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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. 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
Finding the Distance Between Two Points
Interior Angles of a Polygon
Multiplying Monomials
Solving an Inequality
2. 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
Finding the Distance Between Two Points
The 3-4-5 Triangle
Mixed Numbers and Improper Fractions
Direct and Inverse Variation
3. 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
Interior and Exterior Angles of a Triangle
Using the Average to Find the Sum
Solving a Proportion
Multiplying Fractions
4. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Area of a Sector
Characteristics of a Parallelogram
Multiples of 2 and 4
Median and Mode
5. pr^2
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Circle
Identifying the Parts and the Whole
Negative Exponent and Rational Exponent
6. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Raising Powers to Powers
PEMDAS
Multiples of 3 and 9
Tangency
7. To solve a proportion - cross multiply
Solving a Proportion
Even/Odd
Probability
Volume of a Cylinder
8. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Reducing Fractions
Negative Exponent and Rational Exponent
Interior Angles of a Polygon
Tangency
9. 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
Using the Average to Find the Sum
Even/Odd
The 5-12-13 Triangle
Isosceles and Equilateral triangles
10. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Area of a Triangle
Rate
Setting up a Ratio
Identifying the Parts and the Whole
11. 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
Percent Formula
Multiples of 3 and 9
Identifying the Parts and the Whole
12. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Determining Absolute Value
Multiplying/Dividing Signed Numbers
Area of a Triangle
13. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Setting up a Ratio
Rate
Number Categories
14. you can add/subtract when the part under the radical is the same
Factor/Multiple
Multiplying and Dividing Powers
Adding and Subtracting Roots
Identifying the Parts and the Whole
15. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Factor/Multiple
Multiples of 2 and 4
Counting Consecutive Integers
16. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Identifying the Parts and the Whole
Percent Increase and Decrease
Characteristics of a Rectangle
Exponential Growth
17. To divide fractions - invert the second one and multiply
Dividing Fractions
Average Rate
Volume of a Cylinder
Adding/Subtracting Signed Numbers
18. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Area of a Triangle
Rate
Volume of a Rectangular Solid
Greatest Common Factor
19. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Part-to-Part Ratios and Part-to-Whole Ratios
Similar Triangles
Union of Sets
Setting up a Ratio
20. Combine equations in such a way that one of the variables cancel out
Even/Odd
Relative Primes
Length of an Arc
Solving a System of Equations
21. To find the reciprocal of a fraction switch the numerator and the denominator
Rate
Average of Evenly Spaced Numbers
Reciprocal
Multiplying and Dividing Powers
22. 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
Repeating Decimal
Similar Triangles
Rate
Solving an Inequality
23. 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
Negative Exponent and Rational Exponent
Factor/Multiple
Remainders
Triangle Inequality Theorem
24. (average of the x coordinates - average of the y coordinates)
Finding the Missing Number
Using an Equation to Find the Slope
Finding the midpoint
Solving a Quadratic Equation
25. The whole # left over after division
Remainders
Triangle Inequality Theorem
Multiples of 2 and 4
Average Rate
26. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Setting up a Ratio
Combined Percent Increase and Decrease
Intersection of sets
Exponential Growth
27. The smallest multiple (other than zero) that two or more numbers have in common.
PEMDAS
(Least) Common Multiple
The 3-4-5 Triangle
Finding the Distance Between Two Points
28. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Solving a Proportion
Median and Mode
Probability
Parallel Lines and Transversals
29. 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
Reciprocal
Area of a Sector
Relative Primes
The 5-12-13 Triangle
30. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Determining Absolute Value
Multiplying and Dividing Roots
Factor/Multiple
Percent Formula
31. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Solving a Quadratic Equation
Triangle Inequality Theorem
Determining Absolute Value
Function - Notation - and Evaulation
32. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Probability
Pythagorean Theorem
Using an Equation to Find the Slope
33. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Volume of a Cylinder
Dividing Fractions
Evaluating an Expression
Volume of a Rectangular Solid
34. 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
Evaluating an Expression
The 3-4-5 Triangle
Area of a Triangle
Adding and Subtracting Roots
35. 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
Mixed Numbers and Improper Fractions
Evaluating an Expression
Adding and Subtraction Polynomials
Function - Notation - and Evaulation
36. To multiply fractions - multiply the numerators and multiply the denominators
Adding and Subtracting monomials
Multiplying Fractions
Greatest Common Factor
(Least) Common Multiple
37. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Relative Primes
Raising Powers to Powers
Multiplying Fractions
38. 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
Evaluating an Expression
Number Categories
Finding the Missing Number
39. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)
Percent Formula
Characteristics of a Square
Domain and Range of a Function
Length of an Arc
40. Sum=(Average) x (Number of Terms)
Union of Sets
Using the Average to Find the Sum
Characteristics of a Rectangle
Multiplying Fractions
41. 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
Adding and Subtraction Polynomials
Identifying the Parts and the Whole
Area of a Sector
Part-to-Part Ratios and Part-to-Whole Ratios
42. 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
Average Formula -
Adding/Subtracting Signed Numbers
Part-to-Part Ratios and Part-to-Whole Ratios
Even/Odd
43. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Raising Powers to Powers
Area of a Triangle
Average Formula -
Finding the Distance Between Two Points
44. 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
Solving a System of Equations
Using the Average to Find the Sum
Solving an Inequality
Negative Exponent and Rational Exponent
45. 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
Adding and Subtraction Polynomials
The 5-12-13 Triangle
Solving a Proportion
Finding the Original Whole
46. 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
Multiplying Monomials
Adding and Subtracting monomials
The 3-4-5 Triangle
Surface Area of a Rectangular Solid
47. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Using an Equation to Find an Intercept
Finding the Distance Between Two Points
Volume of a Cylinder
Solving a Proportion
48. 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
Intersection of sets
Mixed Numbers and Improper Fractions
Greatest Common Factor
Negative Exponent and Rational Exponent
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
Remainders
Average Rate
Percent Increase and Decrease
Using Two Points to Find the Slope
50. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12
Area of a Sector
Median and Mode
Negative Exponent and Rational Exponent
Finding the Missing Number