Tag Archives: grade 8

Arc of a Circle

is a diameter of a circle of radius unit. is a chord perpendicular to that cuts at . If the arc is of the circumference of the circle, what is the length of the segment ? Source: NCTM Mathematics Teacher, … Continue reading

Posted in Problem solving | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Multiplicative Inverse

If , then in the form of , what does equal? Source: NCTM Mathematics Teacher, September 2006 Solution By definition of multiplication inverse Answer:

Posted in Problem solving | Tagged , , , | Leave a comment

Second Number Larger Than The First

Suppose a six-sided die has sides numbered through . If a person throws the die two times, what is the probability that the second number will be larger than the first? Source: NCTM Mathematics Teacher, September 2006 Solution The desirable … Continue reading

Posted in Problem solving | Tagged , , , , , , , | Leave a comment

Divided by 5

Find the reminder when is divided by ? Source: NCTM Mathematics Teacher, October 2006 Solution is such a large number that it is impractical to use modulo arithmetic to find the remainder. So we are going to find the remainders … Continue reading

Posted in Problem solving | Tagged , , , , | Leave a comment

Divisible by 7

How many four digit positive integers divisible by have the property that, when the first and last digits are interchanged, the result is a (not necessarily four-digit) positive integer divisible by ? Source: NCTM Mathematics Teacher, October 2006 Solution Is … Continue reading

Posted in Problem solving | Tagged , , , , , , , , | Leave a comment

Wins and Losses

A person starting with makes eight bets and wins exactly four times. The wins and losses occur in random order. If each wager is for half the money she has at the time of the bet, how much money will … Continue reading

Posted in Problem solving | Tagged , , , | Leave a comment

TV Game Show

On a television show, a player receives points for answering an easy question and points for a hard one. What is the largest integer that cannot be a contestant’s total score of the game? Source: NCTM Mathematics Teacher, October 2006 … Continue reading

Posted in Problem solving | Tagged , , , , , , , | Leave a comment

Three Intersecting Circles

Circle has a radius of and its center is at . Circle has a radius of and its center at . What is the length of the radius of a third circle (Circle ) that passes through the center of … Continue reading

Posted in Problem solving | Tagged , , , , , , , , , , , | Leave a comment

Complicated Quadratic Root

What is the (simplified) value for which the larger root of is ? Source: NCTM Mathematics Teacher, October 2006 Solution We are going to take advantage of the formulas  and repeatedly in the process of simplifying the complicated root. First, we multiply the … Continue reading

Posted in Problem solving | Tagged , , , , , | Leave a comment

How Many Liars?

Winkin said, “We’re all liars.” Blinkin replied, “Only you are a liar.” Finkin said, “You’re both liars.” If each of them always tells the truth or always lies, how many of the three are liars? Source: NCTM Mathematics Teacher, October … Continue reading

Posted in Problem solving | Tagged , , , , , , | Leave a comment