Sequences and Series
The first term of a geometric sequence is 2; the second term is -6.
Calculate the fourth term of the sequence.
-54
Given the function f(x) = |x + 1| - 2; what is the minimum value of the function?
(-1; -2)
A fair coin is tossed three times one after the other. Give the probability that it comes up Heads - Tails - Heads
p = 0,125
The slant height of a straight cone is 41cm; the radius of the base circle is 9cm. Calculate the height of the cone in centimeters.
40 cm
Vector a(2; 5) is perpendicular to vector b(5; b2). Determine the value of b2
b2 = -2
Three consecutive terms of an arithmetic progression are 32, a, and 28 respectively.
Give the value of a and the common difference.
a = 25; d = -7
Consider the function h(x) = 2 - |x|.
For what values does h(x) = 0,85?
x = 2,85 and x = -2,85
Give five positive integers such that their median is 4 and their mean is 3.
{1; 1; 4; 4; 5} OR {1; 2; 4; 4; 4}
Leg AC of the right triangle ABC is 6 cm, leg BC is 8 cm long.
Calculate the measure of each acute angle of triangle ABC.
a = 53,13 and b = 36,87
The equation of a circle is x2 + y2 - 6y + 5 = 0.
Calculate the center and radius of the circle.
O(0; 3) and r=2
The n-th term of a geometric sequence is an = 3*2n-1.
Calculate the sum of the first 10 terms of this sequence.
3069
Out of the positive even numbers not greater than 50 one number is randomly selected. What is the probability that the selected number is divisible by 4?
p = 0,48
Students use two different measuring cylinders at a Chemistry class. Both the height and the diameter of the base circle of one of these cylinders are exactly half as much as that of the other one. How many times larger is the volume of the larger cylinder than the volume of the smaller one?
8 times the volume
The equation of a line e is 3x + 7y = 21.
Line f goes through point Q(1; -2) and is perpendicular to line e.
Give the equation of line f.
f: -7x + 3y = -13
The town of Orange in South of France has one of the best preserved antique theatres of the world. The seats for spectators are arranged in semicircles. There are 60 seats in the first row. From the second row onwards, each row has 6 more seats than the previous row.
A tourist information booklet states that there ae 6786 seats altogether in the theatre. How many rows are there?
39 rows
Give all positive, real solutions of the equation sin x = 1/2 that are smaller than pi.
pi/6 and 5pi/6
There were seven contestants at a school's table tennis tournament. Every contestant plays every other contestant exactly once. So far, Anita has played all 6 of her games, Zsuzsa has played 2, Gabi, Szilvi, Kati, and Orsi have played one game each. How many games has Flora, the seventh contestant, played so far?
2 games
The number of single person households was 946 thousand in 1990, increasing to 1317 thousand by 2011. We would like to represent these numbers on a poster by two circular discs, such that the area of each disc is proportional to the number it represents. The 1990 data is shown with a 4,5 cm radius disc.
What should the radius of the year 2011 be?
5,3 cm
The angle between vectors AB and AC is 120o and both vectors are 5 units long.
Calculate the length of vector AB - AC.
8,66 units
The first term of a geometric sequence is 60 and its common ratio is 1,1. Starting with the first term, at least how many terms of this sequence need to be added so that the sum reaches 6786?
27th term
The function f(x) = |x - 1|- 3 is defined over the set of real numbers. Determine the zeros of the function.
x = 4 and x = -2
During horse riding, contestants jump across twelve different obstacles. Obstacles are placed into three categories according to difficult: A, B, or C. While warming up before the event, Adam jumped across the five obstacles of category A first, then the four obstacles of category B, and finally the three obstacles of category C, jumping across each of these obstacles exactly once. During the warm-up, the order of jumping across obstacles within the same category is chosen freely.
Calculate the number of possible orders at which Adam can jump across the twelve obstacles during warm-upl.
17280 ways
A plastic products factory manufactures flower boxes the shape of a regular hexagonal truncated pyramid. The base of the truncated pyramid is a regular hexagon with 13 cm sides, the top is a regular hexagon with 7 cm sides, the lateral edges are 8 cm long.
If a molding machine can make a sheet of plastic of 0,93 m2 area from 1 kg of plastic, how many boxes could be produced?
16 boxes
The length of diagonal AC of the rhombus ABCD is 12 cm, the length of diagonal BD is 5 cm.
Calculate the total surface area of the solid obtained from rotating the rhombus around the line of diagonal AC.
102,1 cm2