PSSA - Math

Targeted Review of Major Concepts

The Guess & Check Strategy

The main advantage to taking a multiple choice test is that the correct answer is right in front of you…you simply have to find it. Remember, sometimes the “most mathematical” way to get the answer may not be the easiest!

Example:

What value of k makes the following true?

(53)(25) = 4(10k)

a) 2

b) 3

c) 4

d) 6

Plug your answer choices into the calculator until you find the one that works!!

Use the Calculator!!!

Don’t be afraid to use the calculator to help answer questions. Remember, you can solve any equation simply by entering each half into Y= and finding where the two graphs intersect.

You can enter data into your calculator by using the STAT button and going to EDIT. This is especially helpful for finding mean, median, and quartiles (1-VAR Stats). The same process can also be used for lines of best fit (LinReg)

The Formula SheetPlease be aware that you are permitted the use

of the formula sheet provided – it is very important that you familiarize yourself with

this formula sheet ahead of time!

Some important formulas on the sheet:

Slope, Equations of lines, Area/Volume, Distance, Midpoint

y = mx + b

• Slope-intercept form of a linear function

• m is the slope• b is the y-intercept• ax + by = c can easily be

converted to this form• Know the positive and

negative y-axis• Know slope relationships

Y = 2x + 1

Y = -3x - 4

2x + 3y = 19

3y = -2x + 19

y = (-2/3)x + (19/3)

Slope

• Slope is the rate of change• Difference in y / Difference in x• Parallel Lines – Same slopes • Perpendicular line – Opposite Reciprocal

slopes

Functions

• Domain – Inputs (x’s)• Range – Outputs (y’s)• A relation is a function whenever each x is

paired with exactly one y.

• [ (1,2) (3,5) (-4, 8) (2,5) ]– Function• [ (3,4) (9,1) (5,2) (3,6) ]– Not a Function

since the 3 is paired with two different y’s

Systems of Equations Terminology

Inconsistent

(Parallel - same slope)

Consistent & Independent

(Intersect with one solution)

Consistent & Dependent

(Lines Coincide – Same Line)y = 2x + 4

y = 2x + 4

y = 2x + 4

y = 2x - 3

y = 2x + 4

y = -3x – 3

Exponent Rules

• When multiplying, we add exponents.• When dividing, we subtract exponents.• When raising a power to a power, we

multiply exponents.• Negative exponents can be rewritten as

positive exponents by using the reciprocal.

Finding Maximum or Minimum Values

Example:

Find the maximum height of a projectile whose height at any time, t, is given by h(t) = 160 + 480t – 16t2

Strategy:

1) Enter the function of the Y= screen of calculator

2) Graph and adjust window to view the function

3) Use 2nd “TRACE” – option 3 or 4 to find desired value

Percentages…Percentages !

• A percentage indicates a part of the whole

• Percentages can be expressed as fractions and decimals as well

• 75% = .75 = ¾• 25% = .25 = ¼• 10% = .10 = 1/10

REMEMBER:

=P

100

IS

OF

ProportionsIf 60 out of 370 people surveyed preferred

Doritos over Tostitos, how many people out of 2400 would you expect to prefer Doritos? 60

370 2400

x=

370 x = 144,000

x = 389.19 = 389

Direct Variation• When y varies directly as x, this means that

y always equals the same number multiplied by x, that is: y = kx, where k is the constant of variation.

• k can always be found by taking (y/x) !Example:

When traveling at 50 mph, the number of miles traveled varies directly with the time driven. Find the miles traveled in 4.5 hours.

y = 50x

y = 50(4.5)

y = 225 miles

Inverse VariationWhen y varies inversely as x, this means that the x multiplied by the y will always equal the same number, that is xy = k, where k is the constant of variation.

Workers 2 4 5 6

Hours 36 18 14.4 ?

Example:

The number of hours it takes to paint a room varies inversely as the number of workers according to the chart above. How long would it take 6 workers to complete the room?

(x)(y) = k

(2)(36) = 72

So, k = 72

(6)(y) = 72

Therefore, y = 12 workers

Exponential Functions

y = ax

y = 2x

y = 2(-x)

The independent variable (x) is found in the exponent of the function

Example from PSSA:

What does the graph of y = 2(.25x) look like?

Growth

Decay

Families of Functions

y = x

Linear function (Line)

y = x2

Quadratic Function (Parabola)

y = x3

Cubic Function

Mean – Median - Mode• Mean is the sum of

the data divided by the total number in the data set

• Median is the middle data point – average the middle two if the set has an even number

• Mode is the data point which occurs most

All three of these can be interpreted as the average. Remember that the median is unaffected by really large or small data values. But, the mean can be drastically affected by such values.

Your graphing calculator can calculate the mean and the median quite easily !

STAT, CALC, 1: 1-VAR STATS

Box and Whisker Plots

• Lower quartile (Q1) – middle of the lower half of the data (25% mark)

• Upper quartile (Q3) – middle of the upper half of the data (75% mark)

• Range = Max – Min• IQR = Q3 – Q1

Linear RegressionThe process of “fitting”

a linear function,

y = mx + b

to a particular data set

This process is most efficiently and effectively carried out on a

graphing calculator

STAT, CALC, 4:LinReg

Positive vs. Negative Correlation

• A positive correlation in a set of data points is indicated by a positively sloping (up left to right) line

• A negative correlation is indicated by a negatively sloping (down left to right) line

• Some data display no correlation

Positive

Negative

None

The Pythagorean Theorem

This theorem applies to all right triangles and can be used to find the missing measure of a side of the right triangle. Remember, that “c” is always the side opposite the right angle.

C2 = A2 + B2

A

B

C

If you are missing a leg of the triangle, square the other two sides, subtract, and take thesquare root.

If you are missing the hypotenuse of the triangle, square the two legs, add, and take thesquare root.

Sum of the Interior Angles of a Polygon

• Triangle = 180°• Quadrilateral = 360 °• Any other polygon

180 (n – 2)

Where “n” is the number of sides of the polygon

Exterior angles always add up to 360 °

Angle Relationships

• Vertical angles are congruent (1 and 3, 2 and 4)

• Linear Pairs are supplementary (add up to 180°.

When lines are parallel,

• Corresponding angles are congruent(Ex. 1 and 5, 4 and 8)

• Alt. int. angles are congruent (Ex. 3 and 6, 4 and 5)

• Alt. ext. angles are congruent (Ex. 1 and 8, 2 and 7)

• Same-side int. are supplementary(3 and 5, 4 and 6)

• Same-side ext are supplementary(1 and 7, 2 and 8)