MATH KANGAROO (LEVEL 7-8) - UCLA Department of Mathematics
... (3) The numbers 1, 2, 3, · · · , 1022, 1023, 1024 have been placed around a circle clockwise in the order given. We move around the circle clockwise and erase every other number until only one number is left. Which number will be the last one left if we erase number 1 first. ...
... (3) The numbers 1, 2, 3, · · · , 1022, 1023, 1024 have been placed around a circle clockwise in the order given. We move around the circle clockwise and erase every other number until only one number is left. Which number will be the last one left if we erase number 1 first. ...
Figurative Numbers
... 4. What happens if you add two consecutive triangular numbers? Why does this happen? Can you prove your result geometrically? Can you prove your result algebraically? ...
... 4. What happens if you add two consecutive triangular numbers? Why does this happen? Can you prove your result geometrically? Can you prove your result algebraically? ...
Synthetic Division
... Synthetic Division To use synthetic division, the divisor must be of the first degree and must have the form x − a. In this example, the divisor is x − 2, with a = 2. Procedure to divide x³ − 5x² + 3 x − 7 by x − 2, ...
... Synthetic Division To use synthetic division, the divisor must be of the first degree and must have the form x − a. In this example, the divisor is x − 2, with a = 2. Procedure to divide x³ − 5x² + 3 x − 7 by x − 2, ...
Full text
... The Fibonacci numbers (FQ = Ft = 1; Fn = Fn„i + Fn„2, if /7 > 2) are very useful in describing the laddernetwork of Fig. 1,if r= R (cf. [ 1 ] , [ 2 ] , [3]). If the common value of the resistances/? and r is chosen to be unity, the resistance Zn of the ladder-network can be calculated on the followi ...
... The Fibonacci numbers (FQ = Ft = 1; Fn = Fn„i + Fn„2, if /7 > 2) are very useful in describing the laddernetwork of Fig. 1,if r= R (cf. [ 1 ] , [ 2 ] , [3]). If the common value of the resistances/? and r is chosen to be unity, the resistance Zn of the ladder-network can be calculated on the followi ...
Big Ideas: Chapter 1
... 15. In golf, a golfer must have a score of 0 in order to be at par. A golfer scores 2 above par on the first hole, 1 below par on the second hole, and 2 below par on the third hole. Which expression can be used to decide whether the golfer is at par after the first three holes? ...
... 15. In golf, a golfer must have a score of 0 in order to be at par. A golfer scores 2 above par on the first hole, 1 below par on the second hole, and 2 below par on the third hole. Which expression can be used to decide whether the golfer is at par after the first three holes? ...
2.57 PART E: THE FUNDAMENTAL THEOREM OF ALGEBRA (FTA
... Therefore, all the real zeros of f x must lie in the interval ⎡⎣ −1, 3⎤⎦ . Note: These rules can be used (possibly in conjunction with Descartes’s Rule of Signs and/or a graph) to shrink the list of candidates for zeros resulting from the Rational Zero Test. The information obtained from these rules ...
... Therefore, all the real zeros of f x must lie in the interval ⎡⎣ −1, 3⎤⎦ . Note: These rules can be used (possibly in conjunction with Descartes’s Rule of Signs and/or a graph) to shrink the list of candidates for zeros resulting from the Rational Zero Test. The information obtained from these rules ...
Warm-up Section 1.6/1.7: Simplifying Expressions
... Key words that are code for . . . Addition add ...
... Key words that are code for . . . Addition add ...
Document
... Theorem: Every n ∈ ℕ is the sum of distinct powers of two. Proof: By strong induction. Let P(n) be “n is the sum of distinct powers of two.” We prove that P(n) is true for all n ∈ ℕ. As our base case, we prove P(0), that 0 is the sum of distinct powers of 2. Since the empty sum of no powers of 2 is ...
... Theorem: Every n ∈ ℕ is the sum of distinct powers of two. Proof: By strong induction. Let P(n) be “n is the sum of distinct powers of two.” We prove that P(n) is true for all n ∈ ℕ. As our base case, we prove P(0), that 0 is the sum of distinct powers of 2. Since the empty sum of no powers of 2 is ...
