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Test your basic knowledge |
SAT Math: Concepts And Tricks
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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. 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
Surface Area of a Rectangular Solid
Volume of a Cylinder
Rate
Simplifying Square Roots
2. To divide fractions - invert the second one and multiply
Multiplying Monomials
Dividing Fractions
Mixed Numbers and Improper Fractions
Characteristics of a Square
3. 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
Multiplying Monomials
Characteristics of a Parallelogram
Multiplying Fractions
Even/Odd
4. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Using an Equation to Find the Slope
Exponential Growth
Union of Sets
Characteristics of a Parallelogram
5. you can add/subtract when the part under the radical is the same
Characteristics of a Square
Adding and Subtracting Roots
Volume of a Rectangular Solid
Surface Area of a Rectangular Solid
6. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Average Rate
Solving a Quadratic Equation
Multiples of 3 and 9
Counting the Possibilities
7. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Isosceles and Equilateral triangles
Volume of a Rectangular Solid
Finding the Distance Between Two Points
Raising Powers to Powers
8. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Solving a Quadratic Equation
Characteristics of a Rectangle
Finding the Missing Number
Using Two Points to Find the Slope
9. 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
Multiplying and Dividing Roots
Area of a Triangle
Mixed Numbers and Improper Fractions
Similar Triangles
10. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Intersection of sets
Factor/Multiple
Using the Average to Find the Sum
Using an Equation to Find an Intercept
11. Combine equations in such a way that one of the variables cancel out
Solving a Proportion
Part-to-Part Ratios and Part-to-Whole Ratios
Volume of a Rectangular Solid
Solving a System of Equations
12. Add the exponents and keep the same base
Rate
Solving a Proportion
Multiplying and Dividing Powers
Part-to-Part Ratios and Part-to-Whole Ratios
13. 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)
Area of a Sector
Finding the Original Whole
Characteristics of a Parallelogram
Counting the Possibilities
14. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Comparing Fractions
The 3-4-5 Triangle
Exponential Growth
Intersecting Lines
15. To solve a proportion - cross multiply
Finding the Missing Number
Using Two Points to Find the Slope
Identifying the Parts and the Whole
Solving a Proportion
16. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
The 5-12-13 Triangle
Reciprocal
Using an Equation to Find an Intercept
17. The whole # left over after division
Percent Formula
Remainders
Average Formula -
Pythagorean Theorem
18. 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
Solving an Inequality
The 5-12-13 Triangle
Pythagorean Theorem
Relative Primes
19. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Number Categories
Counting Consecutive Integers
Negative Exponent and Rational Exponent
20. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Percent Increase and Decrease
Adding and Subtracting monomials
Finding the Distance Between Two Points
PEMDAS
21. 2pr
Part-to-Part Ratios and Part-to-Whole Ratios
Circumference of a Circle
Intersection of sets
Rate
22. For all right triangles: a^2+b^2=c^2
Interior and Exterior Angles of a Triangle
Raising Powers to Powers
Pythagorean Theorem
Using an Equation to Find the Slope
23. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Characteristics of a Rectangle
Finding the midpoint
Greatest Common Factor
24. 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
Average of Evenly Spaced Numbers
Multiplying and Dividing Powers
Mixed Numbers and Improper Fractions
Identifying the Parts and the Whole
25. 1. Re-express them with common denominators 2. Convert them to decimals
Isosceles and Equilateral triangles
Triangle Inequality Theorem
Comparing Fractions
Solving a System of Equations
26. To multiply fractions - multiply the numerators and multiply the denominators
Percent Increase and Decrease
Multiplying Fractions
Raising Powers to Powers
Multiplying and Dividing Powers
27. 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
Intersection of sets
Using the Average to Find the Sum
Adding/Subtracting Signed Numbers
Isosceles and Equilateral triangles
28. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Adding/Subtracting Fractions
Negative Exponent and Rational Exponent
Volume of a Cylinder
29. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Solving a System of Equations
Remainders
Raising Powers to Powers
30. Probability= Favorable Outcomes/Total Possible Outcomes
Even/Odd
Probability
Multiples of 2 and 4
Multiples of 3 and 9
31. The largest factor that two or more numbers have in common.
Using an Equation to Find the Slope
Greatest Common Factor
Even/Odd
Percent Increase and Decrease
32. pr^2
Probability
Similar Triangles
Area of a Circle
Part-to-Part Ratios and Part-to-Whole Ratios
33. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Using the Average to Find the Sum
Raising Powers to Powers
Multiplying/Dividing Signed Numbers
34. Sum=(Average) x (Number of Terms)
Prime Factorization
Counting the Possibilities
Using the Average to Find the Sum
Interior Angles of a Polygon
35. 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
Isosceles and Equilateral triangles
Using Two Points to Find the Slope
Percent Formula
Part-to-Part Ratios and Part-to-Whole Ratios
36. Surface Area = 2lw + 2wh + 2lh
Adding and Subtraction Polynomials
Using an Equation to Find an Intercept
Surface Area of a Rectangular Solid
Finding the Missing Number
37. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
PEMDAS
Isosceles and Equilateral triangles
Tangency
38. Change in y/ change in x rise/run
Adding and Subtracting Roots
Simplifying Square Roots
Using Two Points to Find the Slope
Adding and Subtraction Polynomials
39. 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
Multiplying/Dividing Signed Numbers
Union of Sets
Solving an Inequality
Setting up a Ratio
40. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Mixed Numbers and Improper Fractions
Volume of a Rectangular Solid
Percent Increase and Decrease
Multiples of 3 and 9
41. 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
Negative Exponent and Rational Exponent
Domain and Range of a Function
Isosceles and Equilateral triangles
Dividing Fractions
42. 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
Even/Odd
Surface Area of a Rectangular Solid
Reciprocal
Exponential Growth
43. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Raising Powers to Powers
Average Formula -
Remainders
Interior Angles of a Polygon
44. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Finding the Distance Between Two Points
Multiples of 3 and 9
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying and Dividing Roots
45. To find the reciprocal of a fraction switch the numerator and the denominator
Remainders
Reciprocal
Adding/Subtracting Signed Numbers
Adding/Subtracting Fractions
46. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Percent Increase and Decrease
Function - Notation - and Evaulation
Characteristics of a Square
47. 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
Parallel Lines and Transversals
Function - Notation - and Evaulation
Solving an Inequality
Part-to-Part Ratios and Part-to-Whole Ratios
48. 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
Using Two Points to Find the Slope
Even/Odd
Rate
Finding the Original Whole
49. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Adding/Subtracting Fractions
Reducing Fractions
Finding the Distance Between Two Points
Finding the Original Whole
50. Factor out the perfect squares
Reciprocal
Simplifying Square Roots
Interior Angles of a Polygon
Exponential Growth