Golani Act Prep Flashcards For Math

Front 1

A value x, increased by 30% can be written as:

Back 1

1.3x

Front 2

The solutions to a quadratic are 4 and -5. What could be the original equation?

Back 2

Work backwards:

(x-4)(x+5) =0

x^2 +x -20=0

OR ANY MULTIPLE such as 2x^2 +2x -40 =0

Front 3

Function transformations:

f(x+a)

f(x-a)

f(x)+a

f(x)-a

Back 3

f(x+a): Left a units

f(x-a): Right a units

f(x)+a: Up a units

f(x)-a: Down a units

Front 4

Natural or Counting Numbers

Back 4

1, 2, 3, 4,...

Front 5

What comes to mind in this figure?

Back 5

Draw a radius! (From O to B).

Use Pythagorean's Theorem from there. (6-8-10 triangle)

Front 6

Whole Numbers

Back 6

0, 1, 2, 3,...

Front 7

Odd Numbers

Back 7

Whole numbers not divisible by 2.
1, 3, 5, 7,...

Front 8

Even Numbers

Back 8

Whole numbers divisible by 2.
0, 2, 4, 6,...

Front 9

Integers

Back 9

...–2, –1, 0, 1, 2,...

Front 10

Negative Integers

Back 10

...–3, –2, –1

Front 11

Positive Integers

Back 11

The natural numbers.

Front 12

Rational Numbers

Back 12

Can be written as a fraction.
For example, 3/4, 7, 0 are all rational.
Any decimal with a pattern is rational, such as 2.45454545.

Front 13

Irrational Numbers

Back 13

Cannot be written as fraction.
Pi and root 5, for example.

Front 14

Sum

Back 14

The answer in an addition problem

Front 15

Product

Back 15

The answer in a multiplication problem

Front 16

Difference

Back 16

The answer in a subtraction problem

Front 17

Quotient

Back 17

The answer in a division problem

Front 18

Digits

Back 18

There are TEN digits. They are 0–9

Front 19

Units digit

Back 19

The digit in the ones place. In the number 6,789, it's the nine

Front 20

Prime

What is the first prime number?

Back 20

Any number that can be divided by one and itself 2 is the first prime number

Front 21

Factor

Back 21

the integers that can be multiplied into a number; factors of 18 are 1,2,3,6,9,18

Front 22

Multiple

Back 22

The answers you get when you multiply by a number. The Multiples of 7 are 7, 14, 21...

Front 23

Circumference

Back 23

Distance around the perimeter of a circle. C=2(Pi)R

Front 24

Mean

Back 24

Arithmetic average. Add all numbers and divide by the number of numbers

Front 25

Median

Back 25

The middle number in a set of numbers. If there are an even number of numbers, then the median is the mean of the middle two.

Front 26

Mode

Back 26

The most frequently occurring number in a set of numbers.

Front 27

Area of a triangle

Back 27

1/2 x b x h,

b = base

h =height.

Don't forget the 1/2 !!!

Front 28

Area of a rectangle and square

Back 28

l x w,

l =length

w = width

Front 29

Area of a parallelogram

Back 29

b x h

b = base

h = height

Front 30

Area of a trapezoid

Back 30

1/2 x (b1 + b2) x h,

b1 = base 1

b2 = base 2,

h = height

Front 31

Area of a circle

Back 31

pi x r^2

Front 32

Volume of a rectangular box and cube

Back 32

l x w x h, l = length w = width, h = height

Front 33

Absolute Value

Back 33

Absolute Value means how far a number is from zero. The absolute value of 6 is 6, and the absolute value of −6 is also 6.

Front 34

30% of a Number

Back 34

0.3x

Front 35

x^3 *x^6 =

Back 35

x^9

The simplest way to multiply variables with exponents is to just add exponents!

Front 36

x^(-2)

Back 36

1/x^2

A negative exponent means how many times to divide one by the number.

Front 37

x^(1/2)

Back 37

An exponent of 1/2 is actually square root. An exponent of 1/3 is cube root.
An exponent of 1/4 is 4th root
And so on!

Front 38

Plugging In

Back 38

Using real numbers instead of variables to help make math easy

When it can be used
~variables are in the question and answer choice

Front 39

Backsolving Strategy

Back 39

Use answer choices to solve the problem

Start with C. If it is too small, then eliminate smaller answers, if too big, get rid of larger answers.

When it can be used
*when being asked for a value of a variable
*when the answers are simple numbers

Front 40

What method of solving comes to mind?

Back 40

Use your calculator (Casio users). EQUA, POLY, degree of 3.

Front 41

What method comes to mind?

Solve for x: 3x + 2x/3 - 1 = 17x/5

Back 41

Use your calculator (Casio users)

EQUA, Solver.

Front 42

What method of solving comes to mind?

Solve for x and y

2x + 3y = 18

-5x + 31 = 4y

Back 42

Use your calculator (Casio users)

EQUA, SIML. Type in the coefficients, but be sure to first put into ax + by =c form.

Front 43

What method comes to mind? What is greater, 3 3/7 or 3.45

Back 43

Convert all terms to decimals on your calculator

Front 44

A value x decreased by 20% can be written as:

Back 44

0.8x

Front 45

Find the percent change from 20 to 24.

Back 45

4/20 = x/100

x = 20%

Formula:

Change/original = percent /100

Front 46

What comes to mind?

(3+a)/a

Back 46

V for Victory

3/a + a/a = 3/a +1

Front 47

Find the Vertical Asymptote

y= 3/(x-4)

Back 47

At x=4

(When a denominator =0)

Front 48

How would one solve for x?

|x-3|=6

Back 48

Solve two equations:

x-3 = 6

x-3 = -6

Front 49

How would one solve for x?

|x-3|>6

Back 49

Solve two inequalities:

x-3>6

x-3< -6

(Don't forget to negate the second one!)

Front 50

What comes to mind:

"Consecutive Even Integers"

Back 50

x

x+2

x+4

Front 51

What comes to mind:

Consecutive Odd Integers

Back 51

x

x+2

x+4

Front 52

This system of equations has "infinitely many solutions"

2x+4y = 8

kx + 8y = 16

Solve for k

Back 52

The equations must be the same

The second is a multiple of the first when k=4

Front 53

(3x^4)^2

Back 53

9x^8.

Powers get multiplied, coefficient get taken to the power outside the parentheses.

Front 54

3^x + 3^x =

Back 54

2 * 3^x.

NOT 3^2x or 6^x

Front 55

3^3 =

Back 55

27

NOT 9!!!

Front 56

Solve for x

Back 56

Find the common base, in this case, 2.

Front 57

Rationalize 2/Root 3

Back 57

Multiply top and bottom by root 3.

The Casio can do it for you! It can simplify all radicals

Front 58

Cube root of x^15 =

Back 58

x^5

(15 divided by 3)

Front 59

Solve for x

Back 59

Square both sides. x-1 = 16.

x = 17.

check your answer.

Front 60

(2x-4)^2

Back 60

FOIL problem!

Front 61

What comes to mind?

4x^2 -25

Back 61

This is always a difference of two squares problem:

(2x+5)(2x-5)

Rule: (a^2 - b^2) = (a+b)(a-b)

Front 62

Solve for x:

2x^2 =200

Back 62

x^2 = 100

x + 10 OR -10

Two solutions!!!!

Front 63

x^3 = 64

Back 63

x is 4 only (not -4).

When the power is odd, there is only one real solution.

Front 64

Find the maximum or minimum value of a quadratic.

For example, y = 2x^2 +8x

Back 64

Vertex problem

Formula: x = -b/2a

ex) -8/2(2) = -2

Front 65

Find the vertex:

y = 2(x-5)^2 +3

Back 65

Use the formula:

y = a(x-h)^2 +k

In this example, it is (5,3)

Front 66

i^2 =

i^4 =

Back 66

i^2 = -1

i^4 = 1

Your calculator can solve all imaginary number problems

Front 67

One point on a quadratic is (0,-6) and the vertex is at (4,-2). Find another point.

Back 67

Use symmetry. The new point is (8,-6)

Front 68

The ratio of a to b is 2 to 3.

The ratio of b to c is 4 to 7.

Find the ratio of a to c

Back 68

Use the common middle ratio.

a to b becomes 8 to 12

b to c becomes 12 to 21.

The ratio of a to c is 8 to 21

Front 69

What comes to mind with the words "direct variation" or "varies directly"

Back 69

y = kx.

Most problems can be solved as a simple proportion.

Front 70

What comes to mind with the words "inverse variation" or "varies inversely".

ex) y and x vary inversely. x = 2 when y =4. Solve for y when x = 8.

Back 70

yx=k

Use the given information to solve for k

ex) 2 * 4 = 8, so k = 8

Now 8y = 8

so y = 1

Front 71

What is always true about direct variation?

Back 71

It passes through the origin.

(Since y = kx, it is the same as y = kx + 0. The y intercept is zero.)

Front 72

The average of a frequency table.

Find the average number of pets

Number of pets number of people

0 - 3

1 - 8

2 - 5

Back 72

0 * 3 +

1 * 8 +

2 * 5

=18.

Then divide by the number of PEOPLE (not the number of categories!!!)

= 18 / 16 =1.125

Front 73

Range

Back 73

The highest minus the lowest number of a data set.

Front 74

There are 3 colors shirts, 4 pants, and 5 hats. in how many ways can a person choose one of each?

Back 74

The Counting Principle. Multiply 3X4X5

Front 75

In how many ways can I arrange a 4 stripe flag with the colors black, green, red and orange if the last color must be red or orange and no colors can repeat?

Back 75

Start with the point of greatest restriction.

The last color is red or orange -- two options. The others have no restrictions:

= 3 X 2 X 1 X 2 (the last 2 represents red or orange)

Front 76

Find the probability of choosing a king then a queen from a deck (no replacement)

Back 76

"And" or "Then" means MULTIPLY

4/52 X 4/51.

Note how there are fewer cards in the deck after the first pick!

Front 77

In a grade of 70, there are 20 people in class A, 30 in class B and 10 in both. How many are in neither?

Back 77

Venn diagram. Start in the middle!

10 in middle. Then 10 in A only. 20 in B only.

Leaves 30.

Front 78

Arithmetic sequence

Back 78

Has a common difference.

Can be expressed as x, x+c, x+2c, x+3c ...

Ex) 4,8,12,16 ...

The common difference is 4.

Front 79

Geometric sequence

Back 79

Has a common ratio.

Can be expressed as x, xr, xr^2, xr^3.

To find that ratio, just do second term/first term.

Ex) 4, -12, 36, -108...

The common ratio is -3.

Front 80

Find the 47th color:

Blue, yellow, red, pink, blue, yellow, ...

Back 80

BYRP repeats.

Divide 47 by 4. The remainder is 3.

So the 47th color is the same as the 3rd, which is red.

Front 81

f(x) --> f(-x) changes the graph in what way?

Back 81

Reflect over the y axis

Front 82

f(x) --> -f(x) changes the graph in what way?

Back 82

Reflect over the x axis

Front 83

f(x) --> -f(-x) changes the graph in what way?

Back 83

Reflect over the origin

Front 84

How do you find the inverse function?

Back 84

a) Write f(x) as y.

b) Flip the x and y.

c) isolate the new y. This is the inverse function.

Front 85

Domain

Back 85

Possible values that x can take

Front 86

Range

Back 86

Possible values that y or f(x) can take

Front 87

Symbol Problems:

If $x = x^2 - x

Find $ (a+2)

Back 87

a+2 replaces x.

Traps: FOIL and DISTRIBUTION

(a+2)^2 -(a+2) ...

Front 88

f(x) = x^2

Find f(-4)

Back 88

(-4)^2 = 16.

Don't forget parentheses on your calculator!!!

Front 89

Slope

Back 89

aka "Rise over Run"

Front 90

Sketch

Positive, negative, zero and undefined slope.

Back 90

Front 91

y= 5 graphs what kind of line?

Back 91

Horizontal

Front 92

x = -3 graphs what kind of line?

Back 92

vertical.

(Be an "X-Vert" at this!)

Front 93

Parallel lines have slopes that are -

Back 93

Equal

Front 94

Perpendicular lines have slopes that are -

Back 94

negative reciprocals (negative and flip)

Front 95

How can one find the y intercept?

Back 95

Plug in x = 0

For lines, you can use the b in y = mx +b

Front 96

How can one find the x intercept?

Back 96

Plug in y = 0

Front 97

(x,y) becomes what when reflected over the:

x axis

y axis

origin

line y=x

Back 97

x axis: (x,-y)

y axis (-x , y)

origin (-x,-y)

line y=x (y, x)

Front 98

Midpoint Formula

Back 98

Front 99

Point A is at (4,6) and point B is unknown. The Midpoint of A and B is (7,1). Find B.

Back 99

Use the midpoint formula or use intuition.

Answer: (10,-4)

Front 100

Distance Formula

Back 100

Front 101

Find the slope and y intercept of 3y = 6x -1

Back 101

Be sure to isolate y first!!!

y = 2x -1/3

2 = slope

1/3 = y intercept

Front 102

Line a and b are parallel. c and d are not.

What angles are the same as angle 4?

Back 102

4=7 (vertical angles)

From there, use the "Z method"

7 = 12 and 12 = 15.

So 4=7=12=15

There is no connection with the upper half of the diagram since c and d are not parallel.

Front 103

A = 50 degrees.

Find angle B

Back 103

This is a case of parallel line cut by a transversal (even though the top and bottom lines don't continue). The angles are supplementary (clearly, they are not equal).

B = 130

Front 104

Find the area of the yellow.

Back 104

Front 105

Find the arc length from A to B

Back 105

120/360 X 2(pi)R = 1/3 of 8pi.

or 8Pi/3

Front 106

Find the angle measure of AOB

Back 106

AOB is the same angle measure as the arc measure, which is 120 degrees.

Front 107

Find the arc measure (degree) of AC

Back 107

Double the angle that opens up to it from across the circle

Front 108

Equation of a circle

Back 108

(h,k) is the center, r is the radius. (This is also on the Casio Calculator under "Conics")

Front 109

Solve for x

Back 109

Be careful!

3 is to 6 as x is to x+4

Solve the equation algebraically. x = 4

Front 110

What comes to mind in this figure?

Back 110

The triangle is isosceles, because the two radii are the congruent.

Angle A = Angle C .

A +B + C = 180.

Front 111

What 4 methods are there to prove two triangles congruent?

Back 111

SAS

ASA

SSS

AAS

(Hy-Leg also works)

ASS Does NOT work ("Bad - ASS")

Front 112

Three Pythagorean Triples you should know by heart

Back 112

3-4-5 (or any multiple, such as 6-8-10 or 30-40-50)

5-12-13 (or any multiple, such as 10-24-26)

8-15-17 (or any multiple, such as 16-30-34)

Front 113

What comes to mind?

Back 113

Pythagorean's Theorem: 5^2 + x^2 = 13^2

x = 12

Front 114

Area of a rhombus

Back 114

base X height

or (d1 X d2)/2

Front 115

What do we know about angles in a parallelogram?

Back 115

a) Opposite angles are equal

b) Any two adjacent angles are supplementary

c) All angles add to 360

Front 116

Formula for sum of the angles in a polygon.

Back 116

(n-2) 180

Front 117

Volume of a cylinder (usually given)

Back 117

V = pi (r^2)h

h=height of cylinder

r = radius

Front 118

Identify a face, edge and vertex

Back 118

Front 119

Find the Surface Area

Back 119

6X5 twice +

6X11 twice +

5X11 twice =

302 square cm.

Front 120

Define:

Sin <

Cos <

Tan <

Sec <

Csc <

Cot <

Back 120

Front 121

How would one find the value of x?

Back 121

use Inverse Trig Functions

Sin x = 7/25

Use your calculator: sin^-1(7/25) = 16.26 degrees.

Front 122

Convert from radians to degrees and vice versa.

Ex) Convert 30 degrees to radians.

Back 122

Radians/pi = degrees/180

R/pi = 30/180

R = pi/6

(shortcut: pi = 180 degrees)

Front 123

In what quadrants are what trig functions pos and neg?

Back 123

Front 124

y= 2sin 3x.

Find the amplitude, frequence, period

Back 124

y = a sin bx

|a| = amplitude

b = frequency

360 / b (or 2pi/b) = period

amp = 2

freq =3

period = 120 degrees or 2pi/3

Front 125

=

Back 125

Front 126

Rewrite without logs

Back 126

Front 127

Expand the logarithm

Back 127

Front 128

If P--> Q is true, then what else can be concluded?

Back 128

The contrapositive

~Q ---> ~ P

Front 129

Find the horizontal asymptote:

a) (5x +2)/3x

b) (5x^2 +2)/3x

c) (5x +2)/3x^2

Back 129

A horizontal asymptote occurs as x --> infinity

a) 5/3

b) infinity (since the power in the numerator is greater)

c) 0 (since the power in the denominator is greater)

Front 130

Solve:

x^2 -6x -72=0

Back 130

a) (x-12)(x+6) =0

x = 12, or x = -6

b) Use your calculator! EQUA, POLY, degree 2.