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. To solve a proportion - cross multiply






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






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






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






6. 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






7. 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






8. 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






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






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






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






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






13. 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






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






15. 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






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






17. 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






18. 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






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






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






21. Factor out the perfect squares






22. pr^2






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






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






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






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






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






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






29. Add the exponents and keep the same base






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






31. 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






32. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






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






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






35. 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






36. Volume of a Cylinder = pr^2h






37. 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.






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






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






40. 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






41. 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






42. Part = Percent x Whole






43. 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






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






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






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






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






48. The whole # left over after division






49. 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






50. 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