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






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






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






4. 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






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






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






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






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






9. Factor out the perfect squares






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






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






12. 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






13. 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.






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






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






16. Multiply the exponents






17. 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






18. 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






19. To solve a proportion - cross multiply






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






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






22. 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






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






24. 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






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






26. 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






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






28. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






29. 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






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. 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






32. 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






33. The whole # left over after division






34. 2pr






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






36. 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






37. 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






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






39. 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






40. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






41. 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






42. 1. Re-express them with common denominators 2. Convert them to decimals






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






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






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






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






47. Add the exponents and keep the same base






48. Combine like terms






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. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them