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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. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Pythagorean Theorem
Factor/Multiple
Counting Consecutive Integers
2. 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
Characteristics of a Parallelogram
Adding and Subtracting monomials
Even/Odd
Using an Equation to Find the Slope
3. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Combined Percent Increase and Decrease
Median and Mode
Greatest Common Factor
4. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Average Formula -
Rate
Multiplying/Dividing Signed Numbers
Multiples of 2 and 4
5. 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
Domain and Range of a Function
Surface Area of a Rectangular Solid
Finding the Distance Between Two Points
Adding/Subtracting Signed Numbers
6. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Pythagorean Theorem
Surface Area of a Rectangular Solid
Interior Angles of a Polygon
7. Combine equations in such a way that one of the variables cancel out
Raising Powers to Powers
Triangle Inequality Theorem
Volume of a Rectangular Solid
Solving a System of Equations
8. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Multiplying Fractions
Volume of a Rectangular Solid
Reducing Fractions
Parallel Lines and Transversals
9. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Multiples of 3 and 9
Evaluating an Expression
Dividing Fractions
Counting Consecutive Integers
10. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Parallel Lines and Transversals
Similar Triangles
Area of a Sector
Dividing Fractions
11. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Rate
Negative Exponent and Rational Exponent
Using an Equation to Find an Intercept
12. Sum=(Average) x (Number of Terms)
Using Two Points to Find the Slope
Negative Exponent and Rational Exponent
Using the Average to Find the Sum
Multiplying Fractions
13. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Direct and Inverse Variation
Determining Absolute Value
Negative Exponent and Rational Exponent
14. 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
Intersection of sets
Greatest Common Factor
Even/Odd
15. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Multiplying Monomials
Similar Triangles
Volume of a Rectangular Solid
Rate
16. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Using the Average to Find the Sum
Counting Consecutive Integers
Parallel Lines and Transversals
Determining Absolute Value
17. Change in y/ change in x rise/run
Multiples of 2 and 4
Characteristics of a Parallelogram
Average Rate
Using Two Points to Find the Slope
18. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Reciprocal
Percent Formula
Adding/Subtracting Fractions
Parallel Lines and Transversals
19. 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
Number Categories
Isosceles and Equilateral triangles
Function - Notation - and Evaulation
Area of a Triangle
20. Part = Percent x Whole
Solving a System of Equations
Using an Equation to Find the Slope
Percent Formula
Number Categories
21. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding and Subtracting monomials
Interior and Exterior Angles of a Triangle
Solving an Inequality
Multiplying Fractions
22. 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
Multiplying Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Multiples of 3 and 9
Area of a Triangle
23. 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
Pythagorean Theorem
Multiplying and Dividing Powers
Finding the Original Whole
24. Add the exponents and keep the same base
Interior and Exterior Angles of a Triangle
Multiplying/Dividing Signed Numbers
Relative Primes
Multiplying and Dividing Powers
25. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
(Least) Common Multiple
Similar Triangles
Part-to-Part Ratios and Part-to-Whole Ratios
26. 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
Exponential Growth
Multiplying Monomials
Direct and Inverse Variation
Using the Average to Find the Sum
27. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Adding and Subtraction Polynomials
Intersecting Lines
Using an Equation to Find the Slope
28. Volume of a Cylinder = pr^2h
Counting Consecutive Integers
Relative Primes
Volume of a Cylinder
Multiplying Monomials
29. 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
Multiplying Fractions
Solving a Proportion
Exponential Growth
Area of a Circle
30. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Greatest Common Factor
Surface Area of a Rectangular Solid
Average Rate
Multiplying and Dividing Powers
31. 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
Domain and Range of a Function
Similar Triangles
Identifying the Parts and the Whole
Solving a Proportion
32. 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
Solving an Inequality
Setting up a Ratio
Counting the Possibilities
Combined Percent Increase and Decrease
33. pr^2
Determining Absolute Value
Identifying the Parts and the Whole
Area of a Circle
Adding and Subtracting Roots
34. you can add/subtract when the part under the radical is the same
Comparing Fractions
Tangency
Adding and Subtracting Roots
Isosceles and Equilateral triangles
35. To divide fractions - invert the second one and multiply
Parallel Lines and Transversals
Reducing Fractions
Dividing Fractions
Triangle Inequality Theorem
36. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Even/Odd
Combined Percent Increase and Decrease
PEMDAS
37. Factor out the perfect squares
Finding the Distance Between Two Points
Probability
Raising Powers to Powers
Simplifying Square Roots
38. 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
Remainders
Finding the Original Whole
Function - Notation - and Evaulation
Multiples of 3 and 9
39. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
Circumference of a Circle
The 3-4-5 Triangle
Multiplying Fractions
40. 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
Adding/Subtracting Fractions
Interior and Exterior Angles of a Triangle
Adding and Subtraction Polynomials
Reciprocal
41. 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
(Least) Common Multiple
Pythagorean Theorem
Using an Equation to Find an Intercept
Average of Evenly Spaced Numbers
42. 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
Rate
Solving a Proportion
Area of a Sector
Multiplying and Dividing Powers
43. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Percent Increase and Decrease
Using an Equation to Find the Slope
Parallel Lines and Transversals
44. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Median and Mode
Multiples of 3 and 9
Using an Equation to Find the Slope
Factor/Multiple
45. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Simplifying Square Roots
Dividing Fractions
Setting up a Ratio
Identifying the Parts and the Whole
46. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Function - Notation - and Evaulation
Interior Angles of a Polygon
Similar Triangles
Average of Evenly Spaced Numbers
47. 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
The 5-12-13 Triangle
Multiplying/Dividing Signed Numbers
Determining Absolute Value
Greatest Common Factor
48. Multiply the exponents
Using Two Points to Find the Slope
Raising Powers to Powers
Setting up a Ratio
Multiplying and Dividing Roots
49. 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
Finding the Original Whole
Finding the midpoint
Counting the Possibilities
Union of Sets
50. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Determining Absolute Value
Rate
Isosceles and Equilateral triangles