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? K-6 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
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Vyas who is an expert in Geometry‚ informed that how the basic knowledge of Geometry should be applied to solve Olympiad level problems. With the help of Euler’s theorem‚ which is about the concept of 9 point circle in a triangle and Carpet theorem‚ he explained how basic knowledge of junior classes may be used to prove such theorems and Olympiad level questions. In the third lecture Prof. Rawal‚ who is an expert of Vedic Mathematics taught about solving of algebraic equations in two
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indicates that to find the treasure‚ one must get to Castle Rock‚ walk x paces to the north‚ and then walk 2x + 4 paces to the east. If they share their information‚ then they can find x and save a lot of digging. What is x? The Pythagorean Theorem states to find the missing side of a right triangle you can square to know lengths and add the two together. The result will be the distance of the missing length squared. A^2+b^2=C^2 We know that Ahmed has a map with a distance to the treasure
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saw space‚ time‚ and shapes‚ a huge part of the fame of his book stemmed from his extensive proofs and deductive reasoning starting at basic axioms‚ or commonly agreed-on concepts. He took common knowledge and used it to build extremely complex theorems and prove old ones. For example‚ starting with only axioms‚ he was able
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+ –– + ... + –––––––– + ... ‚ – 1 < x < 1 3 5 (2r + 1) Binomial expansions When n is a positive integer n n n (a + b)n = an + 1 an –1 b + 2 an–2 b2 + ... + r an–r br + ... bn ‚ n ∈ ގ where n n n n+1 n! n r = Cr = –––––––– r + r+1 = r+1 r!(n – r)! () () () () () ( ) ( ) 2 Logarithms and exponentials exln a = ax logbx loga x = ––––– logba Numerical solution of equations f(xn) Newton-Raphson iterative formula for solving f(x) = 0‚
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��2 + �� 2 Pythagorean Theorem Geometry Formulas 1 Area = LW Perimeter = 2L + 2W Area = 2bh Circumference = 2πr = πd Area = π�� 2 Volume = LWH Surface area= 2LW+ 2LH+2WH Volume= π�� 2 ℎ =π�� 2 ℎ + 2πrℎ Surface area= Volume= 3 ���� 3 4 Surface area=4π�� 2 Polynomials Special Products Difference of two squares ( �� + �� )2 = �� 2 + 2���� + ��2 ( �� − �� )2 = �� 2 − 2���� + ��2 ( x – a )( x + a ) = �� 2 − ��2 Squares of binomials or perfect squares ( ��
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Easy 1. What is the formula of Circle in circumference? Answer: C=2Π(radius) 2. What is a polynomial with exactly two terms? Answer: Binomial 3. What is the formula for area of the Parallelogram? Answer: A=(base)(height) 4. What is the reciprocal of the tangent function? Answer: Cotangent 5. What is the numbers used to locate a point in space? Answer: Coordinates 6. What is the point at which the axes of a coordinate system cross; the point (0‚0) in
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paces to the north‚ and then walk 2x - 4 paces to the east. If they share their information then they can find x and save a lot of digging. What is x? Given this scenario the Pythagorean Theorem would be the strategy we use to solve for x. I started off with the Pythagorean Theorem. I then plugged the binomials into the Pyth. Thrm. Next I moved (2+6)^2 to le left of the equation by subtracting (2x+6)^2 from both sides. I then squared the expression Next I foiled the expression by multiplying
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Inferential Statistics • Descriptive statistics (mainly for samples) • Our objective is to make a statement with reference to a parameter describing a population • Inferential statistics does this using a two-part process: • (1) Estimation (of a population parameter) • (2) Hypothesis testing Inferential Statistics • Estimation (of a population parameter) - The estimation part of the process calculates an estimate of the parameter from our sample (called a statistic)‚ as a kind of “guess” as to
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Summary Chapter 1-7 Chapter 1 * Population – consists of members of a group which you want to draw a conclusion * Sample – portion of population * Parameter – numerical measure that describes a characteristic of a population * Statistic – numerical measure that describes a characteristic of a sample * Descriptive statistics – collecting‚ summarizing and presenting data e.g. survey * Inferential statistics – drawing conclusions about a population based on sample data
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