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. 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






2. 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






3. Part = Percent x Whole






4. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






5. 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






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






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






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






9. 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






10. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






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. The whole # left over after division






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






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






15. 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






16. 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






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






18. Factor out the perfect squares






19. 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






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






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






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






25. 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






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






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. 2pr






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






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






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






32. 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)






33. pr^2






34. 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






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. 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






37. 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






38. Multiply the exponents






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






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






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






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






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






44. 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)






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






46. 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






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






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






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






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