2nd Grade Math Test Competition Level 2 Geometry Problems

Time limit: 90 minutes. Problems 1-3 are 3 points each. Problems 4-6 are 5 points each. Problems 7-9 are 7 points each. Problem 10 is 15 points. [cite: 2, 3, 6, 7]

Problem 1. How many triangles have point A as a vertex? [cite: 10]

A) 6 B) 9 C) 8 D) 12

Problem 2. The missing numbers in the sequence 2, 3, 5, 8, 12, .., 23, …, 38, 47 are: [cite: 13]

A) 17, 32 [cite: 14] B) 18, 26 [cite: 17] C) 17, 30 [cite: 20] D) 18, 30 [cite: 28]

Problem 3. How many of the subtrahends (second numbers) in the problems 12-9, 8-4, 11+34, 31-7, 27-0, are greater than 6? [cite: 19, 29]

A) 3 [cite: 15] B) 2 [cite: 18] C) 4 [cite: 21] D) 5 [cite: 29]

Problem 4. What is the value of $\odot$, if $12+16=\text{\text{}}$, $\text{\text{}}-20 = \text{\text{}}$, and $\text{\text{}} + \text{\text{☺}} < 9$? [cite: 23, 26, 30]

A) 15 [cite: 24] B) 2 [cite: 25] C) 1 [cite: 22] D) Other answer [cite: 31]

Problem 5. How many of the following numbers: 22, 45, 76, 81, 57, 92, 84, 49, 37, 41, 69, 62, 51 have a ones digit that is at least 2 greater than the tens digit? [cite: 33, 34]

A) 6 [cite: 35] B) 7 [cite: 37] C) 4 [cite: 39] D) Other answer [cite: 42]

Problem 6. Calculate: $(31 + 19) + (78 – 40) – (28 + 22 – 19)$ [cite: 41]

A) 57 [cite: 36] B) 17 [cite: 38] C) 69 [cite: 40] D) Other answer [cite: 43]

Problem 7. The difference between the numbers that should be written in place of the asterisks ($\text{*}$) is: [cite: 44, 55]

[cite: 47, 48, 49, 50, 51, 53]

A) 1 [cite: 45] B) 19 [cite: 46] C) 0 [cite: 54] D) Other answer [cite: 56]

Problem 8. Ani is 4 years older than her brother and 20 years younger than her mother. Ani’s father is 31 years old and is 3 years older than her mother. How old is her brother? [cite: 57, 58, 59]

A) 8 [cite: 60] B) 4 [cite: 61] C) 20 [cite: 62] D) Other answer [cite: 63]

Problem 9. The legs (equal sides) of two triangles are both $15 \text{ cm}$. The base of one is $2 \text{ cm}$ shorter than the base of the other triangle. The sum of their perimeters is $9 \text{ dm}$. How many centimeters is the shorter base? [cite: 64, 65, 66]

A) 2 [cite: 67] B) 30 [cite: 68] C) 16 [cite: 69] D) Other answer [cite: 70]

Problem 10: Garland Challenge [cite: 71, 72, 73, 74, 87, 88, 89, 90, 91]

Yana, her mother, and her brother bought garlands. Using all of them, Yana “drew” a house (Figure 1) and then a Christmas tree made of equilateral triangles (Figure 2). [cite: 72, 73, 88, 89, 90]

Garland	Price	Length
Green	$20 \text{ st.}$	$12 \text{ dm}$
Blue	$50 \text{ st.}$	$15 \text{ dm}$
Red	$25 \text{ st.}$	$30 \text{ dm}$

[cite: 75, 92]

[cite: 78, 79, 94, 95]

10.1: What is the total length of the garlands bought, in meters? [cite: 77, 96] (Answer: 21)

10.2: How many decimeters is the side of the square in the house (Figure 1), “drawn” by all the green garlands? [cite: 80, 101] (Answer: 15)

10.3: How many meters are the legs (sides of the isosceles triangle in the house) “drawn” by all the red garlands? [cite: 81, 82, 103] (Answer: 6)

10.4: How many meters is the side of the top triangle of the Christmas tree (Figure 2)? [cite: 83, 105] (Answer: 3)