Short Answer Practice Problems

1. First, fold a piece of paper in half along the diagonal to make a triangle. Second, cut a hole near each vertex of the triangle you have made. Third, unfold the paper. Which figure can you have?

2.   In the diagram, angles A and D are right angles. AB=4 cm, AD=6 cm, and CD=8 cm. Find the area of ABCD in square centimeters.

3. An ant sits at vertex V of a cube with edge of length 1 meter. The ant moves along the edges of the cube and comes back to vertex V without visiting any other point twice. Find the number of meters in the length of the longest such path.

4. In this diagram, 17 toothpicks are used to form a 2-square by 3-square rectangle. How many toothpicks would be needed to form a 6-square by 8-square rectangle?

5. As shown, the length of each side in the overlapping rectangles is given, in cm. Find the sum of the areas of the shaded regions, in square centimeters.

6. The 14 digits of a credit card number are written in the boxes at the side. If the sum of any 3 consecutive digits is 20, what digit is in box A?

How many times does x occur in the diagram at the right? 7. How many times does x occur in the diagram at the right?

8. A square piece of paper is folded in half as shown, and then cut into two rectangles along the fold. The perimeter of each of the 2 rectangles is 18 inches. What is the perimeter of the original square?

9. In the figure at the right, each number represents the length of the segment that is nearest to it. All angles are right angles. How many square units are in the area of the figure?

10.   People were asked to choose their favorite type of movie. This graph shows the results of the survey. What was the total number of people who were surveyed? A. 60 B. 75 C. 90 D. 170 E. 270

11. A palindromic number is one which is the same read backwards and forwards. For example, 121 and 3443 are palindromic numbers. What is the next palindromic number after 79311397?

12. Insert parentheses into the expression so the result is as large as possible. What is the result?

13. A wall with a hole is shown in the picture. How many bricks are missing?

14. In the picture, 6 dots appear in the first figure, 10, 16, and 24 dots are in the successive figures. If this pattern continues, how many dots are in the 6th figure?

15. This picture shows part of a bee house that is made with hexagons. The middle hexagon is the 1st layer and the six outside hexagons are the second layer. If the bee house has a total of 6 layers and each hexagon has a bee inside, how many bees live in the house?

16. A bat and a ball together cost $10. if the bat costs $9 more than the ball, what is the cost of the bat?

If you roll two dice, what is the probability you will roll two ones? 17. If you roll two dice, what is the probability you will roll two ones?

18. A micron is a thousandth of a millimeter. How many microns are in 8 meters?

“Nine times my age, divided by 12 is equal to 36.” 19. Sara wouldn’t tell her age, but she did agree to give it as an algebra problem: “Nine times my age, divided by 12 is equal to 36.” How old is Sara?

20. What is the probability of getting a pair (like 2 aces or 2 tens), if you are dealt two cards from a standard deck?

21. 1, 2, 6, 15, 31, ____ What is the next number of this sequence?

22. Four consecutive (in a row) numbers add up to 110. What is the smallest number?

What is the product of this multiplication? 23. What is the product of this multiplication?

24. ABCD is a square. AB=4. BEFG is also a square. BE=6. O1 is the center of ABCD and O2 is the center of BEFG. Find the shaded area O1 O2 B.

25. As shown in the figure, a square of side length 5 cm has some area overlapped with another square of side length 4 cm. Find the difference of the non-overlapping areas of the 2 squares (A-B).

26. In the picture, AB is parallel to CD and CE is parallel to FG. If angle BAC = 100 degrees, and GFC = 110 degrees, find x.

27. In this addition different letters represent different digits. What digits do A, B, C, and D represent?

28. A square has an area of 144 square centimeters. Suppose the square is cut into six congruent rectangles as shown here. How many inches are there in the perimeter of one of the rectangles?

29. 3,6,9,12 are some multiples of 3. How many multiples of 3 are there between 13 and 113?

30. one plus two plus three plus four plus five plus one plus two plus three plus four? What is the total of

31. ABCD is a square with area 16 sq. meters. E and F are midpoints of sides AB and BC respectively. What is the area of trapezoid AEFC, the shaded region?

32. A rectangle is 5 cm long and 12 cm wide. A triangle with a 2 cm base and 3 cm height is drawn inside the rectangle. What is the probability that a random point inside the rectangle is also in the triangle?

33. Bob’s age is 4 times Michelle’s age, and Sarah’s age is half Bob’s age. If their ages add up to 84, what is Michelle’s age?

34. As shown in the picture, both ABCD and BEFG are squares. The shaded area is 10. Find the area of ABCD

35 Find the value of y.

36. Two identical squares with sides of length 10 centimeters overlap to form a shaded region as shown. A corner of one square lies in the center of the other square. Find the area of the shaded region, in square cm.

37. At the right, boxes represent digits and different letters represent different non-zero digits. What 3-digit number is the least possible product?

38. As shown, ABCD and AFED are squares with a common side of AD of length 10 cm. Arc BD and arc DF are quarter-circles. How many square centimeters are in the area of the shaded region?

39. There are five Mondays and four Tuesdays in August of a year. What day is August 8th of the year?

40. If you roll four dice, what is the probability that you will roll four ones?

41. Bill and Steve decided that they would always have a money ratio of 9:7 (Bill to Steve). If Steve has $129.50, how much money should Bill have?

42. How many cubic millimeters would fit inside of a cubic box that measures 2 meters per side?