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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. Change in y/ change in x rise/run
Counting Consecutive Integers
Repeating Decimal
Using Two Points to Find the Slope
Multiplying Fractions
2. Domain: all possible values of x for a function range: all possible outputs of a function
Greatest Common Factor
Multiplying and Dividing Roots
Domain and Range of a Function
Multiplying/Dividing Signed Numbers
3. For all right triangles: a^2+b^2=c^2
Probability
Pythagorean Theorem
Multiplying Monomials
Adding/Subtracting Signed Numbers
4. 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
Interior and Exterior Angles of a Triangle
Pythagorean Theorem
Using an Equation to Find the Slope
5. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Average of Evenly Spaced Numbers
Volume of a Cylinder
Multiples of 3 and 9
Using an Equation to Find an Intercept
6. 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
Triangle Inequality Theorem
Multiplying Fractions
Adding and Subtracting Roots
Parallel Lines and Transversals
7. 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
Surface Area of a Rectangular Solid
Repeating Decimal
Even/Odd
Solving a System of Equations
8. Subtract the smallest from the largest and add 1
Direct and Inverse Variation
Isosceles and Equilateral triangles
Counting Consecutive Integers
Adding/Subtracting Fractions
9. 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
Direct and Inverse Variation
Triangle Inequality Theorem
Reducing Fractions
Rate
10. 2pr
Characteristics of a Rectangle
Pythagorean Theorem
Greatest Common Factor
Circumference of a Circle
11. you can add/subtract when the part under the radical is the same
Average Formula -
Multiplying and Dividing Powers
Adding/Subtracting Signed Numbers
Adding and Subtracting Roots
12. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Simplifying Square Roots
Average Rate
Length of an Arc
Combined Percent Increase and Decrease
13. 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
Using an Equation to Find an Intercept
Characteristics of a Square
Using an Equation to Find the Slope
Simplifying Square Roots
14. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Surface Area of a Rectangular Solid
Relative Primes
Average Rate
15. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
(Least) Common Multiple
Average Formula -
Multiplying Fractions
Identifying the Parts and the Whole
16. 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
Finding the midpoint
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
Raising Powers to Powers
17. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Area of a Circle
Adding/Subtracting Fractions
Determining Absolute Value
Exponential Growth
18. The smallest multiple (other than zero) that two or more numbers have in common.
Using Two Points to Find the Slope
Tangency
(Least) Common Multiple
Number Categories
19. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Relative Primes
Adding/Subtracting Fractions
Using an Equation to Find an Intercept
PEMDAS
20. 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
Solving an Inequality
Isosceles and Equilateral triangles
Counting Consecutive Integers
Repeating Decimal
21. 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
Function - Notation - and Evaulation
Greatest Common Factor
Adding and Subtraction Polynomials
The 3-4-5 Triangle
22. Surface Area = 2lw + 2wh + 2lh
Negative Exponent and Rational Exponent
Even/Odd
Percent Increase and Decrease
Surface Area of a Rectangular Solid
23. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Counting the Possibilities
Median and Mode
Adding and Subtraction Polynomials
24. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Evaluating an Expression
Finding the midpoint
Adding and Subtraction Polynomials
25. To divide fractions - invert the second one and multiply
Even/Odd
The 3-4-5 Triangle
Multiplying Monomials
Dividing Fractions
26. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Reducing Fractions
Surface Area of a Rectangular Solid
Function - Notation - and Evaulation
Interior Angles of a Polygon
27. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Prime Factorization
Counting the Possibilities
Solving a Quadratic Equation
Combined Percent Increase and Decrease
28. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Surface Area of a Rectangular Solid
Interior Angles of a Polygon
Average Formula -
29. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Area of a Triangle
The 3-4-5 Triangle
Number Categories
30. 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
Negative Exponent and Rational Exponent
Surface Area of a Rectangular Solid
The 3-4-5 Triangle
Union of Sets
31. 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
Counting the Possibilities
Adding/Subtracting Signed Numbers
Repeating Decimal
Area of a Sector
32. 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
Characteristics of a Rectangle
Prime Factorization
Interior and Exterior Angles of a Triangle
Average Rate
33. Combine equations in such a way that one of the variables cancel out
(Least) Common Multiple
Mixed Numbers and Improper Fractions
Solving a System of Equations
Setting up a Ratio
34. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Tangency
Relative Primes
Characteristics of a Rectangle
Finding the Missing Number
35. 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
Exponential Growth
Dividing Fractions
Percent Increase and Decrease
Volume of a Cylinder
36. Part = Percent x Whole
Probability
Percent Formula
Factor/Multiple
Part-to-Part Ratios and Part-to-Whole Ratios
37. 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
Factor/Multiple
Finding the Original Whole
Characteristics of a Parallelogram
Union of Sets
38. 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
Evaluating an Expression
Counting the Possibilities
Relative Primes
Length of an Arc
39. 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
Intersection of sets
Pythagorean Theorem
Prime Factorization
Identifying the Parts and the Whole
40. The whole # left over after division
Reciprocal
Remainders
Counting the Possibilities
Solving a Proportion
41. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Using an Equation to Find an Intercept
Evaluating an Expression
Parallel Lines and Transversals
Rate
42. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Rate
Finding the Missing Number
Adding and Subtracting Roots
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
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying Fractions
Dividing Fractions
Mixed Numbers and Improper Fractions
44. To solve a proportion - cross multiply
Finding the midpoint
Solving a Proportion
Determining Absolute Value
Solving a Quadratic Equation
45. 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.
Direct and Inverse Variation
Number Categories
PEMDAS
Using an Equation to Find an Intercept
46. 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)
Area of a Sector
Raising Powers to Powers
Average of Evenly Spaced Numbers
Solving a System of Equations
47. Multiply the exponents
Direct and Inverse Variation
Multiples of 3 and 9
Raising Powers to Powers
Area of a Sector
48. Factor out the perfect squares
Part-to-Part Ratios and Part-to-Whole Ratios
Simplifying Square Roots
Average Rate
Average of Evenly Spaced Numbers
49. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Reciprocal
Adding and Subtracting Roots
Dividing Fractions
Volume of a Rectangular Solid
50. To find the reciprocal of a fraction switch the numerator and the denominator
PEMDAS
Negative Exponent and Rational Exponent
Part-to-Part Ratios and Part-to-Whole Ratios
Reciprocal