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






2. 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)






3. Volume of a Cylinder = pr^2h






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






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






6. Factor out the perfect squares






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






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






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






10. 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






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






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






13. 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






14. 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






15. 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






16. 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






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






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






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






20. 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.






21. Add the exponents and keep the same base






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






23. 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






24. 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






25. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






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






27. 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






28. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






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






30. 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






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






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






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






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






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






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






37. 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)






38. 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






39. 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






40. Probability= Favorable Outcomes/Total Possible Outcomes






41. 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






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






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






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






45. 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






46. 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






47. Subtract the smallest from the largest and add 1






48. 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






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. 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