## Test your basic knowledge |

# SAT Math: Concepts And Tricks

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

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

**3. Probability= Favorable Outcomes/Total Possible Outcomes**

**4. 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**

**5. Add the exponents and keep the same base**

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

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

**8. 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**

**9. 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**

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

**11. 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**

**12. To multiply fractions - multiply the numerators and multiply the denominators**

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

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

**16. Multiply the exponents**

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

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

**19. 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**

**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. 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**

**22. The whole # left over after division**

**23. Surface Area = 2lw + 2wh + 2lh**

**24. 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**

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

**26. 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**

**27. (average of the x coordinates - average of the y coordinates)**

**28. To solve a proportion - cross multiply**

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

**30. 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**

**31. Change in y/ change in x rise/run**

**32. 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**

**33. 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**

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

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

**36. 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**

**37. 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.**

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

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

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

**42. 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**

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

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

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

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

**47. pr^2**

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

**49. 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**

**50. 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**