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

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

Explanation:

Substitute –3 for x:–2(–3)2+ 3(–3) – 7 = –2(9) – 9 – 7 = –18 – 16 = –34

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: E

No penguins live at the North Pole, so anything that lives at the North Pole must not be a penguin. If Flipper lives at the North Pole, then he, like all things at the North Pole, is not a penguin.

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

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: D

The volume of a cube is equal to e3, where e is the length of an edge of the cube. The surface area of a cube is equal to 6e2. If the ratio of the number of cubic units in the volume to the number of square units in the surface area is 2:3, then three times the volume is equal to two times the surface area:

The edge of the cube is four units and the surface area of the cube is square units.

Correct Answer: A

Explanation:

If point A is located at (–3,12) and point C is located at (9,5), that means that either point B or point D has the coordinates (–3,5) and the other has the coordinates (9,12). The difference between the different x values is 9 – (–3) = 12 and the difference between the different y values is 12 – 5 = 7. The length of the rectangle is 12 units and the width of the rectangle is seven units. The area of a rectangle is equal to its length multiplied by its width, so the area of ABCD = (12)(7) = 84 square units.

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

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

The surface area of a cube is equal to 6e2, where e is the length of an edge of a cube. The surface area of a cube with an edge equal to one unit is 6 cubic units. If the lengths of the edges are decreased by 20%, then the surface area

becomes cubic units, a decrease of

Correct Answer: E

If Wendy tutors t students the first day, then she tutors 2t students the second day, 4t students the third day, 8t students the fourth day, and 16t students the fifth day. The average number of students tutored each day over the course of the week is equal to the sum of the tutored students divided by the number of days:

Correct Answer: A

Write the equation in slope-intercept form

The line crosses the y-axis at its y-intercept, (0,8). The line crosses the x-axis when

Use the distance formula to find the distance from

Correct Answer: C

If d is the distance Warrick drives and s is the speed Warrick drives, then 30s = d. Gil drives five times farther, 5d, in 40 minutes, traveling 45 miles per hour: 5d = (40)(45). Substitute the value of d in terms of s into the second equation and solve for s, Warrick's speed: 5(30s) = (40)(45), 150s = 1,800, s = 12. Warrick drives 12 mph.