Test your basic knowledge |

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. Subtract the smallest from the largest and add 1






2. 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






3. 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






4. 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






5. 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






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






7. The whole # left over after division






8. 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






9. Factor out the perfect squares






10. Multiply the exponents






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






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






13. 2pr






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






15. Volume of a Cylinder = pr^2h






16. Add the exponents and keep the same base






17. To divide fractions - invert the second one and multiply






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






19. 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






20. 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






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






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






23. 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






24. 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






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






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






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






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






29. (average of the x coordinates - average of the y coordinates)






30. 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






31. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common






32. 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)






33. 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






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






35. 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.






36. 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






37. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






38. Surface Area = 2lw + 2wh + 2lh






39. 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)






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






41. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






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






43. 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






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






45. Domain: all possible values of x for a function range: all possible outputs of a function






46. pr^2






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






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






49. 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






50. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4