Grades 7 & 8 Tests

UND MATHEMATICS TRACK MEET Team Test 2

University of North Dakota Grades 7/8
January 12, 2026
School Team Name
Calculators are NOT allowed.

  • 1.

    The average of five weights is 13 grams. If a 7-gram weight is added, what is the average of the six weights?

      (20 pts) 1.

  • 2.

    The 7-digit numbers 74⁢A⁢52⁢B⁢1 and 326⁢A⁢B⁢4⁢C are multiples of 3. What is the largest possible value for C?

      (20 pts) 2.

  • 3.

    Every day at school, Jo climbs a flight of 6 stairs. Jo can climb using 1, 2, or 3 steps at a time or any combination of them. How many ways can Jo climb the flight of 6 stairs?

      (20 pts) 3.

  • 4.

    Two pendants are made up of the same material. They are equally thick and weigh the same. One of them has a shape of a gray “annulus” formed by two circles with radii 6 cm and 4 cm (see picture). The second has the shape of a solid circle. What is the square of the radius (i.e. radius × radius) of the second pendant?

    Two concentric circles with radii 4cm and 6cm

      (20 pts) 4.

  • 5.

    If A=13,B=5,C=1,D=23,E=32, F=−1, find the value of the expression:

    A⋅B+CD⋅E+F

      (20 pts) 5.

  • 6.

    Each side of a square is trisected at the points shown. What part of the square is shaded? Express your answer as a fraction in simplest terms.

    If we create a square having vertices (0,0), (0,3), (3,3), and (3,0), the shaded region is a pentagon with vertices (0,0), (0,1), (1,3), (3,1), and (3,0).

      (20 pts) 6.

  • 7.

    There are 93 seventh graders and 108 eighth graders entering a raffle. In each grade, the number of cat owners is twice the number of students who do not own a cat. What is the probability that a seventh grader who does not own a cat wins the raffle? Express your answer as a common fraction.

      (20 pts) 7.

  • 8.

    On Friday, Pat bought some cupcakes. On Saturday, Pat gave 12 of the cupcakes to Ryan. On Sunday, Pat gave 13 of the remaining cupcakes to Alice. If Pat has 24 cupcakes left and no other cupcakes were given away or eaten, how many cupcakes did Pat buy on Friday?

      (20 pts) 8.

  • 9.

    What is the sum of the three smallest distinct positive integers that are both a multiple of 5 and also 1 more than a multiple of 7?

      (20 pts) 9.

  • 10.

    Maria runs twice as fast as she walks. It takes 40 minutes for her to walk from her home to school in the morning. She then runs from school to her friend’s house in the afternoon. If her friend lives three times as far from the school as Maria does, how many minutes does Maria spend running in the afternoon?

      (20 pts) 10.

TOTAL POINTS  

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