PSY 138 Math Review Practice

What is a set?

A set is a collection of numbers.

These numbers are called scores.

Each individual score holds a position in the set:

i.e. x = x1, x2, x3, ...

For this class, if there are multiple sets, then they will each have the same number of scores.

x = 3, 40, 7, 8, 200

How many scores are in set x?

There are 5 scores in set x.

3, 40, 7, 8, and 200 are individual scores of set x.

x = 1, 4, 6

y = 7, 10, 12

How many scores are paired between sets x and y?

The are 3 pairs of scores between sets x and y.

x : y

------

1 : 7

4 : 10

6 : 12

If you were to perform an operation using Σ in which these two sets affect each other, these numbers would be paired.

x = 10, 5, 16, 12, 7

Find Σx. (Try on paper before showing the answer)

Σ means to find the sum of, so this question asks you to add all scores in set x together.

Σx = 10 + 5 + 16 + 12 + 7

Answer:

= 50

x = 2, 8, 9, 16

y = 7, 5, 3, 10, 7

Find Σx + Σy

This question asks you to determine the sum of 2 different sets.

1st: Find the sum of set x.

Σx = 2 + 8 + 9 + 16

= 35

2nd: Find the sume of set y.

Σy = 7 + 5 + 3 + 10 + 7

= 32

3rd: Add these two sums together

32 + 35

Answer:

= 67

x = 2, 3, 1

y = 5, 1, 4

Find Σx * Σy

This question asks you to find the product of the sum of set x and the sum of set y

1st: Find the sum of set x

Σx = 2 + 3 + 1

= 6

2nd: Find the sum of set y

Σy = 5 + 1 + 4

= 10

3rd: Multiply these sums together

Σx * Σy = 6 (10)

Answer:

= 60

The Role of Parenthesis. Explain how parenthesis affect the function of Σ and the order of operations.

The parenthesis will help you to know specifically what operations to perform on each individual score vs. the entire sum of scores (Σ).

This means that an equation Σ( x + 4), will add four to every score in x.

The equation Σx + 4, will add 4 to the total of all the scores in x.

SImilarly, the equation: Σ(x^2), is the sum of all the squared scores in x (i.e. (x1 ^2) + (x2 ^2) + ...).

In contrast to this, the equation: Σ(x)^2, will take the sum of all the scores in x and square it.

Summary: Operations inside parenthesis affect each individual score, operation outside affect the entire sum.

x = 10, 16, 20

y = 12, 4, 10

FInd Σ(x + y)

This problem asks you to find each score in set x added to the corresponding (paired) score in set y.

1st: Find the sum of each score individually.

Σ(x + y) = (10 + 12) + (16 + 4) + (20 + 10)

2nd: Add all of these sums together.

= 22 + 20 + 30

Answer:

= 72

x = 1, 3, 0, 7

y = 5, 2, 2, 1

Find Σ(xy) - 10

This question asks you to find the sum of scores from sets x and y multiplied together, Then subtract 10 from the sum.

1st: FInd the sum of paired scores after multiplying them.

(1x5) + (3x2) + (0x2) + (7x1)

5 + 6 + 0 + 7

= 18

2nd: Subtract 10 from total sum.

18 - 10

Answer:

= 8

x = 2, 3, 6, 8

Find Σ(x^2)

This question asks to find the sum of squared x scores.

1st: Square all of the scores individually.

(2^2) + (3^2) + (6^2) + (8^2)

2nd: Add all of the squared scores together.

4 + 9 + 36 + 64

Answer:

= 113

x = 1, 3, 5, 6

Find (Σx)^2

This question asks you to find the sum of set x, then square it.

1st: Find the sum of the scores in x.

Σx = 1 + 3 + 5 + 6 = 15

2nd: Square the sum.

15^2 = 225

Answer:

(Σx)^2 = 225

x = 5, 2, 4, 5

Find Σ(x+4)^2

This question asks you to find each score in x plus 4, square it, then find the sum of these scores.

1st: Find each score + 4.

(5 + 4)^2 + (2 + 4)^2 + (4 + 4)^2 + (5 + 4)^2

2nd: Square all the scores.

= 9^2 + 6^2 + 8^2 + 9^2

3rd: Add them all together:

= 81 + 36 + 64 + 81

Answer:

= 262

x = 2 , 5 , 6, 7, 9

Find Σ(2x -6) + 12

This question asks you to find the sum of each x score multiplied by two, with 6 subtracted from the product.

It then asks you to add 12 to this sum.

1st: Find each x score multiplied by 2.

(2(2) - 6) + (5(2) - 6) + (6(2) -6) + (7(2) - 6) + (9 (2) - 6)

2nd: Subtract 6 from each score.

= (4 - 6) + (10 - 6) + (12 - 6) + (14 - 6) + (18 - 6)

3rd: Find the sum of these scores

= (-2) + 4 + 6 + 8 + 12

= 28

4th: Add 12 to the total sum

28 + 12 = 40

Answer:

= 40

x = 2, 4, 8, 12

Find Σ(x/2) + 2

This question asks you to divide each score in set x by 2, and then add 2 to the sum of scores.

1st: Find the quotient of each score divided by 2.

(2/2) + (4/2) + (8/2) + (12/2)

2nd: Add these scores together.

= 1 + 2 + 4 + 6

= 13

3rd: Add to the sum from part 2.

13 + 2 = 15

Answer:

Σ(x/2) + 2 = 15

x = 9, 3, 7, 6, 11

y = 1, 2, 5

Find (2 * Σx) / (Σy)

This question asks you to find the sum of scores in set x, then multiply it by 2. It then asks you to divide this number by the sum of scores in set y.

1st: Find the sum of set x

9 + 3 + 7 + 6 + 11 = 36

2nd: Multiply this number by 2

36 * 2 = 72

3rd: Find the sum of set y

1 + 2 + 5 = 8

4th: Divide the product from part 2 by the sum from part 3

72 / 8 = 9

Answer:

= 9