Mathematics Practice Test

The correct answer is b] 271. To count how many numbers from 1 to 1,000 contain the digit 4, one must account for occurrences in each digit place (units, tens, hundreds). By manual counting or systematic enumeration, the total is 271. The other options are incorrect as they do not correctly reflect the total count.

The correct answer is a] 37. If 26% of 50 students passed, then 26/100 × 50 = 13 students passed. Thus, 50 - 13 = 37 students failed. The other options do not reflect this calculation accurately.

This question tests the understanding of how to calculate an average (arithmetic mean). The average is found by summing all values and dividing by the number of values. In this case, we sum A, B, and C, then divide by 3 (as there are three values). This corresponds to option c: (A+B+C)/3.

Let's use the compound interest formula: A = P(1 + r)^t <br> Where A is final amount, P is principal, r is annual rate, t is time in years. <br> A = 5000(1 + 0.12)^2 = 5000(1.2544) = 6,272 <br> The closest answer is P6,200.

To calculate the percentage decrease, we need to know the original value of the car. If the current value is P380,000 and it has depreciated by P20,000, the original value was P400,000. The percentage decrease is calculated as: (Amount of decrease / Original value) * 100 = (20,000 / 400,000) * 100 = 0.05 * 100 = 5%. Therefore, the correct answer is 5%.

To calculate the average, we sum all the grades and divide by the number of grades. (93 + 88 + 80 + 86 + 89) / 5 = 436 / 5 = 87.2, which rounds to 87. Therefore, the correct answer is 87.

This is a logical reasoning question. If all of Kay's brothers can swim, then anyone who cannot swim cannot be Kay's brother. This is the contrapositive of the original statement and is logically equivalent. Therefore, the correct answer is "If Fred cannot swim, then he is not Kay's brother".

Congruent figures in geometry are identical in shape and size. Two figures are congruent if one can be transformed into the other by a series of rigid motions (translations, rotations, reflections) without changing its size or shape. This concept is fundamental in geometry for comparing shapes and proving geometric theorems. Understanding congruence is crucial for solving many geometric problems and is distinct from similarity, which preserves shape but not necessarily size.

A taxicab number, named after a famous anecdote involving mathematician Srinivasa Ramanujan, is defined as the smallest number that can be expressed as the sum of two positive cubes in n distinct ways. The most famous is 1729, which can be expressed as 1³ + 12³ and 9³ + 10³. Understanding taxicab numbers provides insight into number theory and the properties of cubic equations. These numbers are significant in demonstrating how seemingly simple mathematical questions can lead to complex and interesting results.