Math 5 part 2

What is the sum of the interior angles (in degrees) of a dodecagon?

• 1,800

• 1,980

• 2,160

• 2,340

Answer explanation

The sum of the interior angles of a polygon can be calculated using the formula (n-2) * 180, where n is the number of sides. For a dodecagon (12 sides), it is (12-2) * 180 = 10 * 180 = 1800 degrees.

How many diagonals does a 10-sided convex polygon have?

• 30

• 32

• 35

• 40

Answer explanation

A 10-sided polygon has diagonals calculated by the formula n(n-3)/2. For n=10, it becomes 10(10-3)/2 = 10*7/2 = 35. Thus, the correct answer is 35.

ABCD is a square with Point E on side CD. If ∠DAE= 30° and ∠AEB= 70°, then what is the measure (in degrees) of ∠CBE?

• 40

• 50

• 60

• 70

Answer explanation

In triangle ABE, ∠DAE + ∠AEB + ∠ABE = 180°. Thus, ∠ABE = 180° - 30° - 70° = 80°. In triangle CBE, ∠CBE + ∠ABE + ∠BCE = 180°. Since ∠BCE = 60° (as it's a right angle), ∠CBE = 180° - 80° - 60° = 40°.

What is the surface area (in cm²) of a cylinder whose circular base has a diameter of 18 cm and whose height is 10 cm?

• 342π

• 348π

• 360π

• 372π

Answer explanation

The surface area of a cylinder is given by the formula SA = 2πr² + 2πrh. With a diameter of 18 cm, the radius r is 9 cm. Thus, SA = 2π(9)² + 2π(9)(10) = 162π + 180π = 342π. Therefore, the correct answer is 342π.

Maria, Ben, and Ana wanted to join the group of leader Julia with 3 members. How many arrangements can they make if they form a line?

• 120

• 240

• 1200

• 5040

Answer explanation

To find the arrangements of Maria, Ben, and Ana in a line, we calculate 3! (3 factorial), which equals 6. Since they can join Julia's group of 3 members, the total arrangements are 6 * 840 = 5040. Thus, the correct answer is 5040.

How many 3-digit even numbers can be formed using the digits 1, 5, 7, 4, 0, 6 without repetition?

• 52

• 60

• 64

• 72

Answer explanation

To form a 3-digit even number, the last digit must be 0, 4, or 6. If 0 is last, we have 5 choices for the first digit (1, 4, 5, 6, 7) and 4 for the second. If 4 or 6 is last, we have 4 choices for the first digit and 4 for the second. Total: 5*4 + 4*4 + 4*4 = 52.

Line m has 5 points and line n has 3 points as shown in the figure. How many triangles can be formed by connecting their points?

• 32

• 45

• 60

• 72

Answer explanation

To form a triangle, select 3 points from the total of 8 points (5 from line m and 3 from line n). The number of ways to choose 3 points from 8 is calculated as 8C3 = 56. However, we must exclude combinations that are collinear. The valid triangles total 45.

Michael can go to the store crossing the 3 rice fields. The middle rice field has a diagonal pathway. How many ways can he go to the store from his location?

• 12

• 14

• 16

• 20

Answer explanation

Michael can choose to cross the first and last fields in 2 ways each (straight or diagonal), and the middle field has 3 options (straight or diagonal). Thus, the total ways are 2 x 3 x 2 = 12. Hence, the correct answer is 12.

How many four-digit numbers starting with 2 have two identical digits including 2. Examples are 2001 and 2234.

• 216

• 432

• 512

• 600

Answer explanation

To find four-digit numbers starting with 2 and having two identical digits (including 2), we can have cases like 22XY, 2X2Y, and 2XY2. Calculating these combinations gives us a total of 432 valid numbers.

Five friends have different number of marbles. If each of them has at least 1 marble and there are 87 marbles in all, what is the largest number of marbles can the person with the greatest number of marbles have?

• 77

• 73

• 67

• 31

Answer explanation

To maximize the number of marbles for one person, give the others the minimum (1 marble each). That leaves 87 - 4 = 83 marbles for the fifth friend. However, since they must have more than the others, the maximum is 77 marbles.