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

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

**3. 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**

**4. 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**

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

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

**7. 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**

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

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

**10. 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**

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

**12. 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**

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

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

**16. 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**

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

**18. 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**

**19. 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**

**20. 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**

**21. 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**

**22. 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**

**23. 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**

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

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

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

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

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

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

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

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

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

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

**34. Combine like terms**

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

**36. 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**

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

**39. 2pr**

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

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

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

**43. 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**

**44. 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**

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

**46. Volume of a Cylinder = pr^2h**

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

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

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

**50. Part = Percent x Whole**