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. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






2. 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






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






4. Probability= Favorable Outcomes/Total Possible Outcomes






5. 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






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






7. Multiply the exponents






8. The smallest multiple (other than zero) that two or more numbers have in common.






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






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






11. 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






12. Combine like terms






13. 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)






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






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






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






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






18. 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






19. 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






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






21. 2pr






22. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






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






24. 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






25. 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






26. 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






27. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






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






29. 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






30. 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






31. Part = Percent x Whole






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






33. Volume of a Cylinder = pr^2h






34. 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






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. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






37. 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






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






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






40. 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






41. Subtract the smallest from the largest and add 1






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






43. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






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






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






46. 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






47. Factor out the perfect squares






48. 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






49. For all right triangles: a^2+b^2=c^2






50. 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