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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
:
sat
,
math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The largest factor that two or more numbers have in common.
The 5-12-13 Triangle
Negative Exponent and Rational Exponent
Greatest Common Factor
Finding the midpoint
2. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50
Percent Increase and Decrease
Negative Exponent and Rational Exponent
Triangle Inequality Theorem
Finding the Distance Between Two Points
3. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
PEMDAS
Using Two Points to Find the Slope
Multiplying Fractions
4. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side
Solving a Quadratic Equation
Average Formula -
Rate
The 3-4-5 Triangle
5. To solve a proportion - cross multiply
Surface Area of a Rectangular Solid
Greatest Common Factor
Characteristics of a Square
Solving a Proportion
6. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Characteristics of a Square
Intersection of sets
Union of Sets
Counting the Possibilities
7. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Reciprocal
Factor/Multiple
Using an Equation to Find the Slope
Determining Absolute Value
8. Probability= Favorable Outcomes/Total Possible Outcomes
Characteristics of a Parallelogram
Prime Factorization
Union of Sets
Probability
9. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen
Average of Evenly Spaced Numbers
Counting the Possibilities
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Square
10. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg
Counting Consecutive Integers
Domain and Range of a Function
Isosceles and Equilateral triangles
Greatest Common Factor
11. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Union of Sets
Volume of a Cylinder
Determining Absolute Value
12. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Multiples of 3 and 9
Solving a Quadratic Equation
Similar Triangles
13. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr
Number Categories
The 5-12-13 Triangle
Adding/Subtracting Signed Numbers
Using an Equation to Find the Slope
14. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Similar Triangles
Determining Absolute Value
Finding the midpoint
15. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110
Greatest Common Factor
Percent Formula
Combined Percent Increase and Decrease
Counting Consecutive Integers
16. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Setting up a Ratio
Characteristics of a Rectangle
Isosceles and Equilateral triangles
Even/Odd
17. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is
Repeating Decimal
Greatest Common Factor
Triangle Inequality Theorem
Direct and Inverse Variation
18. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign
Finding the midpoint
Multiples of 2 and 4
Solving an Inequality
Determining Absolute Value
19. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520
Factor/Multiple
Identifying the Parts and the Whole
Area of a Circle
Finding the Original Whole
20. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height
Characteristics of a Parallelogram
Percent Formula
Solving a System of Equations
Triangle Inequality Theorem
21. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Multiplying and Dividing Roots
Percent Increase and Decrease
Exponential Growth
22. Combine like terms
Adding/Subtracting Fractions
Adding/Subtracting Signed Numbers
Finding the Distance Between Two Points
Adding and Subtraction Polynomials
23. To divide fractions - invert the second one and multiply
Reducing Fractions
Mixed Numbers and Improper Fractions
Dividing Fractions
Identifying the Parts and the Whole
24. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle
Solving a Proportion
Simplifying Square Roots
Multiplying Monomials
The 5-12-13 Triangle
25. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Surface Area of a Rectangular Solid
Simplifying Square Roots
Interior Angles of a Polygon
Solving an Inequality
26. Add the exponents and keep the same base
Using the Average to Find the Sum
Counting the Possibilities
Multiplying and Dividing Powers
Combined Percent Increase and Decrease
27. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Prime Factorization
Adding and Subtracting monomials
Using an Equation to Find the Slope
Interior Angles of a Polygon
28. For all right triangles: a^2+b^2=c^2
Tangency
Comparing Fractions
Pythagorean Theorem
Raising Powers to Powers
29. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Parallel Lines and Transversals
Reducing Fractions
Percent Increase and Decrease
Determining Absolute Value
30. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Length of an Arc
Adding/Subtracting Fractions
Factor/Multiple
Determining Absolute Value
31. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x
Adding and Subtracting monomials
Remainders
Using an Equation to Find an Intercept
Volume of a Cylinder
32. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of
Average Rate
Exponential Growth
Using the Average to Find the Sum
Multiplying Monomials
33. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get
Interior Angles of a Polygon
The 5-12-13 Triangle
Mixed Numbers and Improper Fractions
Using an Equation to Find the Slope
34. The smallest multiple (other than zero) that two or more numbers have in common.
Prime Factorization
Factor/Multiple
(Least) Common Multiple
Domain and Range of a Function
35. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Relative Primes
Triangle Inequality Theorem
Using an Equation to Find the Slope
Characteristics of a Parallelogram
36. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12
Average Formula -
Finding the Missing Number
Intersection of sets
Multiplying Fractions
37. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Adding and Subtracting Roots
Determining Absolute Value
Multiplying Monomials
Multiplying/Dividing Signed Numbers
38. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet
Adding and Subtracting Roots
Rate
Area of a Triangle
Determining Absolute Value
39. The whole # left over after division
Using Two Points to Find the Slope
Remainders
Intersecting Lines
Adding and Subtracting Roots
40. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Finding the midpoint
Using an Equation to Find the Slope
Median and Mode
41. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)
Area of a Sector
Volume of a Cylinder
The 3-4-5 Triangle
Determining Absolute Value
42. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Repeating Decimal
Multiplying and Dividing Roots
Similar Triangles
Multiples of 3 and 9
43. 2pr
Percent Formula
Domain and Range of a Function
Circumference of a Circle
Area of a Circle
44. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Area of a Sector
Raising Powers to Powers
Adding/Subtracting Signed Numbers
45. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Area of a Triangle
Median and Mode
Adding and Subtraction Polynomials
Determining Absolute Value
46. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Using Two Points to Find the Slope
Surface Area of a Rectangular Solid
Using the Average to Find the Sum
47. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Direct and Inverse Variation
Multiplying and Dividing Roots
Determining Absolute Value
Intersecting Lines
48. Part = Percent x Whole
Surface Area of a Rectangular Solid
Percent Formula
The 5-12-13 Triangle
Mixed Numbers and Improper Fractions
49. A square is a rectangle with four equal sides; Area of Square = side*side
Average of Evenly Spaced Numbers
Characteristics of a Square
Finding the Original Whole
Repeating Decimal
50. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3
Triangle Inequality Theorem
Part-to-Part Ratios and Part-to-Whole Ratios
Counting Consecutive Integers
(Least) Common Multiple