Apr. 16th, first test: Mathcounts: Beginning Level

First Test: The answers will be posted after all the e-learning students have submitted their answers.

#1: A straight line passes through the three points (3, -4), (5, 1) and (11, y).
What is the value of y?

#2: The sum of 6 consecutive even integers is 162. What is the largest number?

#3: Carrie has an 86% average in biology after all 4 of the marking periods. If the final exam counts twice as much as each of the 4 marking periods, what percent must Carrie make on the final exam to have a final average of 90% for the course?

#4: How many times does the digit 7 appear in the list of all integers from 1 to 300?

#5: What is the area of the triangle with vertexes (2, 9), (3, 1) and (15, 1)?

#6: On Maria’s 8th birthday, in 2004, her father said, &! #8220;My age is now four times your age”. In what year will Maria’s father be able to say, “My age is now three times your age”. on Maria’s birthday?

#7: Isosceles trapezoid ABDC and rectangle CDEF are shawn, with DE = 8 inches and CD = 16 inches. The area of trapezoid ABDC is 88 square inches. What is BE?

#8: A pair of six-sided dice is rolled, and the sum is recorded. What is the probability that this sum is a multiple of four? Express your answer as a common fraction.

#9: A bug crawls at a rate of 21 units per hour around a circle with a radius of 3.5 units. How many hours does it take the bug to complete 27 revolutions of the circle?

#10: A set of magnetic strips and balls are connected in an alternating fashion! , as strip-ball-strip-ball. The length of the first four items! in the chain is 14 cm, and the length of the first seven items is 25 cm. What is the length of the first 19 items in the chain?

#11: At Martha’s Mothball Antiques, a group of shirts was not selling. Martha decided to mark the price of each shirt down by 22%. The discounted price for each shirt is now $39. What was the original price of a shirt?

#12: Julia jogs at a rate of 3 miles per hour. What is her rate in feet per second? Express your answer as a decimal to the nearest tenth.

#13: How many two-digit prime numbers have a units digit of 1?

#14: A wheel has a circumference of 5 meters. The radius can be expressed as with relatively prime integers A and B. What is the value of A + B?

#15:When the expression is multiplied out 8⁶ x 5¹² (written in decimal notation), how many digits does the number have?

#16: What is the value of x + y if the sequence 3, 7, 11, ., x, y, 83 is an arithmetic s! equence?

#17: The lines 3x + 2y = 6 and x + y = 8 together with the x-axis and y-axis are drawn on a coordinate grid to form quadrilateral ABCD. What is the area of quadrilateral ABCD?

#18: What is the area of the largest integer quadrilateral you can make with a rope that’s 38 inches long?

#19, I have 30 quarters and dimes and their total sum is 5.7. How many quarters do I have?

#20.At a party, each person shakes hands only once with every other person. If there are total 28 handshakes. How many people are at the party?

arithmetic sequence problems