Praxis Math
slope-intercept form
(y = mx + b). The b value gives you the y-intercept and the m value equals the slope of the line. Think of slope as rise over run.
0.0039 in (thickness of a piece of paper
0.0039 ⟹ 3.9×10^−3
Units
1 m = 100 cm 1 yd = 0.9144 m 3 ft = 1 yd 1 mi = 1760 yd 1 in = 2.54 cm 10 mm = 1 cm 1000 m = 1 km 12 in = 1 ft
Reduce 5/15
1/3
100 times as much as x
100x
82 fewer than 117
117-82
The mean of 8, 11, 17, 18, 20, 30 is ______.
17.3
13𝑥 + 6𝑥 − 4 + 1
19x - 3
A blueprint (scaled drawing) is made before constructing a building. The blueprint uses a scale of 2 inches on the drawing represents 3 feet on the building. If the blueprint has the side of the building drawn at 7 inches, what is the actual dimension for that side of the building?
2 𝒊𝒏𝒄𝒉𝒆𝒔/3 𝒇𝒕=7 𝒊𝒏𝒄𝒉𝒆𝒔/𝑥𝒇𝒕 Now solve for x by cross multiplication. 2/3=7/𝑥 2𝑥 = 21 𝑥 = 10.5
2/3×4/5
2/3×4/5= 2×4/3×5= 8/15
The range of 4, 6, 7, 8, 10, 15, 21 is ___.
21-4 = 17
239,000 miles (Approximate distance between the Earth and the Moon)
239,000 ⟹ 2.39×10^5
The mode of 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5 is ___.
3
Solve for x: 𝑥/3= 6
3(𝑥/3) = 3(6) 𝑥 = 18
3/7÷2/3
3/7÷2/3=3/7×3/2=9/14
Which value(s) of 𝑧 make the equation true? 3𝑧 = 21
3𝑧 = 21 3 ̅̅̅ 3 ̅̅̅ 𝑧 = 7
What is the probability of getting a two or a seven?
4/52+4/52=8/52=2/13
A right triangle has both legs = 5cm, what is the third side length?
5^2 + 5^2 = 𝑐^2 25+25 = 𝑐^2 50 = 𝑐^2 √50 = 𝑐 5√2 = 𝑐
The median of 4, 6, 7, 8, 10, 15, 21, is ___.
8
The median of 5, 6, 7, 8, 10, 21, 23, 26 is ___.
9
triangle's interior angles
A triangle's interior angles always have a sum of 180°.
Write an equation to represent the following situation. The difference between the cost of television A and television B is $200 less than television B.
A-B=B-200
Area of a triangle
A=1/2 bh
Area of a trapezoid
A=1/2 h(b1+b2)
Area of a rectangle
A=bh
Are of a square
A=s^2
exponent rule
An exponent rule states that when multiplying you add the exponents. Therefore, (3𝑥)(4𝑥) = 12𝑥^2
exterior angle
An exterior angle of a triangle is equal to the sum of the two remote interior angles.
Formulas for a circle: Area
Area = 𝝅𝒓𝟐 - The space inside a circle is the area of a circle.
Formulas for a circle: Area of a sector(part) of a circle
Area of a sector(part) of a circle = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝑖𝑛 𝑝𝑎𝑟𝑡 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑙𝑒 / 360° 𝜋𝑟2
Formulas for a circle: Circumference
Circumference =𝟐𝝅𝒓 - The distance around a circle is called the circumference. The formulas for area and circumference of a circle have 2 things in common - π and r. If you know either the area or circumference of a circle, you can find the other by solving for r.
Determining if the graph is a function
Determining if the graph is a function. For problem numbers 26 and 27 use the vertical line test to determine if the graph represents a function. If you can put a vertical line in the coordinate plane that crosses the given graph in more than one place, then it is not a function
Determining if the relation (set of ordered pairs) is a function.
Determining if the relation (set of ordered pairs) is a function. When determining if number sets are functions remember that each x value can only be associated with one specific y value.
The Triangle Inequality Theorem
Given the lengths of 2 sides of a triangle, the 3rd side(longest) must be between the difference and the sum of the 2 sides. A triangle cannot have the side lengths of 4 - 6 - 19 because 6 -4 = 2 and 4 + 6 = 10 and 19 is not between 2 and 10. A triangle can have the side lengths of 4 - 8 - 10 because 8 - 4 = 4 and 8 + 4 = 12 and 10 is between 4 and 12.
isosceles triangle
If 2 sides of a triangle are equal, then the opposite angles are also equal. This is an isosceles triangle. The measure of angle A = the measure of angle C. Both equal °.
Percent and Percent Increase/Decrease
In short, a percent is measuring in parts per 100. We can convert a fraction (for example 5/7) to a percent by determining the decimal representation (5/7 = 5÷7 ≈ 0.714) and then multiplying the result by 100 (0.714×100 = 71.4%).
Units
Length Weight Volume 1 centimeter pencil eraser 1 gram 1 liter 1 foot 1 pound 1 gallon 1 kilometer 1 kilogram 1 pint 1 yard 1 ton 1 milliliter 1 meter 1 ounce 1 quart
Metric Conversion
Prefix kilo hecto deca base deci centi milli Value 1000 100 10 1 0.1 0.01 0.001
If you don't replace the card after picking it, what is the probability of getting two kings?
Probability of first king=4/52 Probability of second king=3/51 since you are not replacing the card 4/52∙3/51=1/13∙1/17=1/221
If you replace the card after picking it, what is the probability of getting two kings?
Probability of first king=4/52 Probability of second king=4/52 4/52∙4/52=1/13∙1/13=1/169
Scientific Notation
Scientific notation is a method for representing quite small or quite large values. It expands on our place value system, recognizing that each place value is different from its surrounding place values by a factor of 10. For example, the distance from the Sun to Earth is approximately 93,000,000 miles, which, when written in scientific notation is 9.3×107miles. The exponent (7) tells us the magnitude of the number. After the 9, there are 7 more place values.
Add: 4/9 + 1/9
Since the denominators are the same, add the numerators. 4/9 + 1/9 = 4+1/9 = 5/9
Mean
Sum of the values divided by the number of items
Supplementary angles
Supplementary angles =180°. A straight line forms a straight angle which measures 180°
The Pythagorean Theorem
The Pythagorean Theorem can be used to determine the length of any side of a Right Triangle when given the measure of any 2 sides. 𝒂𝟐 +𝒃𝟐 = 𝒄𝟐 The Pythagorean Theorem is 𝒂𝟐 +𝒃𝟐 = 𝒄𝟐. The legs of the triangle are a and b or the sides coming from the right angle and the hypotenuse is c. The hypotenuse is always the side directly across from the right angle. Given any 2 sides of a right triangle, you can find the third side of the right triangle.
Range
The difference between highest and lowest value. Range = high-low
Median
The middle number.
Circles
There are 360° in a circle.
Add: 1/4+1/3
These denominators are NOT the same. We start by finding the LCD by listing their multiples and finding the smallest number common to both lists. The LCD is 12 1×3/4×3+1×4/3×4 3/12+4/12=7/12
Proportion
Two ratios (think fractions) which are equal to each other. 𝑎/𝑏 = 𝑐/𝑑 We can solve a proportion by "cross-multiplying," that is, multiply the numerator of one fraction to the denominator of the other and set the results equal to each other: 𝑎/𝑏 = 𝑐/𝑑 𝑎𝑑 = 𝑏𝑐
vertical angles
When straight lines intersect, their intersection creates vertical angles.
Function or no? {(3,4) (−1,9) (3,5) (0,9) (−3,−3)}
Would NOT be a function because you have (3,4) and (3,5) within the same set. The 3 cannot be paired with both a 4 and 5 and be a function.
Which of the following lists the numbers in order from least to greatest? a. 3 7 , 7 3 , 3.7, 7.3, 71 3 b. 71 3 , 7 3 , 7.3, 3 7 , 3.7 c. 3.7, 7.3, 71 3 , 7 3 , 3 7 d. 7 3 , 3 7 , 71 3 , 3.7, 7.3
You will probably want to convert these to decimal using your calculator. a
A pet store has 34 cats, 22 dogs, and 13 birds to purchase. What percent of the animals at the pet store are birds? Round your answer to the nearest whole percent. a. 19% b. 23% c. 38% d. 59% e. 73%
a
Multiply: (2.7×10^5)(3.1×10^3) a. 8.37×10^8 b. 8.37×10^2 c. 8.37×10^11 d. 1.15×10^2 e. 1.15×10^8
a
The grassy circle in the middle of the brick path has a diameter of 5 feet. The brick path has a uniform width of 5 feet. Find the area of the brick path around the grassy circle. a) 50π b) 56.25π c) 5π d) 225
a
Which of the following could be the measures of angles of a triangle? Choose all that apply. a) 20°, 30°, 130° b) 50°, 65°, 75° c) 100°, 55°, 25° d) 85°, 25°, 60° e) 60°, 60°, 60° f) 60°, 80°, 50
a,c,e
Statistical question
asking something about a group
If the circumference of a circle is 96 feet, which of the following is closest to the area of the circle? a) 301 square feet b) 730 square feet c) 2200 square feet d) 3500 square feet
b
Joanne has a room in her house which is in the shape of a trapezoid. She would like to purchase new flooring for the room. How much will she need to spend at a price of $3.75 per square foot? a) $132.00 b) $247.50 c) $315.00 d) $495.00
b
Gili needs to paint the wall of his apartment building. The outside measurements of this side of the building are 25 feet x 25 feet. Each window is 5 feet by 5 feet. How many square feet will he need to paint? a) 225 square feet b) 325 squre feet c) 400 squre feet d) 625 squre feet
c
The right circular cone below has a base radius of 8 and a height of 30. The shaded portion of the cone has a height of 15. The volume of the smaller cone is what fraction of the volume of the larger cone? (The formula for the volume of a right circular cone is V = 1/3π𝑟2ℎ.) a) 1/2 b) 1/5 c) 1/8 d) 1/10
c
Which of the following are ordered from least to greatest? a. −.12,−1.2,−2.1,−12,−21 b. −2.1,−1.2,−21,−12,−.12 c. −21,−12,−2.1,−1.2,−.12 d. −1.2,−2.1,−.12,−21,−12
c
If trapezoid ABCD is mapped to trapezoid A'B'C'D' so that trapezoid ABCD is not congruent to trapezoid A'B'C'D', which of the following is a possible transformation? Select all that apply. a) A 180° counter-clockwise rotation about the origin. b) A reflection over the y-axis. c) A dilation of scale 2. d) A translation of 2 units down and 4 unit to the right. e) A reduction of scale ½.
c,e
Divide: 4.03×10^8 / 1.3×10^4 a. 5.239×10^12 b. 5.239×10^4 c. 3.1×10^12 d. 3.1×10^4
d
It's time for Dave to clean his fish tank. What is the volume of clean water he will need to refill his tank that is 36" by 13" by 24"? a) 468 cubic inches b) 864 cubic inches c) 5,616 cubic inches d) 11,232 cubic inches
d
Which of the following lists the numbers in order from greatest to least? a. 3.72, 3.71999, 3.72001, 3.71299, 3.72999 b. 3.72999, 3.72, 3.72001, 3.71299, 3.71999 c. 3.71299, 3.71999, 3.72, 3.72001, 3.72999 d. 3.72001, 3.72, 3.71299, 3.72999, 3.71999 e. 3.72999, 3.72001, 3.72, 3.71999, 3.71299
e
3𝑥 +2 = 11
equation 3𝑥 +2 = 11 Step 1 3𝑥 +2−2 = 11−2 (subtract 2 from both sides) Step 2 3𝑥 3 = 9 3 (divide both sides by 3) Answer 𝑥 = 3
−4𝑥 + 1 < 21
equation −4𝑥 + 1 < 21 Step 1 −4𝑥 + 1−1 < 21−1 (subtract 1 from both sides) Step 2 −4𝑥 −4 < 20 −4 (divide both sides by -4) Answer 𝑋 > −5 (reverse the inequality sign)
Radius(r)
half the distance across a circle
Reflection
is a "flip" over a line on the plane, typically the x or y-axis. Think of this like turning the page in a book.
transformation
is a manipulation of an object, shape, line or point, on a plane. You start with a preimage(A - A) and then complete the transformation and end with an image(A' - A prime).
Translation
is a movement from one place on the plane to another, also known as a slide. Like giving directions on a map, go 2 blocks north and 3 blocks to the left.
cross-section
is a shape that is created when a solid figure is cut by a plane. If the shape is cut by a plane parallel to the base of the figure, the shape of the cross-section will be similar to the base of the figure. If the plane is not parallel to the base of the figure, careful examination is necessary.
Rotation
is a turn about a point. You need to know which way to make the turn(clockwise or counter-clockwise, right or left) and by how much(90°, 180°, 270°, 360°).
Sampling
is the act of selecting your sample. The best way to select your sample is randomly, where all possibilities are included.
Surface Area
is the amount needed to cover a solid figure. To find surface area, we need to find the area of each face of an object
Volume
is the amount of space a substance will occupy. It is also known as capacity, how much an object can hold. Volume is labeled in cubic units and is a three-dimensional measure. When finding the volume, you can include the height/depth to an area measure(multiplying length by width and then by height) and find the volume. Volume equals the area of the base multiplied by the height (or depth).
Probability
measures likelihood 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑒𝑠 (𝑤ℎ𝑎𝑡 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡) _______________________________________ 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 Probability is always a number between 0 and 1. It can be 0 (no chance) or 1 (a sure thing). Some other rules include the addition rule and the multiplication rule. When it says "or", use addition. When it says "and," use multiplication.
Mode
most frequent number that occurs.
The cost of a bus ticket to Chicago is $15 less than a ticket to New York.
n-15
Write an equation to represent the following situation. Sherry has five more marbles than Kelly and Jenny combined.
s=(k+j)+5
Sue has 8 more books than Dan. (use s for Sue and d for Dan)
s=d+8
Diameter(d)
the distance across a circle that goes through the center of the circle.
Linear regression
tries to find a relationship between two variables. A strong positive linear relationship means the points almost form a straight line that is increasing from left to right. A strong negative relationship means the points almost form a straight line that is decreasing from left to right. When thinking of positive or negative relationship, think slope.
Reduction
will have a scale factor(0.5 or ½) to tell you how much smaller the object is to be. Think of reducing/losing weight - you are getting smaller.
Dilation
will have scale factor(2 means twice as large) to tell you how many times larger the object is to be. Think of getting your pupils dilated at the optometrist. They get larger!
100 more than x
x=100
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 Multiplication rule
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝐴 𝑎𝑛𝑑 𝐵 = 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝐴 × 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝐵 Depending on the situation, the probability of B might be different.
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 Addition rule
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝐴 𝑜𝑟 𝐵 = 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝐴+𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝐵 −𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝐴 𝑎𝑛𝑑 𝐵 If A and B cannot happen at the same time, then probability of A and B is equal to 0.
use a standard 52 deck of cards, what is the probability of getting an ace?
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑔𝑒𝑡𝑡𝑖𝑛𝑔 𝑎𝑛 𝑎𝑐𝑒 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑐𝑒𝑠 𝑡𝑜𝑡𝑎𝑙 _______________________________ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠 = 4/52 = 1/13
Solve: 𝑦 −15 = 8
𝑦 −15 = 8 +15 +15 𝑦 = 23
