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. 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






2. 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






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






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






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






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






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






9. 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






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






11. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






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






13. 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






14. 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






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






16. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)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. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






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






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






21. To solve a proportion - cross multiply






22. 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






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






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






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






26. 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






27. 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






28. 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






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






30. 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.






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






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






33. 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






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






35. Subtract the smallest from the largest and add 1






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






37. Factor out the perfect squares






38. 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






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






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






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






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






43. 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






44. 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






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






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






47. 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






48. Part = Percent x Whole






49. 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






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