AoPS Mock Test

1. Alex adds five different two-digit numbers. The sum is a perfect square. What is the smallest possible sum of Alex’s five numbers?

2. What is 3 divided by 27? Write your answer as a fraction in simplest form.

3. What is the area of a square with sides measuring 12 feet?

4. Four congruent rectangles, each with a perimeter of 12, are arranged as shown. What is the perimeter of the big square they make?

5. When Winnie colors the multiples of a number in her 100 chart, she colors in exactly 8 numbers. What is Winnie’s number?

6. Alex is decorating cookies. Each cookie gets exactly 3 chocolate chips and 4 cinnamon candies. Alex has 100 chocolate chips and 125 cinnamon candies. How many cookies can Alex decorate?

7. There are fewer than 75 students in the Beast Academy Marching Band. When they stand in rows of 3, there is 1 extra band member. When they stand in rows of four, there are 2 extra band members. When they stand in rows of 5, there are 3 extra band members. How many students are in the Beast Academy Marching Band?

8. A heptagon has 14 diagonals, and an octagon has 20. Look for a pattern in the number of diagonals of a quadrilateral, pentagon, hexagon, heptagon, and octagon. Continue the pattern to guess the number of diagonals of a nonagon.

9. Lizzie read a total of 61 pages on Wednesday, Thursday, and Friday. She read 7 pages more on Friday than she read on Wednesday. On Thursday, she read 6 pages fewer than she read on Wednesday. How many pages did Lizzie read on Wednesday?

Use the following to answer question

Jana has two clocks on her nightstand: a digital clock and an analog clock. When the power goes out, both clocks stop running. When the power comes back on, her digital clock resets to 12:00. Her analog clock continues running from the previous time.

10. One morning, Jana wakes up to find her clocks displaying the time below. What time was it when the power went out?

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