SAT2-MATHEMATICS Online Practice Questions and Answers

Correct Answer: C

Line AB is perpendicular to line BC, which makes triangle ABC a right triangle. Angles DAF and DCH are alternating angles -- angles made by a pair of parallel lines cut by a transversal. Angle DAF angle DCH, therefore, angle DCH = 120 degrees. Angles DCH and ACB form a line. There are 180 degrees in a line, so the measure of angle ACB = 180 ?120 = 60 degrees. Triangle ABC is a 30-60-90 right triangle, which means that the length of the hypotenuse, AC, is equal to twice the length of the leg opposite the 30-degree angle, BC. Therefore, the length of BC is 10/2, or 5. The length of the leg opposite the 60-degree angle, AB, is 3 times the length of the other leg, BC. Therefore, the length of AB is.

Correct Answer: C

Explanation: M#n is a function definition. The problem is saying “m#n” is the same as “m2– n”. If m#n isn2– n, then n#misn2– m. So, to find m#(n#m), replace (n#m) with the value of (n#m), which isn2– m:m#(n2 – m). Now, use the function definition again. The function definition says “take the value before the # symbol, square it, and subtract the value after the # symbol”: m squared ism2minus the second term, (n2– m), is equal tom2-(n2– m) = m2– n2+ m.

Correct Answer: E

To find the total number of different guitars that are offered, multiply the number of neck choices by the number of body choices by the number of color choices: (4)(2)(6) = 48 different guitars.

Correct Answer: C

Explanation: The equation of a parabola with its turning point c units to the left of they-a x is written as y=(x + c)2. The equation of a parabola with its turning point d units above the x-axis is written as y= x2+d. The vertex of the parabola formed by the equation y = (x+1)2+2is found one unit to the left of the y-a x is and two units above the x-axis, at the point (–1,2). Alternatively, test each answer choice by plugging the x value of the choice into the equation and solving for y. Only the coordinates in choice c, (-1, 2, represent a point on the parabola(y = (x+1)2+2, 2=(-1+1)2+2, 2 = 02+2, 2=2, so it is the only point of the choices given that could be the vertex of the parabola.

Correct Answer: C

The perimeter of a rectangle is equal to 2l+2w, where l is the length of the rectangle and w is the width of the rectangle. If the length is one greater than three times the width, then set the width equal to x and set the length equal to 3x+1:

The width of the rectangle is 3 ft and the length of the rectangle is 10 ft. The area of a rectangle is equal to lw;(10 ft)(3 ft) = 30 ft2.

Correct Answer: A

To increased by 50%, multiply d by 1.5:d= 1.5d. To find 50% of 1.5d, multiply 1.5d by 0.5: (1.5d)(0.5) = 0.75d. Compared to its original value, d is now 75% of what it was. The value of d is now 25% smaller.

Correct Answer: D

40% of j= 0.4j, 50% of k = 0.5k. If 0.4j= 0.5k, = 1.25kis equal to 125% of k, which means that j is 25% larger thank.

Correct Answer: A

Explanation:

The equation of a parabola with its turning point five units to the right of the y-axis is written as y = (x - 5)2.

The equation of a parabola with its turning point four units below the x-axis is written as y = x2- 4.

Therefore, the equation of a parabola with its vertex at (5, 4) is y= (x - 5)2 – 4.

Correct Answer: B

If r is the radius of this circle, then the area of this circle, r2, is equal to four times its circumference, 2r: r2= 4(2r), r2= 8r,r2= 8r,r= 8 units. If the radius of the circle is eight units, then its circumference is equal to 2(8) = 16 units.

Correct Answer: B

Parallel lines have the same slope. When an equation is written in the for my = mx + b the value of m (the coefficient of x) is the slope. The line y = -2x + 8 has a slope of-2. The line 1/2y = -x +3 is equal to y = -2x +

6. This line has the same slope as the line y = -2x + 8; therefore, these lines are parallel.