1.
Find the area of the triangle RST.
Correct Answer
A. 16 ft squared
Explanation
You can use trig to find the missing sides of the triangle or you can use pythagorean theorem if you realize that both sides are the same length (x). Once you have the side length you can then use the standard area formula for a triangle.
2.
Which two lines are parallel?
Correct Answer
B. 3x + 4y = 12 and 6x + 8y = 12
Explanation
The two lines 3x + 4y = 12 and 6x + 8y = 12 are parallel because they have the same slope. The slope of both lines can be found by rearranging the equations into slope-intercept form (y = mx + b), where m is the slope. For the first equation, rearranging gives y = -3/4x + 3, and for the second equation, rearranging gives y = -3/4x + 3/2. Since both equations have the same slope of -3/4, the lines are parallel.
3.
What is the approximate length of MN when the coordinates of its endpoints are (-4,5) and (-6,9)?
Correct Answer
B. 4.5 units
Explanation
Use the distance formula.
4.
Which type of parent function is represented by the function graphed below?
Correct Answer
D. Quadratic
Explanation
The given function is a quadratic function because its graph is a parabola. Quadratic functions are characterized by having a variable raised to the power of 2 as the highest power in the equation. The graph of a quadratic function is always a symmetrical U-shape or an inverted U-shape. In this case, the graph clearly shows a U-shape, confirming that it is a quadratic function.
5.
Which of the following is the solution for this system of linear equations?
Correct Answer
C. (-3, 4)
Explanation
It is set up for substitution. But you can reorder the second equation to make it y= as well so you can graph them.
6.
Use the graph to solve the the equation for x when y = -3.
Correct Answer
A. X = -6
Explanation
Based on the graph, when y = -3, the corresponding value of x is -6.
7.
Start with a 1 unit by 1 unit unshaded square. In each iteration, the following steps occur for the smallest unshaded squares resulting from the previous iteration.Step 1: Divide the square into a 3 by 3 grid of squares.Step 2: Shade only the center square of this 3 by 3 grid.What fraction of the 1 unit by 1 unit square is shaded after the second iteration?
Correct Answer
C. 17/81
Explanation
I think this is an example of a badly worded, unclear TAKS question. In order to get even one of the answers listed in the answer choices, not to mention the right one, you must subdivide all the squares (even the previously shaded one) and then count all of the shaded squares.
8.
An astronomer mathematically expressed the amount of space occupied by the Earth. She reported Earth's _______?
Correct Answer
B. Volume
Explanation
The correct answer is volume. The question asks for the mathematical expression of the amount of space occupied by the Earth. Volume is a measure of three-dimensional space, so it is the most appropriate answer in this context. The radius, surface area, and circumference are all measurements related to the Earth, but they do not directly express the amount of space occupied.
9.
The map below shows 2 different routes Ms. Bentsen can take to drive to the airport from her house.How many miles can she save by traveleing on Airport Road instead of Mountain Highway and Oak Road to get to the airport?
Correct Answer
20
Explanation
You can use Pythagorean Therem to find the missing side or you can divide the 25 and 65 by five to reduce to the special triangle 5,12,13.
10.
Find the slope of the line identified by the equation 4x + 5y = 20.
Correct Answer
C. -4/5
Explanation
The given equation is in the form of a linear equation, which is in the form of y = mx + b, where m represents the slope of the line. To find the slope, we need to rearrange the equation in this form. By subtracting 4x from both sides of the equation and then dividing by 5, we get y = (-4/5)x + 4. Therefore, the slope of the line is -4/5.
11.
Over a 50 day period, a statistics professor recorded the data shown for the traffic lights he encountered each day while driving to work.
Correct Answer
C. 0.16
Explanation
The given data shows the probabilities of encountering different types of traffic lights over a 50 day period. The answer of 0.16 represents the probability of encountering a specific type of traffic light on any given day.