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 multiply fractions - multiply the numerators and multiply the denominators






2. 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






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






4. 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






5. 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






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






7. 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






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






9. 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






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






11. 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






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






13. 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






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






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






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






17. 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






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






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






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






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






22. 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)






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






24. 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






25. pr^2






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






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






28. Factor out the perfect squares






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






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






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. 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






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






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






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






36. 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






37. 2pr






38. 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






39. Subtract the smallest from the largest and add 1






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






41. Part = Percent x Whole






42. 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






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






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






45. 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






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






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






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






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






50. 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