SAT2-MATHEMATICS Online Practice Questions and Answers

Correct Answer: C

There is an inverse relationship between the number of people and the time needed to clean the office. Multiply the number of people by the hours needed to clean the office: (8)(12) = 96. Divide the total number of hours by the new number of people, = 16. It takes six people 16 hours to clean the office.

Correct Answer: A

The measure of an exterior angle of a triangle is equal to the sum of the two interior angles of the triangle to which the exterior angle is NOT supplementary. Angle i is supplementary to angle g, so the sum of the interior angles e and f is equal to the measure of angle

Correct Answer: B

Solve

Substitute 3x-2 for y in the second equation and solve for x:

Substitute the value of x into the first equation to find the value of y:

Correct Answer: A

At the start, there are 5 + 3 + 2 = 10 pens in the box, 3 of which are black. Therefore, the probability of selecting a black pen is 3/10 After the black pen is removed, there are nine pens remaining in the box, five of which are blue. The

probability of selecting a blue pen second is 5/9 To find the probability that both events will happen, multiply the probability of the first event by the probability of the second event:

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: A

Lines OF and OE are radii of circle O and since a tangent and a radius form a right angle, triangles OFH and OGE are right triangles. If the length of the diameter of the circle is 24 in, then the length of the radius is 12 in. The sine of angle OHF is equal to 12/24, or1/2. The measure of an angle with a sine of 1/2 is 30 degrees. Therefore, angle OHF measures 30 degrees. Since angles BGH and OHF are alternating angles,

they are equal in measure. Therefore, angle BGH also measures 30 degrees.

Correct Answer: B

Since ABC is a right triangle, the sum of the squares of its legs is equal to the square of the hypotenuse: (AB)2+82=102, (AB)2+ 64 = 100, (AB)2= 36, AB= 6 units. The diameter of circle O is 2/3 of AB, or 2/3(6) = 4 units. The area of a triangle is equal to 1/2bh where b is the base of the triangle and h is the height of the triangle.

The area of ABC square units.

The area of a circle is equal to r2, where r is the radius of the circle. The radius of a circle is equal to half the diameter of the circle, so the radius of O is 1/2(4) = 2 units. The area of circle O = (2)2= 4. The shaded area is equal to the area of the triangle minus the area of the circle: 24 ?4 square units.

Correct Answer: A

Explanation:

Of the concert attendees, 41% were between the ages of 18–24 and 24% were between the ages of 25–

34. Therefore, 41 + 24 = 65% of the attendees, or (1,560)(0.65) = 1,014 people between the ages of 18 and 34 attended the concert.

Correct Answer: A

Solve-6b + 2a – 25 = 25 for a in terms of b: -6b + 2a – 25 = 5, -3b + a = 15, a = 15+3b. Substitute a in terms of b into the second equation:

Substitute b into the first equation to find the value of a: -6b + 2a – 25 = 5, -6(-3) 2a – 25 = 5, 18+2a = 30, 2a = 12, a = 6. Finally, ,

Correct Answer: B

Explanation: Since triangle DEC is a right triangle, triangle AED is also a right triangle, with a right angle at AED. There are 180 degrees in a triangle, so the measure of angle ADE is 180 – (60 + 90) = 30 degrees. Angle A and angle EDC are congruent, so angle EDC is also 60 degrees. Since there are 180 degrees in a line, angle BDC must be 90 degrees, making triangle BDC a right triangle. Triangle ABC is a right triangle with angle A measuring 60 degrees, which means that angle B must be 30 degrees, and BDC must be a 30-60- 90 right triangle. The leg opposite the 30-degree angle in a 30-60-90 right triangle is half the length of the

hypotenuse. Therefore, the length of DC is 15/2 units.