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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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 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
Circumference of a Circle
Reciprocal
Mixed Numbers and Improper Fractions
Relative Primes
2. 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
Even/Odd
Intersecting Lines
Identifying the Parts and the Whole
Percent Increase and Decrease
3. Combine like terms
Multiplying Fractions
Adding and Subtraction Polynomials
Reciprocal
Even/Odd
4. Surface Area = 2lw + 2wh + 2lh
Solving a System of Equations
Surface Area of a Rectangular Solid
Dividing Fractions
Finding the midpoint
5. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Solving a System of Equations
Volume of a Rectangular Solid
Adding/Subtracting Fractions
Determining Absolute Value
6. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
The 3-4-5 Triangle
Average of Evenly Spaced Numbers
Rate
Exponential Growth
7. 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
Intersecting Lines
Adding/Subtracting Signed Numbers
Finding the midpoint
Interior and Exterior Angles of a Triangle
8. 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
Relative Primes
Rate
PEMDAS
(Least) Common Multiple
9. To solve a proportion - cross multiply
Solving a Proportion
Dividing Fractions
Even/Odd
Part-to-Part Ratios and Part-to-Whole Ratios
10. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Union of Sets
Isosceles and Equilateral triangles
Solving a Quadratic Equation
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
Intersection of sets
Average of Evenly Spaced Numbers
Mixed Numbers and Improper Fractions
Multiplying/Dividing Signed Numbers
12. Add the exponents and keep the same base
Determining Absolute Value
Relative Primes
Evaluating an Expression
Multiplying and Dividing Powers
13. 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
Parallel Lines and Transversals
PEMDAS
Raising Powers to Powers
Finding the Original Whole
14. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Simplifying Square Roots
Area of a Triangle
Direct and Inverse Variation
Multiples of 2 and 4
15. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Area of a Sector
(Least) Common Multiple
Remainders
16. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
The 5-12-13 Triangle
Average Rate
Dividing Fractions
Repeating Decimal
17. Change in y/ change in x rise/run
Counting Consecutive Integers
Characteristics of a Square
Using Two Points to Find the Slope
Average Rate
18. The largest factor that two or more numbers have in common.
Greatest Common Factor
Adding/Subtracting Signed Numbers
Simplifying Square Roots
Interior Angles of a Polygon
19. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Powers
Multiplying and Dividing Roots
Negative Exponent and Rational Exponent
Determining Absolute Value
20. Factor out the perfect squares
Characteristics of a Parallelogram
Mixed Numbers and Improper Fractions
Remainders
Simplifying Square Roots
21. pr^2
Multiples of 2 and 4
Area of a Circle
Remainders
Union of Sets
22. 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
Area of a Sector
Remainders
Function - Notation - and Evaulation
Adding and Subtracting Roots
23. Part = Percent x Whole
Surface Area of a Rectangular Solid
Average Formula -
Multiples of 2 and 4
Percent Formula
24. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Length of an Arc
(Least) Common Multiple
Counting the Possibilities
Interior Angles of a Polygon
25. 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
Area of a Circle
Exponential Growth
Area of a Triangle
Direct and Inverse Variation
26. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Characteristics of a Square
Average Formula -
Pythagorean Theorem
Similar Triangles
27. For all right triangles: a^2+b^2=c^2
Using Two Points to Find the Slope
Solving an Inequality
Pythagorean Theorem
Multiples of 3 and 9
28. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Finding the Missing Number
Surface Area of a Rectangular Solid
Reducing Fractions
Evaluating an Expression
29. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Surface Area of a Rectangular Solid
Parallel Lines and Transversals
Volume of a Cylinder
30. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Using an Equation to Find the Slope
Multiplying Monomials
Adding/Subtracting Fractions
31. (average of the x coordinates - average of the y coordinates)
Relative Primes
Circumference of a Circle
Area of a Sector
Finding the midpoint
32. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Mixed Numbers and Improper Fractions
Raising Powers to Powers
Intersection of sets
Counting the Possibilities
33. 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
Area of a Circle
Average Rate
Volume of a Rectangular Solid
Area of a Triangle
34. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Triangle Inequality Theorem
Finding the Distance Between Two Points
Multiplying Fractions
Average Rate
35. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Finding the Distance Between Two Points
Factor/Multiple
Adding and Subtraction Polynomials
Solving an Inequality
36. 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
Rate
Area of a Circle
Solving a Proportion
Counting the Possibilities
37. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Multiples of 2 and 4
Tangency
Median and Mode
The 3-4-5 Triangle
38. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Intersection of sets
Solving an Inequality
Domain and Range of a Function
Evaluating an Expression
39. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Identifying the Parts and the Whole
Domain and Range of a Function
Using an Equation to Find the Slope
Union of Sets
40. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 3 and 9
Rate
Function - Notation - and Evaulation
Intersection of sets
41. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
Area of a Triangle
Adding and Subtracting monomials
Exponential Growth
42. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Parallel Lines and Transversals
Adding and Subtracting monomials
Characteristics of a Parallelogram
Finding the Missing Number
43. 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
The 3-4-5 Triangle
Multiples of 3 and 9
Setting up a Ratio
44. Multiply the exponents
Probability
Combined Percent Increase and Decrease
Raising Powers to Powers
Using an Equation to Find an Intercept
45. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Triangle Inequality Theorem
Tangency
The 5-12-13 Triangle
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
Using an Equation to Find the Slope
PEMDAS
Multiplying and Dividing Powers
Triangle Inequality Theorem
47. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Adding/Subtracting Signed Numbers
Median and Mode
Intersecting Lines
Volume of a Rectangular Solid
48. 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
Mixed Numbers and Improper Fractions
Using Two Points to Find the Slope
Solving an Inequality
Interior Angles of a Polygon
49. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Interior Angles of a Polygon
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Sector
Determining Absolute Value
50. 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
Adding and Subtracting monomials
Isosceles and Equilateral triangles
Characteristics of a Rectangle
Domain and Range of a Function