Chapter Competition Problems
Chapter
Chapter 5
Section
Chapter Competition Problems
Solutions 14 Videos

Determine the value of x such that \dfrac{8^{29}-8^{28}}{7} = 2^x.

A. 29

B. 84

C. 58

D. 56

Q1

The sum of 300 - 299 + 298 - 297 + 296 - 295 + ... - 3 + 2 - 1 is

A. 149

B. 151

C. 300

D. 150

Q2

Determine the values of three positive integers x, y, and z given that x + \dfrac{1}{y + \dfrac{1}{z} = \dfrac{38}{11}}.

Q3

If the fraction \dfrac{5}{13} is written in expanded decimal form, what is the 153rd digit after the decimal point?

A. 4

B. 6

C. 8

D. 1

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Q4

Three consecutive integers less than 20 have a sum of 27 and a product of 720. What are the numbers?

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Q5

If f(x) = \dfrac{1}{x^2 - 4} and g(x) = \dfrac{2x}{x - 2}, determine the value of x such that (f + g)(x) = 2.

A. -2

B. -\dfrac{5}{2}

C. -\dfrac{9}{4}

D. \dfrac{7}{4}

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Q6

How many different-sized squares can be made on a 5-by-5 geoboard? A. 43

B. 10

C. 6

D. 8

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Q7

A sequence of numbers has the terms 0.3, 0.33. 0.333, 0.3333, ... What value does the sequence approach?

A. 0.34

B. 0.4

C. \dfrac{1}{3}

D. 1

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Q8

A sequence of numbers has the terms \sqrt 2, \sqrt {2 \sqrt 2}, \sqrt {2 \sqrt {2 \sqrt 2}}, \sqrt {2 \sqrt {2 \sqrt {2 \sqrt 2}}} What is the limit of the value of the terms in the sequence?

A.2

B. 1.5

C. 3

D. 1.4

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Q9

When a number is divided by 18, the remainder is 13. What is the remainder When the number is divided by 6?

A. 2

B. 1

C. 3

D. 5

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Q10

The period of y = |5 sin (4x - 120^{\circ})| is

A. 45^{\circ}

B. 90^{\circ}

C. 120^{\circ}

D. 360^{\circ}

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Q11

If the number 6912 can be written in the form 2^x3^y4^z, then the value is x^2 + y^2 + z^2 is

A. 9

B. 14

C. 33

D. 29

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Q12

If y = \sqrt x, what is the value of x^{21} + 3 \sqrt 2 - y^{63}?

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Q13

If n \choose r = \dfrac{n!}{r!(n-r)!} where n! = n \times (n-1) \times (n-2) \times ... 3 \times 2 \times 1 determine the value of \dfrac{100 \choose 98}{2}.

A. 4950

B. 2475

C. 9900

D. 10 540