Division Achievement Test

A designer is planning to create a garden in the shape of a regular hexagon. Each side of the hexagon must be 4 meters long, and the angles between adjacent sides must be 120 degrees. To ensure accuracy, the designer uses a ruler and a protractor.

If the designer accidentally creates a polygon with the following measurements, which one does not match the original regular hexagon design?

• A polygon with sides measuring 4 meters and angles of 100 degrees each.

• A polygon with all sides measuring 4 meters and angles of 120 degrees.

• A polygon with all sides measuring 4 meters but angles slightly more than 120 degrees.

• A polygon with sides measuring 4 meters and angles alternating between 115 degrees and 125 degrees.

The Parthenon, a famous temple in Athens, Greece, was constructed in the 5th century BCE. It is known for its symmetrical design and precise geometry. Imagine one of the triangular pediments on the Parthenon, which forms part of the architectural structure of the roof. Consider the Scalene Triangle DEF with the following angle measures:

Angle D = 50°

Angle E = 75°

Which illustration of triangle has complete measures of angles.

• 
• 
• 
• 

The Eiffel Tower in Paris, France, was completed in 1889 for the World's Fair, celebrating the 100th anniversary of the French Revolution. Engineers who designed the tower carefully calculated angles and forces to ensure its stability. Suppose two beams of the Eiffel Tower form intersecting lines as shown in the diagram below:

<A= 65°

<B= 115°

What is the measure of the angle vertically opposite to ∠A?

• 25°

• 65°

• 90°

• 115°

A group of students is sorting different polygons based on their properties. Here are the descriptions of four polygons:

Polygon A: Has 5 sides of equal length, and all angles are equal.

Polygon B: Has 8 sides, with sides and angles of varying measures.

Polygon C: Has 6 sides, all of equal length, and one angle greater than 180°.

Polygon D: Has 4 sides, with all angles less than 180°.

Which of the following correctly classifies the polygons based on these descriptions?

• Polygon A: Regular and convex,

  Polygon B: Irregular and non-convex,

  Polygon C: Regular and non-convex,

  Polygon D: Irregular and convex

• Polygon A: Regular and convex,

  Polygon B: Regular and convex,

  Polygon C: Regular and convex,

  Polygon D: Irregular and non-convex

• Polygon A: Irregular and convex,

  Polygon B: Irregular and non-convex,

  Polygon C: Regular and convex,

  Polygon D: Irregular and convex

• Polygon A: Regular and convex,

  Polygon B: Irregular and convex,

  Polygon C: Regular and non-convex,

  Polygon D: Irregular and convex

In a regular polygon, the exterior angle at one vertex is 30°. What is the measure of the adjacent interior angle?

• 30°

• 60°

• 150°

• 180°

A regular polygon has each interior angle measuring 120°. How many sides does this polygon have?

• 6

• 8

• 10

• 12

In a small town, a local bakery sells two types of pastries: chocolate croissants and fruit tarts. Last year, the bakery sold 500 chocolate croissants each month. This year, the sales of chocolate croissants have increased by 20%. At the same time, the bakery sold 200 fruit tarts last year. However, due to seasonal changes, the sales of fruit tarts have decreased by 15%.

What is the total number of chocolate croissants the bakery expects to sell per month this year?

• 400

• 500

• 600

• 700

In a small town, a local bakery sells two types of pastries: chocolate croissants and fruit tarts. Last year, the bakery sold 500 chocolate croissants each month. This year, the sales of chocolate croissants have increased by 20%. At the same time, the bakery sold 200 fruit tarts last year. However, due to seasonal changes, the sales of fruit tarts have decreased by 15%.

What is the total change in the number of pastries (chocolate croissants and fruit tarts) sold this year, compared to the previous year?

• Decrease of 50 pastries

• Decrease of 70 pastries

• Increase of 50 pastries

• Increase of 70 pastries

Sarah is buying a pair of shoes that costs ₱5,000.00. The store is offering a 10% discount. After the discount, she will also need to pay a 5% sales tax on the discounted price. What is the total price Sarah will pay after the sales tax is added?

• ₱4,725.00

• ₱4,625.00

• ₱4,750.00

• ₱4,900.00

You are planning to buy a new Apple iPhone 15. The iPhone is priced at ₱50,000.00 on the Apple website. However, Apple is offering a 10% cashback promotion for purchases made in the next week. How much money will you get back after buying the phone?

• ₱2,500.00

• ₱3,750.00

• ₱5,000.00

• ₱7,500.00