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






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






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






5. 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






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






7. 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.






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






9. Combine like terms






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






11. 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






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






13. 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






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






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






16. 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






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






18. The whole # left over after division






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






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






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






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






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






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






25. 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






26. 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






27. 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






28. Probability= Favorable Outcomes/Total Possible Outcomes






29. To solve a proportion - cross multiply






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. Subtract the smallest from the largest and add 1






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






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






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






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






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






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






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






39. 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






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






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






42. Factor out the perfect squares






43. 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






44. 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






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






46. 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






47. 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






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






49. Volume of a Cylinder = pr^2h






50. 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