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






2. Volume of a Cylinder = pr^2h






3. Factor out the perfect squares






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






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






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






7. 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






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






9. Subtract the smallest from the largest and add 1






10. 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






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






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






13. pr^2






14. 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






15. Part = Percent x Whole






16. 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






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






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






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






20. 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






21. 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)






22. 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






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






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






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






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






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






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






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






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






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






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 find the reciprocal of a fraction switch the numerator and the denominator






34. 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






35. The whole # left over after division






36. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






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






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






39. 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






40. 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






41. Combine like terms






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






43. 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.






44. 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






45. 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






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. 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






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






49. 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






50. 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