions Prime factorization Greatest common factor Least common multiple Factoring Sample algebra problemsCoordinate System Grid graph Slope coordinatesGeometry Basics Squares, rectangles, circles, trianglesMath Definitions 
ENGLISH 
Proof reading / spellingReading comprehensionMain theme of a paragraphLogical sequence of a paragraphKey wordEnglish grammarBasic word meanings 
ABILITY TO ASSIST 
Worker roles and responsibilitiesStudent discipline / behavior 
WRITING 
ContentFormatGrammarSpellingPunctuation 
MDUSD Proficiency Test Study Guide / Page 2
MATH
Key Words and Converting Words to Equations
Sometimes math questions use key words to indicate what operation to perform. Becoming familiar with these key words will help you determine what the question is asking for.
OPERATION  OTHER WORDS WHICH INDICATE THE OPERATION 
Addition  Increased by; more than; combined...
...TEST CODE
OI234O2O
FORM TP 2009092
SECONDARY EDUCATION CERTIF'ICATE
MAY/JUNE2OO9
CARIBBEAN EXAMINATIONS COUNCIL
EXAMINATION MATHEMATICSPaper 02  General Proficiency
2 hours 40 minutes 20 MAY 2009 (a.m.)
INSTRUCTIONS TO CANDIDATES
1. 2. 3. 4.
Answer ALL questions in Section I, and ANY TWO in Section IL
'Write
your answers in the booklet provided.
All working must be shown clearly.
A list of formulae is provided on page 2 of this booklet.
Examination Materials
N
Electronic calculator (nonprogrammable) Geometry set Mathematical tables Graph paper (provided)
I I
I I I I
DO NOT TURN TIIIS PAGE TINTIL YOU ARE TOLD TO DO SO.
Copyright @ 2OO7 Caribbean Examinations Council@. All riehts reserved.

01234020tF 2009
Page2
LIST OF FORMULAE
Volume of a prism
V = Ah where A is the
length.
V
area of a crosssection and å is the perpendicular
Volume of cylinder Volume of a right pyramid Circumference Area of a circle Area of trapezium
=n/hwhere r is fhe radius of the base
ancl l¿ is the perpendicular height.
y = elrwhereA is the area of the base and /¿ is the perpendicular !
C =2nr where r is the radius of the circle.
height'
A
= nf
where r is the radius af the circle.
¡ = ){n
+ b)
lz
where a anú b are the iengtirs of the parailel sides and
l¿
is
the perpendicular distance between the parallel sides.
Roots of...
...SOUTH AFRICAN MATHEMATICS OLYMPIAD
Organised by the
SOUTH AFRICAN MATHEMATICS FOUNDATION
2012 FIRST ROUND
SENIOR SECTION: GRADES 10, 11 AND 12 19 March 2012 Time: 60 minutes Number of questions: 20
Instructions 1. This is a multiple choice questionpaper. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct. 2. Scoring rules: 2.1. Each correct answer is worth 5 marks. 2.2. There is no penalty for an incorrect answer or any unanswered question. 3. You must use an HB pencil. Rough work paper, a ruler and an eraser are permitted. Calculators and geometry instruments are not permitted. 4. Figures are not necessarily drawn to scale. 5. Indicate your answers on the sheet provided. 6. Start when the invigilator tells you to do so. 7. Answers and solutions will be available at www.samf.ac.za
Do not turn the page until you are told to do so. Draai die boekie om vir die Afrikaanse vraestel.
PRIVATE BAG X173, PRETORIA, 0001 TEL: (012) 3929323 Email: ellie@samf.ac.za
Organisations involved: AMESA, SA Mathematical Society, SA Akademie vir Wetenskap en Kuns
PRACTICE EXAMPLES
1. As a decimal number 6.28% is equal to (A) 0.0628 (B) 0.628 (C) 6.28 (D) 62.8 (E) 628
2. The value of 1 +
1 3+ 1 2 7 6
is
(A)
6 5
(B)
(C)
9 2
(D)
6 7
(E)
9 7
3. The tens digit of the product 1 × 2 × 3 ×...
...ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Mathematics and Statistics)
WARNING
1. PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
2. SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN “AIOU PLAGIARISM POLICY”.
Course: Business Mathematics (1429) Semester: Spring, 2012
Level: BA, B.Com, BBA Total Marks: 100
ASSIGNMENT No. 1
(Units 1–4)
Note: All questions carry equal marks.
Q.1 (a) In a game show, the contestant is shown 10 boxes, 3 of which contain prizes. If a contestant is allowed to select any three boxes then what is the probability that
i) The contestant wins all the three prizes.
ii) Only one selected box contains prize.
(b) Explain the rolling of a fair die and then flipping of a fair coin with the help of tree diagram.
Q.2 (a) How can we differentiate between continuous and discrete random variables. Explain with the help of examples.
(b) Let X be a random variable having normal distribution with mean 48 and standard deviation 10. Then find [pic].
Q.3 (a) Compute the mean, median, mode and standard deviation for the following discrete probability distribution.
Value of X 20 30 40 50 60 
Frequency...
...SECTION A (Reading)
1. Read the passage and answer the questions that follow. (06 x ½=03)
Hibernation is one of the main adjustments that allow certain northern animals to survive in long winters, cold winters. Hibernation is like a very deep sleep that allows animals to save their energy when there is little or no food available. The body functions of ‘true hibernators’ go through several changes while they are hibernating. The body temperature drops and the heart rate slows down. True hibernators include the jumping mouse, little brown bat, eastern chipmunk and several ground squirrels. Other animals such as the skunk and raccoon are not considered true hibernators as they wake up in the winter and their body functions do not change as much. Since they sleep for a little bit, the term ‘light sleeping’ is used to describe their behaviour.
a. Hibernation allows
i. animals in the south to survive in winter
ii. animals in the west to survive in winter
iii. animals in the north to survive in winter
iv. animals in the tropics to survive in winter
b. Hibernation is
i. a very deep sleep
ii. a very light sleep
iii. no sleep
iv. none of the above
c. Hibernation helps animals
i. to save their energy
ii. to waste their energy
iii. to use their energy
iv. to reduce their energy
d. The body functions of ‘true hibernators’ go through
i. no changes
ii. some changes
iii. several...