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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. 2pr
Tangency
Adding and Subtracting Roots
Area of a Triangle
Circumference of a Circle
2. 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 3 and 9
Adding/Subtracting Signed Numbers
Raising Powers to Powers
Function - Notation - and Evaulation
3. 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
Parallel Lines and Transversals
Adding and Subtraction Polynomials
Rate
Setting up a Ratio
4. 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
Area of a Sector
Characteristics of a Parallelogram
Part-to-Part Ratios and Part-to-Whole Ratios
Direct and Inverse Variation
5. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Adding and Subtracting monomials
Interior and Exterior Angles of a Triangle
Reducing Fractions
Using an Equation to Find the Slope
6. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Simplifying Square Roots
Pythagorean Theorem
Multiplying Monomials
Tangency
7. Factor out the perfect squares
Isosceles and Equilateral triangles
Simplifying Square Roots
Multiples of 3 and 9
Average of Evenly Spaced Numbers
8. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
The 5-12-13 Triangle
Finding the Original Whole
Length of an Arc
9. Sum=(Average) x (Number of Terms)
Adding and Subtraction Polynomials
Parallel Lines and Transversals
Using the Average to Find the Sum
Determining Absolute Value
10. pr^2
Surface Area of a Rectangular Solid
Interior and Exterior Angles of a Triangle
Area of a Circle
Solving a Proportion
11. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Multiplying and Dividing Powers
Part-to-Part Ratios and Part-to-Whole Ratios
Solving an Inequality
12. To multiply fractions - multiply the numerators and multiply the denominators
Relative Primes
Multiplying Fractions
The 3-4-5 Triangle
Average Formula -
13. Change in y/ change in x rise/run
Median and Mode
Characteristics of a Square
Using Two Points to Find the Slope
Similar Triangles
14. you can add/subtract when the part under the radical is the same
Solving a Quadratic Equation
Multiplying/Dividing Signed Numbers
Multiplying and Dividing Roots
Adding and Subtracting Roots
15. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Using the Average to Find the Sum
Part-to-Part Ratios and Part-to-Whole Ratios
Comparing Fractions
Adding and Subtracting monomials
16. 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
Multiplying and Dividing Powers
Function - Notation - and Evaulation
Dividing Fractions
17. 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
Intersecting Lines
Adding and Subtraction Polynomials
Even/Odd
The 5-12-13 Triangle
18. 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)
Isosceles and Equilateral triangles
Length of an Arc
Surface Area of a Rectangular Solid
Intersecting Lines
19. 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
Using Two Points to Find the Slope
Using the Average to Find the Sum
Characteristics of a Parallelogram
Interior and Exterior Angles of a Triangle
20. 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
Evaluating an Expression
Union of Sets
Multiplying and Dividing Powers
Identifying the Parts and the Whole
21. The whole # left over after division
Parallel Lines and Transversals
Remainders
Counting the Possibilities
Multiplying/Dividing Signed Numbers
22. 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 Angles of a Polygon
Circumference of a Circle
Multiples of 2 and 4
Part-to-Part Ratios and Part-to-Whole Ratios
23. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Even/Odd
Circumference of a Circle
Intersecting Lines
24. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
(Least) Common Multiple
Interior and Exterior Angles of a Triangle
Interior Angles of a Polygon
Percent Formula
25. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Counting Consecutive Integers
Average Formula -
Greatest Common Factor
26. Surface Area = 2lw + 2wh + 2lh
Multiples of 3 and 9
Surface Area of a Rectangular Solid
Characteristics of a Rectangle
Using the Average to Find the Sum
27. 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
Volume of a Cylinder
Factor/Multiple
Characteristics of a Parallelogram
Combined Percent Increase and Decrease
28. Combine equations in such a way that one of the variables cancel out
Using an Equation to Find an Intercept
Multiples of 3 and 9
Volume of a Cylinder
Solving a System of Equations
29. 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
Direct and Inverse Variation
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
Intersection of sets
30. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Greatest Common Factor
Determining Absolute Value
Evaluating an Expression
Using the Average to Find the Sum
31. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Intersection of sets
Using an Equation to Find an Intercept
Finding the Original Whole
32. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations
Area of a Sector
Circumference of a Circle
Finding the Distance Between Two Points
Relative Primes
33. 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 Proportion
Characteristics of a Parallelogram
The 3-4-5 Triangle
Intersecting Lines
34. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Pythagorean Theorem
Counting the Possibilities
Characteristics of a Rectangle
35. 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
Surface Area of a Rectangular Solid
Characteristics of a Square
Raising Powers to Powers
Adding/Subtracting Signed Numbers
36. 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
Area of a Triangle
Finding the Missing Number
Negative Exponent and Rational Exponent
Using the Average to Find the Sum
37. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Multiples of 2 and 4
Adding/Subtracting Fractions
Average Rate
Median and Mode
38. 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
Similar Triangles
Median and Mode
Multiplying/Dividing Signed Numbers
Adding/Subtracting Fractions
39. Add the exponents and keep the same base
Determining Absolute Value
Multiplying and Dividing Powers
Median and Mode
Average Formula -
40. 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
Average of Evenly Spaced Numbers
Percent Increase and Decrease
Determining Absolute Value
Using Two Points to Find the Slope
41. To find the reciprocal of a fraction switch the numerator and the denominator
Solving a System of Equations
Identifying the Parts and the Whole
Reciprocal
Greatest Common Factor
42. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Solving a Quadratic Equation
Multiplying/Dividing Signed Numbers
Counting Consecutive Integers
43. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Intersection of sets
Counting the Possibilities
Surface Area of a Rectangular Solid
44. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Isosceles and Equilateral triangles
Greatest Common Factor
Using Two Points to Find the Slope
45. 1. Re-express them with common denominators 2. Convert them to decimals
Prime Factorization
Multiplying Fractions
Factor/Multiple
Comparing Fractions
46. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Using an Equation to Find the Slope
Finding the Distance Between Two Points
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
47. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Multiples of 2 and 4
Percent Increase and Decrease
Length of an Arc
48. Probability= Favorable Outcomes/Total Possible Outcomes
Percent Formula
Probability
Relative Primes
Domain and Range of a Function
49. 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
Negative Exponent and Rational Exponent
Solving a Proportion
Finding the Original Whole
Finding the midpoint
50. 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
Interior and Exterior Angles of a Triangle
Percent Increase and Decrease
Factor/Multiple
Adding and Subtracting monomials