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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. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Using the Average to Find the Sum
Domain and Range of a Function
Similar Triangles
Median and Mode
2. 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
Evaluating an Expression
Percent Increase and Decrease
Even/Odd
The 3-4-5 Triangle
3. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Function - Notation - and Evaulation
Remainders
Median and Mode
Solving a Proportion
4. (average of the x coordinates - average of the y coordinates)
Multiples of 3 and 9
Finding the midpoint
(Least) Common Multiple
Reciprocal
5. 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
Characteristics of a Rectangle
Raising Powers to Powers
Function - Notation - and Evaulation
Average Rate
6. 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
Exponential Growth
Raising Powers to Powers
Solving an Inequality
7. To find the reciprocal of a fraction switch the numerator and the denominator
Characteristics of a Rectangle
Reciprocal
Percent Formula
Average Formula -
8. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Percent Formula
Percent Increase and Decrease
Volume of a Cylinder
9. 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
Finding the midpoint
Tangency
Dividing Fractions
10. 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
Even/Odd
The 3-4-5 Triangle
Exponential Growth
Multiplying and Dividing Roots
11. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Triangle Inequality Theorem
The 5-12-13 Triangle
Repeating Decimal
12. Part = Percent x Whole
Percent Formula
Using the Average to Find the Sum
Finding the Original Whole
Median and Mode
13. 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 Roots
Solving an Inequality
Adding/Subtracting Fractions
Adding and Subtracting monomials
14. you can add/subtract when the part under the radical is the same
Multiples of 3 and 9
Number Categories
Characteristics of a Rectangle
Adding and Subtracting Roots
15. Factor out the perfect squares
Multiples of 3 and 9
Finding the Original Whole
Simplifying Square Roots
Union of Sets
16. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Relative Primes
Part-to-Part Ratios and Part-to-Whole Ratios
Parallel Lines and Transversals
Solving a Quadratic Equation
17. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Length of an Arc
Determining Absolute Value
Interior Angles of a Polygon
18. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Reciprocal
Factor/Multiple
Even/Odd
Exponential Growth
19. 1. Re-express them with common denominators 2. Convert them to decimals
Combined Percent Increase and Decrease
Intersecting Lines
Comparing Fractions
Circumference of a Circle
20. 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
Tangency
Similar Triangles
Union of Sets
Adding/Subtracting Signed Numbers
21. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Counting the Possibilities
Probability
Characteristics of a Rectangle
Similar Triangles
22. 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
Solving a Quadratic Equation
Using the Average to Find the Sum
Finding the midpoint
23. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Interior and Exterior Angles of a Triangle
Multiplying and Dividing Roots
The 3-4-5 Triangle
Raising Powers to Powers
24. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Solving an Inequality
Area of a Sector
Tangency
Mixed Numbers and Improper Fractions
25. 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
Determining Absolute Value
Solving an Inequality
Solving a System of Equations
Even/Odd
26. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Median and Mode
Adding/Subtracting Signed Numbers
Area of a Circle
27. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Tangency
Interior Angles of a Polygon
Intersecting Lines
Volume of a Cylinder
28. 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
Counting the Possibilities
Part-to-Part Ratios and Part-to-Whole Ratios
Even/Odd
Relative Primes
29. 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
Multiples of 2 and 4
Domain and Range of a Function
Relative Primes
Multiplying Fractions
30. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Tangency
Area of a Circle
Area of a Sector
Average Formula -
31. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Similar Triangles
Union of Sets
Multiplying Monomials
Repeating Decimal
32. To divide fractions - invert the second one and multiply
Probability
Dividing Fractions
Using the Average to Find the Sum
Comparing Fractions
33. 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 the Average to Find the Sum
Using an Equation to Find an Intercept
Dividing Fractions
Similar Triangles
34. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Volume of a Rectangular Solid
Finding the Original Whole
Prime Factorization
Average of Evenly Spaced Numbers
35. 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)
Using an Equation to Find an Intercept
Multiplying and Dividing Powers
Length of an Arc
Characteristics of a Parallelogram
36. 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
Solving a Quadratic Equation
Direct and Inverse Variation
Even/Odd
PEMDAS
37. pr^2
Repeating Decimal
Area of a Circle
Multiplying and Dividing Roots
Multiples of 3 and 9
38. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Adding/Subtracting Fractions
Characteristics of a Square
Using an Equation to Find the Slope
Function - Notation - and Evaulation
39. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Greatest Common Factor
Area of a Sector
Determining Absolute Value
Multiples of 2 and 4
40. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height
Combined Percent Increase and Decrease
Characteristics of a Parallelogram
Intersecting Lines
Percent Increase and Decrease
41. 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
Using Two Points to Find the Slope
Interior and Exterior Angles of a Triangle
Finding the Distance Between Two Points
Using an Equation to Find the Slope
42. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
The 3-4-5 Triangle
Solving an Inequality
Triangle Inequality Theorem
43. Add the exponents and keep the same base
Multiplying and Dividing Powers
Using an Equation to Find an Intercept
PEMDAS
Raising Powers to Powers
44. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiples of 2 and 4
Remainders
Reducing Fractions
Finding the Distance Between Two Points
45. The whole # left over after division
Comparing Fractions
Remainders
Using an Equation to Find the Slope
Volume of a Rectangular Solid
46. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Multiplying Monomials
Using the Average to Find the Sum
Relative Primes
47. Multiply the exponents
Volume of a Cylinder
Raising Powers to Powers
Using the Average to Find the Sum
The 3-4-5 Triangle
48. 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
Characteristics of a Rectangle
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying and Dividing Roots
Finding the Missing Number
49. 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
Multiplying Fractions
Rate
Probability
Identifying the Parts and the Whole
50. A square is a rectangle with four equal sides; Area of Square = side*side
Characteristics of a Square
Adding/Subtracting Signed Numbers
Mixed Numbers and Improper Fractions
Greatest Common Factor