Skill 1

When you see variables or unknowns in the questions and numbers in the answers....

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

"Use the Answers"

Skill 3

"What is m in terms of p and q" is just a fancy way of saying...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

"solve for m" or "use algebra to get m alone."

Skill 4

 When you see the word "mean" or "average" on the ACT, use...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

                          Average =    sum

               ______

                             number of items

Skill 5

When you see vertical angles, a linear pair, or a triangle...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

calculate the measures of all angles

Skill 6

When you see two parallel lines that are crossed by another line, eight angles are formed and...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

all of the bigger-looking angles are equal and all of the smaller-looking angles are equal

Skill 7

When you see a triangle with two equal sides...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

mark the two opposite angles as equal, and when all sides of a triangle are equal, mark all of the angles as 60°

Skill 8

When you see an expression like (2x-5)(5x-4).......

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

 multiply 2x into the second parenthesis, multiply -5 into the second parenthesis, and collect like terms.

(2x-5)(5x-4)=

10x²-8x-25x+20=

10x²-33x+20

Skill 9

Anytime you see a math vocab term...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

underline it.

Skill 10

Define the terms "integer," "prime," "factor," "multiple," "units digit," and "consecutive"

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Integer- numbers w/o decimals or fractions

Prime- a number whose only factors are 1 & itself

Factors- numbers that divide into a number evenly

Multiples- all the numbers that are divisible by a certain number

Units digit- "ones" spot in a number (2 in 672)

Consecutive numbers- numbers in a row

Skill 11

How do you find a least common multiple?

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Write out the multiples of the largest number, and then choose the smallest one that is also a multiple of the other numbers.

Ex. 30 is the LCM of 3,10,15

Skill 13

To find the slope or "rate of change" or a line, use the formula... 

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

                     Slope=                y₁-y₂

                  ________

                   x_1-x₂

Skill 14

Parallel lines have ______ slopes

Perpendicular lines have ________ slopes

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

equal ; 2/3 and 2/3

negative reciprocal ; 2/3 and -3/2

Skill 15

The key to understanding charts and graphs is to read the.....

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

intro material and the "note" if there is one, and to expect an average, percent, and/or probability question about the data.

Skill 16

ƒ(3) means...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

plug 3 in for x

Skill 17

Midpoint formula =

Distance formula = 

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Midpoint= (x+x/2, y+y/2)

Distance= √(x-x)²+(y-y)²

Skill 18

When a question with variables is way too theoretical...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Make it Real

Skill 19 

What are the formulas for the area of a triangle, rectangle, square, parallelogram, and circle?

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

           Triangle..                   A=½bh

           Rectangle..                A=bh

          Square..                      A=s²

         Parallelogram..            A=bh

               Circle..                  A=Πr² 

Skill 20

The area of a donut equals...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

the area of the big guy minus the area of the donut hole.

Skill 21, card 1

4 boys to 5 girls could also be expressed as....

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

4 to 5

4:5

4/5

4 boys to 9 total students

5 girls to 9 total students

Skill 21 Card 2

When you see a proportion on the ACT...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Skill 22

Tell me about matrices.

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Skill 23

When a picture is described but not shown...

draw it

Skill 24

When you see a right triangle, try...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

a²+b²=c²

Skill 26

Similar triangles have sides that are...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

proportional

Skill 25

When you see a 30°, 45°, or 60° angle in a right triangle try using the...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Special right triangles

Skill 27

Translate the following from English to math:

Four less than twenty percent of a number is four

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

.20x-4=4

Skill 29

When something can be factored, FOILed, reduced, or simplified...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Skill 30

Name the law of exponents.

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

n⁶ x n² = n⁸ 

(n⁶)² = n¹²

n¹ = n

2n² + n² = 3n²

n^4/3 = ³√n⁴

n⁶/n² = n⁴

n⁰ = 1

n^-2 = 1/n²

2n + n² does not combine

Skill 31

n^-3/4 =

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

1 

_____

⁴√n³ 

Skill 32

For the equation y = mx + b, the m is the _____ and the b is the _____

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

m is the slope

b is the y-intercept

Skill 33

When you see an arrangement question....

 McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

draw a blank for each position, fill in the # of possibilities to fill in each position, and multiply

Skill 34

What is SohCahToa?

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

sin = opp/hyp

cos = adj/hyp

tan = opp/adj

Skill 36

When you see the word "probability," use the equation...

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Probability = want / total

Skill 37

What are the solutions to the equation

x² - 5x + 4 = O

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

x² - 5x + 4 = 0

           (x-4) (x-10) = 0    factor

so x = 4 or 1     

Skill 38

For the equation y = ax² + bx + c the a tells _____, and the c tells _______.

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

a tells whether the U-shaped graph opens up or down

c tells the y intercept

Skill 39, card 1

For the equation of a circle ( x-3)² + (y+2)² = 25,

the center of is at point __________ and the radius is _______ units long.

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

center =(3,-2)

radius = 25 units long

Skill 39, card 2

Name the equation for a circle.

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Equation = (x-h)² + (y-k)² = r²

where (h,k) is the center and r is the radius of the circle.

Skill 41

When you see absolute value on the ACT....

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

"Use the Answers," or "Make it Real," and remember that absolute value means "ditch the negative sign"

Skill 42, Card 1

What is the difference between an arithmetic sequence and a geometric sequence?

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

An arithmetic sequence is a sequence of numbers where a cetrain number is added to each term to arrive at the next

A geometric sequence is a sequence of numbers where a certain number is multiplied by each term to arrive at the next

Skill 42, Card 2

What is the next term in the geometric sequence 5, -15, 45, -135, _______

McGraw-Hill's Top 50 Skills for a Top Score: ACT MATH by Brian Leaf, M.A.©

Each term is multiplied by -3 to arrive at the next term.

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