Sequences and Patterns
The arithmetic sequence is 7,12, 17,22, and so on. Find the 20th term.
102
Factor x2 - 11x + 24 completely.
(x - 3)(x - 8)
Find the midpoint of the segment joining (-3,5) and (7,-1).
(2,2)
A 30-60-90 triangle has a shorter leg of 6 cm. Find the longer leg.
6√3
Find the smallest positive integer that is divisible by 5 and leaves a remainder of 2 when divided by both 3 and 4.
50
Find the seventh term of the geometric sequence: 3,-6,12,-24,...
192
Simplify √75 + 2√12 - √27.
6√3
Find the distance between (-1,2) and (5,10).
d = 10
In a right triangle, the side opposite to angle A measures 12, and the adjacent side measures 5. Find sin A.
12/13
Two real numbers x and y satisfy x + y = 10 and xy = 21. Without finding x and y individually, determine x2 + y2.
58
Find the sum of the first 25 terms of the arithmetic sequence: 4,9,14,19,...
1600
Solve 2/(x-1) + 1/(x+1) = 1.
x = (3 + √17)/2 or x = (3 - √17)/2
Find the equation of the line perpendicular to 3x - 2y = 7 and passing through (4,-1).
2x + 3y = 5
Two similar triangles have corresponding side lengths in the ratio 3:5. If the area of the smaller triangle is 54 cm2, find the area of the larger triangle.
150 cm2
A rectangle has a perimeter of 46 cm and a diagonal of 17 cm. Find its area.
120 cm2
Find the sum of: 2 + 6 + 18 + 54 + ... + 1458.
2186
Find the remainder when 2x4 - 3x3 + 5x - 7 is divided by x - 2.
11
Determine the center and the radius of the equation x2 + y2 - 6x + 8y - 11 =0.
C(3,-4) and r = 6
A triangle has side lengths 13,14,15. Find its area.
84 square units
Using the digits 1,2,3,4,5, how many three-digit even numbers greater than 300 can be formed?
15
Three consecutive terms of an increasing arithmetic sequence have a sum of 36 and a product of 1680. Find the three terms.
10,12,14
If x + 1/x = 3, find x3 + 1/x3.
18
A circle has radius 13 cm. A chord is 5 cm from the center of the circle. Find the length of the chord.
24 cm
From a point on level ground, the angle of elevation to the top of the tower is 30 degrees. After moving 20 meters directly toward the tower, the angle becomes 60 degrees. Find the height of the tower.
10√3 m
Two positive integers have a greatest common factor of 6 and a least common multiple of 180. What is the least possible sum of the two integers?
66