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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 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
Even/Odd
Probability
Mixed Numbers and Improper Fractions
Adding/Subtracting Signed Numbers
2. 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)
Length of an Arc
Volume of a Rectangular Solid
Adding/Subtracting Signed Numbers
Percent Formula
3. 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
Combined Percent Increase and Decrease
Intersecting Lines
Multiplying/Dividing Signed Numbers
Area of a Sector
4. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Intersection of sets
Reducing Fractions
Parallel Lines and Transversals
Triangle Inequality Theorem
5. 2pr
Multiples of 3 and 9
Finding the midpoint
Circumference of a Circle
Adding/Subtracting Signed Numbers
6. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Solving a Quadratic Equation
Area of a Circle
Intersection of sets
Using Two Points to Find the Slope
7. 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
Repeating Decimal
Intersecting Lines
Mixed Numbers and Improper Fractions
Intersection of sets
8. To divide fractions - invert the second one and multiply
Dividing Fractions
Greatest Common Factor
Average of Evenly Spaced Numbers
Multiplying/Dividing Signed Numbers
9. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Combined Percent Increase and Decrease
Multiplying Monomials
(Least) Common Multiple
Percent Formula
10. To multiply fractions - multiply the numerators and multiply the denominators
Probability
Reciprocal
Multiplying Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
11. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Finding the Original Whole
Repeating Decimal
Multiples of 2 and 4
Number Categories
12. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Relative Primes
Characteristics of a Rectangle
Evaluating an Expression
Counting Consecutive Integers
13. Combine equations in such a way that one of the variables cancel out
Even/Odd
Solving a System of Equations
Volume of a Cylinder
Combined Percent Increase and Decrease
14. To find the reciprocal of a fraction switch the numerator and the denominator
Multiplying/Dividing Signed Numbers
Solving an Inequality
Interior Angles of a Polygon
Reciprocal
15. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Area of a Triangle
Adding/Subtracting Fractions
Probability
Comparing Fractions
16. 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
Length of an Arc
Characteristics of a Parallelogram
Factor/Multiple
Finding the Distance Between Two Points
17. Add the exponents and keep the same base
Multiplying and Dividing Powers
Exponential Growth
Reducing Fractions
Probability
18. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Setting up a Ratio
PEMDAS
Determining Absolute Value
Characteristics of a Rectangle
19. you can add/subtract when the part under the radical is the same
Characteristics of a Square
PEMDAS
Average Formula -
Adding and Subtracting Roots
20. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Similar Triangles
Average Formula -
Remainders
Function - Notation - and Evaulation
21. Combine like terms
Adding and Subtraction Polynomials
Rate
Adding and Subtracting Roots
Multiples of 2 and 4
22. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Interior Angles of a Polygon
Factor/Multiple
Counting the Possibilities
Reducing Fractions
23. 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
Function - Notation - and Evaulation
Combined Percent Increase and Decrease
The 5-12-13 Triangle
Using an Equation to Find the Slope
24. 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
Adding and Subtracting Roots
Multiplying and Dividing Powers
Interior and Exterior Angles of a Triangle
Area of a Triangle
25. The smallest multiple (other than zero) that two or more numbers have in common.
Adding/Subtracting Fractions
(Least) Common Multiple
Percent Formula
Multiplying Fractions
26. A square is a rectangle with four equal sides; Area of Square = side*side
Average Formula -
Characteristics of a Square
Surface Area of a Rectangular Solid
Triangle Inequality Theorem
27. 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
Interior Angles of a Polygon
Similar Triangles
Direct and Inverse Variation
Factor/Multiple
28. For all right triangles: a^2+b^2=c^2
Remainders
Characteristics of a Parallelogram
Reciprocal
Pythagorean Theorem
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
Average Rate
Characteristics of a Rectangle
Finding the Distance Between Two Points
Exponential Growth
30. 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
Reciprocal
Identifying the Parts and the Whole
PEMDAS
The 5-12-13 Triangle
31. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Number Categories
Using an Equation to Find the Slope
Isosceles and Equilateral triangles
Multiplying and Dividing Roots
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
Adding/Subtracting Signed Numbers
Triangle Inequality Theorem
Finding the Original Whole
Interior and Exterior Angles of a Triangle
33. The largest factor that two or more numbers have in common.
Adding and Subtraction Polynomials
Tangency
Greatest Common Factor
Solving a System of Equations
34. 1. Re-express them with common denominators 2. Convert them to decimals
Part-to-Part Ratios and Part-to-Whole Ratios
Using an Equation to Find the Slope
Comparing Fractions
Raising Powers to Powers
35. Probability= Favorable Outcomes/Total Possible Outcomes
Adding/Subtracting Signed Numbers
Probability
Similar Triangles
Interior and Exterior Angles of a Triangle
36. Multiply the exponents
Probability
Raising Powers to Powers
Exponential Growth
Area of a Triangle
37. 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
Dividing Fractions
Area of a Circle
Median and Mode
38. Surface Area = 2lw + 2wh + 2lh
The 3-4-5 Triangle
Adding/Subtracting Signed Numbers
Surface Area of a Rectangular Solid
Adding and Subtraction Polynomials
39. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Multiplying Fractions
Similar Triangles
Reducing Fractions
Area of a Circle
40. 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
Intersecting Lines
Percent Increase and Decrease
Domain and Range of a Function
Simplifying Square Roots
41. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Mixed Numbers and Improper Fractions
Adding/Subtracting Fractions
Multiples of 3 and 9
Exponential Growth
42. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Even/Odd
Using an Equation to Find an Intercept
Percent Increase and Decrease
43. 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
Percent Formula
Probability
Area of a Triangle
Repeating Decimal
44. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Rate
Union of Sets
Percent Formula
45. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Characteristics of a Parallelogram
Part-to-Part Ratios and Part-to-Whole Ratios
Raising Powers to Powers
Tangency
46. 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
Area of a Circle
The 3-4-5 Triangle
Adding/Subtracting Fractions
Multiplying/Dividing Signed Numbers
47. Subtract the smallest from the largest and add 1
Area of a Triangle
Reciprocal
Counting Consecutive Integers
Evaluating an Expression
48. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Exponential Growth
Using an Equation to Find the Slope
Multiples of 2 and 4
Union of Sets
49. 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
Solving an Inequality
Relative Primes
Factor/Multiple
Area of a Sector
50. 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
Average of Evenly Spaced Numbers
Surface Area of a Rectangular Solid
Finding the Missing Number
The 3-4-5 Triangle