class 1

algebra

geometry questions

probability

mix

mental math

factorize

4x-x³

x(2-x) x (2+x)

The sum of two nonzero real numbers is 4 times their product. What is the sum of the reciprocals of the two numbers?

1, 2, 4, 8, 12

Two coins are tossed 500 times, and we get:

Two heads: 105 times

One head: 275 times

No head: 120 times

Find the probability of each event to occur.

Solution: Let us say the events of getting two heads, one head and no head by E1, E2and E3, respectively.

P(E1) = 105/500 = 0.21

P(E2) = 275/500 = 0.55

P(E3) = 120/500 = 0.24

The Sum of probabilities of all elementary events of a random experiment is 1.

P(E1)+P(E2)+P(E3) = 0.21+0.55+0.24 = 1

What number doesn’t have its own Roman numeral?

20/ 5 x (10+5)

2x² +4(x²+3)-2=22

find x

x= -root 2/ root 2

Find the curved surface area of a hemisphere whose radius is 14 cm.

Solution:

Given: Radius = 14 cm.

1232

One card is drawn from a deck of 52 cards, well-shuffled. Calculate the probability that the card will

(i) be an ace,

(ii) not be an ace.

P(F) = 48/52 = 12/13

what are the first 5 digits of pi

3.141592

(5x6)x3²/3-8+4

7x-11=17

find x

What is the area of a circle with a diameter of 16?

64(picm^2)

Two players, Sangeet and Rashmi, play a tennis match. The probability of Sangeet winning the match is 0.62. What is the probability that Rashmi will win the match?

The probability of Sangeet to win = P(S) = 0.62

The probability of Rashmi to win = P(R) = 1 – P(S)

= 1 – 0.62 = 0.38

What is next in the following number series: 256, 289, 324, 361 . . . ?

400

140,368 - 12,439

127929

A= (-20,12)

B= (15,-40)

what is the midpoint of line AB

(-2.5, -14).

The lengths of the sides of a triangle are x, 16 and 31, where x is the shortest side. If the triangle is not isosceles, what is a possible value of x?

By the triangle rule, x lies between 31 – 16 = 15 and 31 + 16 = 47. That is, we have 15 < x < 47. But we are also given that x is the length of the shortest side of the triangle. So x < 16.Therefore we can grid in any number between 15 and 16. For example, we can grid in 15.1.

In a class there are 35 boys and 15 girls. What is the probability of a randomly selected student of the class to be a girl?

0.3, or 30%.

At a Christmas party, everyone shook hands with everyone else. There were a total of 66 handshakes that happened during the party. How many people were present?

√169/256

0.0507812

13/ 256

n⁴+2n³+2n²+2n+1

factorize completely

(n+1)²(n²+1)

In rectangle ABCD, both diagonals are drawn and intersect at point E.

Let the measure of angle AEB equal x degrees.

Let the measure of angle BEC equal y degrees.

Let the measure of angle CED equal z degrees.

Find the measure of angle AED in terms of x, y, and/or z.

180 – 1/2(x + z)

11 A bag contains 5 blue (B) and 3 white (W) marbles and two marbles are selected without

replacement.

a Draw a tree diagram showing all outcomes and probabilities.

b Find the probability of selecting:

i a blue marble followed by a white marble (B, W)

ii 2 blue marbles iii) exactly one blue marble

c If the experiment was repeated with replacement, find the answers to each question in part b .

a) The tree diagram for selecting two marbles without replacement from a bag containing 5 blue (B) and 3 white (W) marbles would look like this:

B W
/ \ / \
B W B W
/ \ / \ / \ / \
B W B W B W B W

b)
i) The probability of selecting a blue marble followed by a white marble (B, W) can be calculated by multiplying the probabilities of each event:

P(B, W) = P(B) * P(W after B)
= (5/8) * (3/7)
= 15/56

ii) The probability of selecting two blue marbles can be calculated similarly:

P(2 blue marbles) = P(B, B)
= P(B) * P(B after B)
= (5/8) * (4/7)
= 20/56
= 5/14

iii) The probability of selecting exactly one blue marble can be calculated by considering two cases: selecting a blue marble and then a white marble, or selecting a white marble and then a blue marble. We can add the probabilities of these two cases:

P(exactly one blue marble) = P(B, W) + P(W, B)
= (5/8) * (3/7) + (3/8) * (5/7)
= 15/56 + 15/56
= 30/56
= 15/28

c) If the experiment is repeated with replacement, the probabilities will change because after each selection, the marble is put back into the bag.

i) The probability of selecting a blue marble followed by a white marble (B, W) would be:

P(B, W) = P(B) * P(W)
= (5/8) * (3/8)
= 15/64

ii) The probability of selecting two blue marbles would be:

P(2 blue marbles) = P(B, B)
= P(B) * P(B)
= (5/8) * (5/8)
= 25/64

iii) The probability of selecting exactly one blue marble would be:

P(exactly one blue marble) = P(B, W) + P(W, B)
= (5/8) * (3/8) + (3/8) * (5/8)
= 15/64 + 15/64
= 30/64
= 15/32

An object is thrown into the air. After a while, it falls back to the Earth. The flight path of the object traces what shape?

parabola

3x+1

no answer