Karteikarten
maths revision
Karten in diesem Stapel (8)
- 1—From the tree diagram, we can see that there are eight possible outcomes. To find out the probability of a particular outcome, we need to look at all the available paths (set of branches).
The sum of the probabilities for any set of branches is always 1.
Also note that in a tree diagram to find a probability of an outcome we multiply along the branches and add vertically.
The probability of three heads is:
P (H H H) = 1/2 × 1/2 × 1/2 = 1/8
P (2 Heads and a Tail) = P (H H T) + P (H T H) + P (T H H)
= 1/2 × 1/2 × 1/2 + 1/2 × 1/2 × 1/2 + 1/2 × 1/2 × 1/2
= 1/8 + 1/8 + 1/8
= 3/8 - 2From the tree diagram, we can see that there are eight possible outcomes. To find out the probability of a particular outcome, we need to look at all the available paths (set of branches). The sum of the probabilities for any set of branches is always 1. Also note that in a tree diagram to find a probability of an outcome we multiply along the branches and add vertically. The probability of three heads is: P (H H H) = 1/2 × 1/2 × 1/2 = 1/8 P (2 Heads and a Tail) = P (H H T) + P (H T H) + P (T H H) = 1/2 × 1/2 × 1/2 + 1/2 × 1/2 × 1/2 + 1/2 × 1/2 × 1/2 = 1/8 + 1/8 + 1/8 = 3/8It shows Set A = {1, 5, 6, 7, 8, 9, 10, 12} and Set B = {2, 3, 4, 6, 7, 9, 11, 12, 13}
If we look at the overlapping section of the Venn diagram, this represents A ∩ B = {6, 7, 9, 12} (The intersection of A and B). This contains the numbers that are in both Set A and Set B.
Taking the two circles in their entirety gives us A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} (The union of A and B).
- 3—If you toss a coin, the probability of obtaining a head is 1/2 and the probability of obtaining a tail is also 1/2.P(head) + P(tail) = 1 / 2 + 1 / 2 = 1
the sum of the probability is always 1
- 4When multiplying out a pair of brackets, multiply each term in the first bracket by each term in the second bracket. So that this doesn't become too confusing, we use FOIL to help us. First: Multiply the first terms from each bracket (1st term in 1st bracket with 1st term in 2nd bracket) Outside: Multiply the two outside terms (1st term in 1st bracket with 2nd term in 2nd bracket) Inside: Multiply the two inside terms (2nd term in 1st bracket with 1st term in 2nd bracket) Last: Multiply the last terms from each bracket (2nd term in 1st bracket with 2nd term in 2nd bracket)
- 5simplify(2x+5)(3x-4)
=(2x X 3x) + (2x X -4) + (5 X 3x) +( 5 X -4)
= 6x (squared) - 8x + 15x - 20
= 6x (squared) +7x -20 - 6Solve the equation 2x + 2 = x + 4 Subtract x from both sides to give x + 2 = 4 Subtract 2 from both sides to give x = 2Solve the equation 5x - 2 = 12 - 2x
Your aim is to get all the unknown x terms on one of the equation side only, so start by adding 2x to both sides:
7x - 2 = 12
Next add 2 to both sides: 7x = 14
And finally, divide by 7 to give x = 2
As always, you can check your answer in the original equation. So substitute x = 2 back into 5x - 2 = 12 - 2x
(5 × 2) - 2 = 12 - (2 × 2)
10 - 2 = 12 - 4
8 = 8
This makes sense, so the value x = 2 is correct. - 7If y is directly proportional to x. When x = 12 then y = 3 Find the constant of proportionality and the value of x when y = 8. We know that y is proportional to x so y = kx We also know that when x = 12 then y = 3 To find the value of k substitute the values y = 3 and x = 12 into y = kx 3 = k × 12 So k = 3/12 = 1/4 To find the value of x , when y = 8 substitute y = 8 and k = 1/4 into y = kx 8 = (1/4) x So x = 32 when y = 8y is inversely proportional to x. When y = 3, x = 12 .
Find the constant of proportionality, and the value of x when y = 8.
y ∝ 1/x
y = k/x
So xy = k
Substitute the values x = 12 and y = 3 into xy = k
3 × 12 = 36
So k = 36
To find the value of x when y = 8, substitute k = 36 and y = 8 into xy = k
8x = 36
So x = 4.5 - 8—
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- Karteikarten am maths revision, erstellt von freya k am 31/01/2018.
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