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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. The whole # left over after division
Reciprocal
Remainders
Greatest Common Factor
Finding the midpoint
2. 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 Triangle
Adding/Subtracting Fractions
Percent Increase and Decrease
Counting Consecutive Integers
3. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Multiplying Fractions
Reducing Fractions
Multiples of 3 and 9
4. 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
Area of a Triangle
Solving an Inequality
Finding the Missing Number
Determining Absolute Value
5. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Finding the Original Whole
Circumference of a Circle
Interior Angles of a Polygon
6. To find the reciprocal of a fraction switch the numerator and the denominator
Raising Powers to Powers
Percent Formula
Using an Equation to Find the Slope
Reciprocal
7. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Adding/Subtracting Fractions
Volume of a Rectangular Solid
Average of Evenly Spaced Numbers
Rate
8. Part = Percent x Whole
Adding and Subtraction Polynomials
Evaluating an Expression
Percent Formula
Using Two Points to Find the Slope
9. pr^2
Area of a Circle
Number Categories
Adding and Subtracting monomials
Negative Exponent and Rational Exponent
10. Factor out the perfect squares
(Least) Common Multiple
Simplifying Square Roots
Volume of a Rectangular Solid
Intersection of sets
11. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Similar Triangles
Average of Evenly Spaced Numbers
Number Categories
Exponential Growth
12. 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
Mixed Numbers and Improper Fractions
Multiplying Fractions
Solving a Proportion
Even/Odd
13. A square is a rectangle with four equal sides; Area of Square = side*side
The 5-12-13 Triangle
Using an Equation to Find the Slope
Finding the midpoint
Characteristics of a Square
14. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Area of a Sector
Adding/Subtracting Fractions
Union of Sets
Tangency
15. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Multiplying and Dividing Roots
Multiplying Monomials
Greatest Common Factor
Characteristics of a Rectangle
16. Probability= Favorable Outcomes/Total Possible Outcomes
Repeating Decimal
Probability
Characteristics of a Square
Interior Angles of a Polygon
17. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Combined Percent Increase and Decrease
Reducing Fractions
Direct and Inverse Variation
Part-to-Part Ratios and Part-to-Whole Ratios
18. 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
Number Categories
Percent Increase and Decrease
Identifying the Parts and the Whole
Multiplying Fractions
19. 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
The 3-4-5 Triangle
Triangle Inequality Theorem
PEMDAS
Tangency
20. 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
Triangle Inequality Theorem
Relative Primes
Characteristics of a Rectangle
Isosceles and Equilateral triangles
21. The largest factor that two or more numbers have in common.
Evaluating an Expression
Multiplying Fractions
Intersecting Lines
Greatest Common Factor
22. To divide fractions - invert the second one and multiply
Factor/Multiple
Dividing Fractions
Negative Exponent and Rational Exponent
Characteristics of a Rectangle
23. 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
Pythagorean Theorem
Counting Consecutive Integers
Similar Triangles
Direct and Inverse Variation
24. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Finding the Distance Between Two Points
Average Rate
Even/Odd
Domain and Range of a Function
25. 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
Repeating Decimal
Factor/Multiple
Isosceles and Equilateral triangles
Relative Primes
26. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Isosceles and Equilateral triangles
Factor/Multiple
Exponential Growth
Average Rate
27. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
(Least) Common Multiple
Solving a Quadratic Equation
Characteristics of a Square
Average Formula -
28. 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
Rate
Multiplying/Dividing Signed Numbers
Counting Consecutive Integers
Multiplying Monomials
29. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Solving a System of Equations
Parallel Lines and Transversals
Greatest Common Factor
Number Categories
30. 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
Volume of a Cylinder
Repeating Decimal
Solving a Quadratic Equation
31. 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
Volume of a Cylinder
Volume of a Rectangular Solid
Multiplying and Dividing Powers
32. 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 Increase and Decrease
Length of an Arc
Domain and Range of a Function
Triangle Inequality Theorem
33. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Evaluating an Expression
Exponential Growth
Simplifying Square Roots
Adding and Subtracting monomials
34. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Multiples of 3 and 9
Using an Equation to Find the Slope
Finding the Missing Number
35. 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
Triangle Inequality Theorem
Counting the Possibilities
Tangency
Solving a System of Equations
36. Combine like terms
Reciprocal
Average of Evenly Spaced Numbers
Counting the Possibilities
Adding and Subtraction Polynomials
37. 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)
Probability
Prime Factorization
Area of a Sector
Even/Odd
38. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Exponential Growth
Reducing Fractions
Multiplying and Dividing Roots
Average of Evenly Spaced Numbers
39. 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
Function - Notation - and Evaulation
Combined Percent Increase and Decrease
Average Formula -
Dividing Fractions
40. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Finding the Original Whole
Evaluating an Expression
Adding and Subtraction Polynomials
Multiplying and Dividing Roots
41. 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
Solving a Quadratic Equation
Adding/Subtracting Fractions
Function - Notation - and Evaulation
Reciprocal
42. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Parallel Lines and Transversals
Direct and Inverse Variation
Interior and Exterior Angles of a Triangle
43. 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
Finding the midpoint
Solving a Quadratic Equation
Factor/Multiple
Part-to-Part Ratios and Part-to-Whole Ratios
44. 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
Area of a Triangle
Average Rate
Interior and Exterior Angles of a Triangle
Even/Odd
45. you can add/subtract when the part under the radical is the same
Direct and Inverse Variation
Remainders
Solving a System of Equations
Adding and Subtracting Roots
46. Combine equations in such a way that one of the variables cancel out
Similar Triangles
Simplifying Square Roots
Solving a System of Equations
Multiplying/Dividing Signed Numbers
47. 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.
Number Categories
Pythagorean Theorem
Multiples of 2 and 4
Tangency
48. Volume of a Cylinder = pr^2h
Identifying the Parts and the Whole
Volume of a Cylinder
The 3-4-5 Triangle
Similar Triangles
49. 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
Identifying the Parts and the Whole
Finding the Original Whole
Characteristics of a Square
50. 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
Pythagorean Theorem
Even/Odd
Area of a Triangle
Negative Exponent and Rational Exponent