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. Part = Percent x Whole






2. Volume of a Cylinder = pr^2h






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






4. 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






5. 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






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






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






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






9. 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)






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






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






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






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






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






15. 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






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






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






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






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






20. 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






21. 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






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






23. 2pr






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






26. 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)






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






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






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






30. 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






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






32. 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






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






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






35. 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






36. 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






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. 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






39. 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






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






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






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






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






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






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






46. Factor out the perfect squares






47. 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






48. 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






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






50. Probability= Favorable Outcomes/Total Possible Outcomes