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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 find the reciprocal of a fraction switch the numerator and the denominator
The 3-4-5 Triangle
Comparing Fractions
Median and Mode
Reciprocal
2. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Parallel Lines and Transversals
Tangency
Evaluating an Expression
Solving a Proportion
3. 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.
Area of a Circle
Circumference of a Circle
Number Categories
Reciprocal
4. 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
Area of a Triangle
Isosceles and Equilateral triangles
Similar Triangles
Interior and Exterior Angles of a Triangle
5. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Determining Absolute Value
Percent Increase and Decrease
Multiplying Fractions
6. The whole # left over after division
Using an Equation to Find an Intercept
Remainders
Circumference of a Circle
(Least) Common Multiple
7. Subtract the smallest from the largest and add 1
Interior Angles of a Polygon
Domain and Range of a Function
Mixed Numbers and Improper Fractions
Counting Consecutive Integers
8. 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
Percent Increase and Decrease
Setting up a Ratio
Area of a Sector
Interior Angles of a Polygon
9. 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
The 5-12-13 Triangle
Dividing Fractions
Length of an Arc
Median and Mode
10. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Surface Area of a Rectangular Solid
Adding and Subtracting monomials
Adding/Subtracting Signed Numbers
Average Formula -
11. 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
Area of a Circle
Solving a Proportion
Even/Odd
Domain and Range of a Function
12. For all right triangles: a^2+b^2=c^2
Tangency
Pythagorean Theorem
Union of Sets
Combined Percent Increase and Decrease
13. 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
Surface Area of a Rectangular Solid
Multiplying/Dividing Signed Numbers
Function - Notation - and Evaulation
Reciprocal
14. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Area of a Circle
Raising Powers to Powers
Characteristics of a Rectangle
15. 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
Even/Odd
Interior and Exterior Angles of a Triangle
Average Rate
Length of an Arc
16. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110
Direct and Inverse Variation
Adding/Subtracting Signed Numbers
Combined Percent Increase and Decrease
Characteristics of a Square
17. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations
Part-to-Part Ratios and Part-to-Whole Ratios
Negative Exponent and Rational Exponent
Repeating Decimal
Relative Primes
18. 2pr
Using an Equation to Find an Intercept
Circumference of a Circle
The 5-12-13 Triangle
Average of Evenly Spaced Numbers
19. Sum=(Average) x (Number of Terms)
Finding the Missing Number
Comparing Fractions
Adding/Subtracting Fractions
Using the Average to Find the Sum
20. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Using an Equation to Find an Intercept
Combined Percent Increase and Decrease
The 5-12-13 Triangle
21. 1. Re-express them with common denominators 2. Convert them to decimals
Relative Primes
Counting the Possibilities
Combined Percent Increase and Decrease
Comparing Fractions
22. Multiply the exponents
Using the Average to Find the Sum
Interior Angles of a Polygon
Raising Powers to Powers
Relative Primes
23. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Solving a Quadratic Equation
Identifying the Parts and the Whole
Finding the Original Whole
Parallel Lines and Transversals
24. 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
Function - Notation - and Evaulation
Finding the Distance Between Two Points
Interior Angles of a Polygon
25. Probability= Favorable Outcomes/Total Possible Outcomes
Triangle Inequality Theorem
Solving a System of Equations
Domain and Range of a Function
Probability
26. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Probability
Average Formula -
Multiples of 2 and 4
Isosceles and Equilateral triangles
27. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Determining Absolute Value
Average Formula -
Average of Evenly Spaced Numbers
Finding the Original Whole
28. 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
Length of an Arc
Direct and Inverse Variation
Area of a Triangle
Average Formula -
29. The smallest multiple (other than zero) that two or more numbers have in common.
Pythagorean Theorem
(Least) Common Multiple
PEMDAS
Adding and Subtracting Roots
30. 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
Rate
Using an Equation to Find the Slope
Domain and Range of a Function
31. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Volume of a Rectangular Solid
Average Formula -
Determining Absolute Value
Multiples of 2 and 4
32. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Exponential Growth
Solving an Inequality
Comparing Fractions
Tangency
33. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Parallelogram
Characteristics of a Square
Combined Percent Increase and Decrease
Rate
34. 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
Area of a Sector
Median and Mode
Volume of a Rectangular Solid
35. 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
Even/Odd
Multiples of 2 and 4
Using Two Points to Find the Slope
36. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Finding the midpoint
Multiplying Fractions
The 3-4-5 Triangle
Average Formula -
37. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Counting the Possibilities
Using an Equation to Find an Intercept
Comparing Fractions
Median and Mode
38. (average of the x coordinates - average of the y coordinates)
Part-to-Part Ratios and Part-to-Whole Ratios
Surface Area of a Rectangular Solid
Finding the Original Whole
Finding the midpoint
39. 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
Finding the Missing Number
Volume of a Rectangular Solid
Adding/Subtracting Fractions
Finding the Original Whole
40. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Multiplying Monomials
Volume of a Rectangular Solid
Solving a Proportion
Raising Powers to Powers
41. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Finding the Missing Number
Reducing Fractions
Evaluating an Expression
42. 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
Area of a Sector
Finding the Original Whole
Adding/Subtracting Signed Numbers
Volume of a Cylinder
43. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Number Categories
Adding and Subtraction Polynomials
Using Two Points to Find the Slope
Intersection of sets
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
Multiplying and Dividing Roots
(Least) Common Multiple
Reciprocal
Combined Percent Increase and Decrease
45. 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
Solving an Inequality
Finding the Original Whole
Intersection of sets
46. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Characteristics of a Parallelogram
PEMDAS
Direct and Inverse Variation
47. Factor out the perfect squares
Area of a Triangle
Simplifying Square Roots
Direct and Inverse Variation
Interior and Exterior Angles of a Triangle
48. Combine equations in such a way that one of the variables cancel out
Characteristics of a Parallelogram
Solving a System of Equations
Comparing Fractions
Finding the Original Whole
49. Surface Area = 2lw + 2wh + 2lh
Direct and Inverse Variation
Surface Area of a Rectangular Solid
Adding and Subtracting Roots
The 5-12-13 Triangle
50. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Union of Sets
Solving a Quadratic Equation
Area of a Sector
Finding the Original Whole