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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. 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
Multiplying Fractions
Remainders
Solving an Inequality
Setting up a Ratio
2. 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
Area of a Triangle
Using an Equation to Find an Intercept
Area of a Circle
The 3-4-5 Triangle
3. 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
The 3-4-5 Triangle
Counting Consecutive Integers
Mixed Numbers and Improper Fractions
Volume of a Cylinder
4. you can add/subtract when the part under the radical is the same
Percent Increase and Decrease
Adding and Subtracting Roots
(Least) Common Multiple
Adding/Subtracting Fractions
5. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa
Multiplying and Dividing Roots
Adding and Subtracting Roots
Direct and Inverse Variation
Interior Angles of a Polygon
6. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Parallel Lines and Transversals
Multiples of 3 and 9
Using an Equation to Find an Intercept
PEMDAS
7. Combine equations in such a way that one of the variables cancel out
Repeating Decimal
Solving a System of Equations
Volume of a Cylinder
Comparing Fractions
8. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Adding and Subtracting monomials
PEMDAS
Mixed Numbers and Improper Fractions
Average Formula -
9. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides
PEMDAS
Union of Sets
Triangle Inequality Theorem
The 5-12-13 Triangle
10. 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
Union of Sets
Multiplying and Dividing Roots
Solving a System of Equations
Mixed Numbers and Improper Fractions
11. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Dividing Fractions
Percent Formula
Repeating Decimal
Volume of a Rectangular Solid
12. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Isosceles and Equilateral triangles
Median and Mode
Dividing Fractions
Domain and Range of a Function
13. For all right triangles: a^2+b^2=c^2
Multiplying and Dividing Powers
Solving an Inequality
Pythagorean Theorem
Tangency
14. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)
Length of an Arc
Triangle Inequality Theorem
Even/Odd
Parallel Lines and Transversals
15. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the
Isosceles and Equilateral triangles
Using Two Points to Find the Slope
Solving a Proportion
Negative Exponent and Rational Exponent
16. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign
Triangle Inequality Theorem
Determining Absolute Value
Median and Mode
Multiplying/Dividing Signed Numbers
17. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Dividing Fractions
Using an Equation to Find the Slope
Combined Percent Increase and Decrease
Simplifying Square Roots
18. 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
Finding the Missing Number
Identifying the Parts and the Whole
Finding the Original Whole
Exponential Growth
19. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex
Function - Notation - and Evaulation
Finding the Original Whole
Comparing Fractions
Area of a Triangle
20. To find the reciprocal of a fraction switch the numerator and the denominator
Dividing Fractions
(Least) Common Multiple
Solving a System of Equations
Reciprocal
21. 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
Comparing Fractions
Counting the Possibilities
Average Formula -
Characteristics of a Square
22. Probability= Favorable Outcomes/Total Possible Outcomes
The 5-12-13 Triangle
Remainders
Probability
Average Rate
23. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
The 3-4-5 Triangle
Volume of a Cylinder
Prime Factorization
Multiples of 2 and 4
24. Combine like terms
Adding and Subtraction Polynomials
Solving an Inequality
Using an Equation to Find the Slope
Area of a Sector
25. Factor out the perfect squares
Simplifying Square Roots
Area of a Sector
Exponential Growth
(Least) Common Multiple
26. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds
Multiplying/Dividing Signed Numbers
Length of an Arc
Identifying the Parts and the Whole
Union of Sets
27. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them
Finding the Missing Number
Reciprocal
Even/Odd
Direct and Inverse Variation
28. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Finding the midpoint
Volume of a Cylinder
Multiplying Monomials
Isosceles and Equilateral triangles
29. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiplying Monomials
Solving a Proportion
Multiplying and Dividing Roots
Multiples of 2 and 4
30. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Counting Consecutive Integers
Intersection of sets
Area of a Sector
Raising Powers to Powers
31. The largest factor that two or more numbers have in common.
Negative Exponent and Rational Exponent
Adding and Subtracting monomials
Greatest Common Factor
Characteristics of a Parallelogram
32. 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
Finding the Missing Number
Raising Powers to Powers
Finding the midpoint
Solving a System of Equations
33. A square is a rectangle with four equal sides; Area of Square = side*side
Setting up a Ratio
Characteristics of a Square
Multiplying Fractions
The 3-4-5 Triangle
34. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Reducing Fractions
Union of Sets
Adding and Subtracting monomials
Repeating Decimal
35. pr^2
Area of a Circle
Part-to-Part Ratios and Part-to-Whole Ratios
(Least) Common Multiple
Adding and Subtraction Polynomials
36. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Area of a Circle
Number Categories
Factor/Multiple
Combined Percent Increase and Decrease
37. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Even/Odd
Intersecting Lines
Multiplying and Dividing Roots
Adding and Subtraction Polynomials
38. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Repeating Decimal
Multiples of 3 and 9
Determining Absolute Value
Even/Odd
39. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.
Multiplying and Dividing Powers
Intersection of sets
Number Categories
Adding and Subtraction Polynomials
40. 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
Mixed Numbers and Improper Fractions
The 3-4-5 Triangle
Using an Equation to Find the Slope
Finding the Original Whole
41. Add the exponents and keep the same base
PEMDAS
Adding and Subtraction Polynomials
Raising Powers to Powers
Multiplying and Dividing Powers
42. To solve a proportion - cross multiply
Solving a Proportion
Adding and Subtracting monomials
Multiplying Monomials
Identifying the Parts and the Whole
43. Sum=(Average) x (Number of Terms)
Determining Absolute Value
Factor/Multiple
Area of a Sector
Using the Average to Find the Sum
44. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Mixed Numbers and Improper Fractions
Area of a Circle
PEMDAS
Intersecting Lines
45. (average of the x coordinates - average of the y coordinates)
Probability
Finding the midpoint
Rate
Average of Evenly Spaced Numbers
46. Surface Area = 2lw + 2wh + 2lh
Using Two Points to Find the Slope
Surface Area of a Rectangular Solid
Area of a Circle
Multiples of 2 and 4
47. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Multiplying Fractions
Reducing Fractions
Solving a Quadratic Equation
Exponential Growth
48. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees
Percent Formula
Multiplying and Dividing Powers
Interior and Exterior Angles of a Triangle
Similar Triangles
49. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Multiplying and Dividing Roots
Exponential Growth
Triangle Inequality Theorem
50. 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
Interior Angles of a Polygon
Relative Primes
Part-to-Part Ratios and Part-to-Whole Ratios