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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. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Area of a Circle
Negative Exponent and Rational Exponent
Adding and Subtracting Roots
2. 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
Percent Formula
Mixed Numbers and Improper Fractions
Solving an Inequality
Using the Average to Find the Sum
3. 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
Multiplying and Dividing Powers
Finding the Missing Number
Solving a System of Equations
Adding and Subtracting monomials
4. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Mixed Numbers and Improper Fractions
Repeating Decimal
Interior Angles of a Polygon
Even/Odd
5. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding and Subtracting monomials
Intersection of sets
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
6. The largest factor that two or more numbers have in common.
Finding the Distance Between Two Points
Tangency
Circumference of a Circle
Greatest Common Factor
7. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Isosceles and Equilateral triangles
Factor/Multiple
Domain and Range of a Function
Parallel Lines and Transversals
8. 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
Adding/Subtracting Fractions
Adding and Subtracting Roots
Rate
Area of a Triangle
9. (average of the x coordinates - average of the y coordinates)
Solving an Inequality
Finding the midpoint
Interior Angles of a Polygon
Circumference of a Circle
10. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Reciprocal
Percent Formula
Intersecting Lines
Area of a Triangle
11. 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
Median and Mode
Multiplying/Dividing Signed Numbers
Intersection of sets
Finding the Missing Number
12. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Mixed Numbers and Improper Fractions
Adding/Subtracting Fractions
Factor/Multiple
Multiplying and Dividing Roots
13. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
PEMDAS
Average of Evenly Spaced Numbers
Tangency
Finding the Distance Between Two Points
14. 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
Negative Exponent and Rational Exponent
Probability
Finding the midpoint
Using an Equation to Find an Intercept
15. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Solving a System of Equations
Exponential Growth
Setting up a Ratio
Length of an Arc
16. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Volume of a Rectangular Solid
Solving a Proportion
Counting the Possibilities
17. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Tangency
Adding and Subtracting Roots
Intersection of sets
Prime Factorization
18. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Adding and Subtracting monomials
Solving a System of Equations
Using the Average to Find the Sum
19. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Adding/Subtracting Signed Numbers
Tangency
Area of a Triangle
Multiplying Monomials
20. The smallest multiple (other than zero) that two or more numbers have in common.
Multiplying and Dividing Powers
Evaluating an Expression
(Least) Common Multiple
Adding and Subtracting monomials
21. pr^2
Similar Triangles
Adding/Subtracting Signed Numbers
The 5-12-13 Triangle
Area of a Circle
22. 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
Even/Odd
Circumference of a Circle
Percent Increase and Decrease
Direct and Inverse Variation
23. 1. Re-express them with common denominators 2. Convert them to decimals
Even/Odd
Simplifying Square Roots
Comparing Fractions
Multiplying Monomials
24. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
Negative Exponent and Rational Exponent
Direct and Inverse Variation
Percent Increase and Decrease
25. To find the reciprocal of a fraction switch the numerator and the denominator
Intersecting Lines
Domain and Range of a Function
Remainders
Reciprocal
26. A square is a rectangle with four equal sides; Area of Square = side*side
Evaluating an Expression
Relative Primes
Characteristics of a Square
Number Categories
27. 2pr
Isosceles and Equilateral triangles
Similar Triangles
Circumference of a Circle
The 5-12-13 Triangle
28. 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
Isosceles and Equilateral triangles
Dividing Fractions
Area of a Circle
Finding the midpoint
29. 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
Isosceles and Equilateral triangles
Adding/Subtracting Signed Numbers
Interior and Exterior Angles of a Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
30. 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
Identifying the Parts and the Whole
Percent Increase and Decrease
Setting up a Ratio
Using an Equation to Find an Intercept
31. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Circumference of a Circle
Characteristics of a Square
Repeating Decimal
32. Add the exponents and keep the same base
Volume of a Rectangular Solid
Using an Equation to Find the Slope
Repeating Decimal
Multiplying and Dividing Powers
33. you can add/subtract when the part under the radical is the same
Repeating Decimal
Combined Percent Increase and Decrease
Mixed Numbers and Improper Fractions
Adding and Subtracting Roots
34. 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
Factor/Multiple
Repeating Decimal
Using the Average to Find the Sum
Characteristics of a Parallelogram
35. 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
Setting up a Ratio
Average of Evenly Spaced Numbers
Negative Exponent and Rational Exponent
Tangency
36. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Intersecting Lines
Domain and Range of a Function
PEMDAS
Determining Absolute Value
37. 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)
Relative Primes
Median and Mode
Length of an Arc
Negative Exponent and Rational Exponent
38. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Area of a Triangle
Simplifying Square Roots
Multiplying and Dividing Roots
Solving a Quadratic Equation
39. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Part-to-Part Ratios and Part-to-Whole Ratios
The 3-4-5 Triangle
Counting the Possibilities
40. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Tangency
Raising Powers to Powers
Evaluating an Expression
Finding the Missing Number
41. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Mixed Numbers and Improper Fractions
Tangency
Solving a Proportion
Reducing Fractions
42. Probability= Favorable Outcomes/Total Possible Outcomes
Mixed Numbers and Improper Fractions
Adding and Subtracting Roots
Reciprocal
Probability
43. 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
Interior and Exterior Angles of a Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
Circumference of a Circle
Rate
44. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Triangle Inequality Theorem
Average Rate
Characteristics of a Parallelogram
Part-to-Part Ratios and Part-to-Whole Ratios
45. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 2 and 4
Multiplying Monomials
Multiplying/Dividing Signed Numbers
Multiples of 3 and 9
46. 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
Volume of a Rectangular Solid
Repeating Decimal
Finding the Original Whole
Intersection of sets
47. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Solving a Proportion
Negative Exponent and Rational Exponent
Median and Mode
Using an Equation to Find the Slope
48. Multiply the exponents
Even/Odd
Raising Powers to Powers
Multiplying and Dividing Roots
Interior Angles of a Polygon
49. Sum=(Average) x (Number of Terms)
Evaluating an Expression
Reducing Fractions
Number Categories
Using the Average to Find the Sum
50. 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.
Adding/Subtracting Signed Numbers
Volume of a Rectangular Solid
Simplifying Square Roots
Number Categories