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SAT Math: Concepts And Tricks

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 add or subtract fraction - first find a common denominator - then add or subtract the numerators






2. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






3. 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






4. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






5. Combine equations in such a way that one of the variables cancel out






6. 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






7. 2pr






8. A square is a rectangle with four equal sides; Area of Square = side*side






9. 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






10. 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






11. you can add/subtract when the part under the radical is the same






12. 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.






13. 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






14. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






15. 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






16. 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






17. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






18. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






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






20. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






21. 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)






22. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact






23. The largest factor that two or more numbers have in common.






24. The median is the value that falls in the middle of the set - the mode is the value that appears most often






25. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






26. 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






27. Volume of a Cylinder = pr^2h






28. The whole # left over after division






29. Part = Percent x Whole






30. pr^2






31. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






32. 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






33. 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






34. Combine like terms






35. 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






36. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






37. Sum=(Average) x (Number of Terms)






38. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






39. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






40. 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






41. Change in y/ change in x rise/run






42. Add the exponents and keep the same base






43. To find the reciprocal of a fraction switch the numerator and the denominator






44. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






45. To multiply fractions - multiply the numerators and multiply the denominators






46. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






47. Probability= Favorable Outcomes/Total Possible Outcomes






48. Subtract the smallest from the largest and add 1






49. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3






50. 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