Test on TSIA2 Mathematics Sample Questions

Question 1: If the slope of the line y = mx - 4 is greater than the slope of the line y = x - 4, then m must be less than 1.

A. Ano

B. Ne

Explanation: According to the materials, if the slope of the line y = mx - 4 is less than the slope of the line y = x - 4, then it must be true that m < 1. Therefore, if the slope of the line y = mx - 4 were greater than the slope of the line y = x - 4, m would need to be greater than 1, not less than 1.

Question 2: The expression (x^(-5)y^(-2))^(-1) is equivalent to x^5y^2.

A. Ano

B. Ne

Explanation: The expression (x^(-5)y^(-2))^(-1) is equivalent to x^5y^2 because the power of a product distributes over each factor, meaning that (x^a y^b)^c = x^(ac) y^(bc). In this case, (x^(-5))^(-1) = x^((-5)*(-1)) = x^5 and (y^(-2))^(-1) = y^((-2)*(-1)) = y^2, resulting in x^5y^2.

Question 3: In a right triangle ABC, with angle C being the right angle, the cosine of angle A is given as 5/8. What is the value of the cosine of angle B?

A. 3/8

B. 5/8

C. sqrt(39)/8

D. sqrt(89)/8

Explanation: Given a right triangle ABC with angle C as the right angle, cos A is defined as the ratio of the length of the side adjacent to angle A to the length of the hypotenuse. If cos A = 5/8, we can consider the length of the side adjacent to angle A to be 5 and the hypotenuse to be 8. Using the Pythagorean theorem, a^2 + 5^2 = 8^2, where 'a' is the length of the side opposite angle A. Solving for 'a', we get a^2 = 64 - 25 = 39, so a = sqrt(39). The side opposite angle A is also the side adjacent to angle B. Therefore, cos B, which is the ratio of the length of the side adjacent to angle B to the length of the hypotenuse, is sqrt(39)/8.

Question 4: A triangle has a base of length x and a height of length x + 1. If the area of this triangle is 21, what is the value of x?

A. 3

B. 6

C. 7

D. 11

Explanation: The area of a triangle is calculated as half the product of its base and height (A = 1/2 bh). Given the base is x and the height is x + 1, the area is 1/2 * x * (x + 1) = (x^2 + x) / 2. Since the area is 21, we set up the equation: (x^2 + x) / 2 = 21. Multiplying both sides by 2 gives x^2 + x = 42. Rearranging this into a quadratic equation yields x^2 + x - 42 = 0. Factoring the quadratic equation gives (x + 7)(x - 6) = 0. This results in two possible values for x: x = -7 or x = 6. Since the height of a triangle cannot be negative, the value of x must be 6.

Question 5: If the first coin Reyna chooses is a 10-cent coin, the probability that the second coin chosen will also be a 10-cent coin is 5/9.

A. Ano

B. Ne

Explanation: If the first coin chosen is a 10-cent coin, 4 coins worth 10 cents each and 4 coins worth 25 cents each remain. Therefore, the probability that the second coin will also be a 10-cent coin is 4/8, or 1/2, not 5/9.