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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. 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
Exponential Growth
Solving a Proportion
Reducing Fractions
2. 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
Rate
Adding/Subtracting Signed Numbers
Function - Notation - and Evaulation
3. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Solving a System of Equations
Using Two Points to Find the Slope
Parallel Lines and Transversals
4. Sum=(Average) x (Number of Terms)
Circumference of a Circle
Characteristics of a Parallelogram
Counting Consecutive Integers
Using the Average to Find the Sum
5. For all right triangles: a^2+b^2=c^2
Mixed Numbers and Improper Fractions
Area of a Sector
Characteristics of a Square
Pythagorean Theorem
6. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Median and Mode
Multiplying Monomials
Triangle Inequality Theorem
Parallel Lines and Transversals
7. Probability= Favorable Outcomes/Total Possible Outcomes
Volume of a Rectangular Solid
Probability
Intersection of sets
Reducing Fractions
8. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Simplifying Square Roots
Using an Equation to Find the Slope
Average of Evenly Spaced Numbers
Exponential Growth
9. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Adding/Subtracting Signed Numbers
Negative Exponent and Rational Exponent
Solving an Inequality
Intersection of sets
10. 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
Similar Triangles
Length of an Arc
The 5-12-13 Triangle
11. you can add/subtract when the part under the radical is the same
Finding the midpoint
Adding/Subtracting Signed Numbers
Adding and Subtracting Roots
Average of Evenly Spaced Numbers
12. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Using an Equation to Find the Slope
Solving a Proportion
Union of Sets
Adding and Subtraction Polynomials
13. Subtract the smallest from the largest and add 1
Volume of a Cylinder
Counting Consecutive Integers
Circumference of a Circle
PEMDAS
14. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Area of a Circle
Interior Angles of a Polygon
Even/Odd
Raising Powers to Powers
15. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Solving an Inequality
Raising Powers to Powers
Probability
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
Solving a Quadratic Equation
Pythagorean Theorem
Using an Equation to Find the Slope
Combined Percent Increase and Decrease
17. 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.
Comparing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying Monomials
Number Categories
18. Add the exponents and keep the same base
Multiplying and Dividing Powers
Identifying the Parts and the Whole
Area of a Sector
Exponential Growth
19. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Triangle Inequality Theorem
Factor/Multiple
Identifying the Parts and the Whole
Average Rate
20. 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
Using an Equation to Find the Slope
Multiplying/Dividing Signed Numbers
Relative Primes
21. 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
Comparing Fractions
Relative Primes
Negative Exponent and Rational Exponent
Parallel Lines and Transversals
22. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a System of Equations
Solving a Quadratic Equation
Factor/Multiple
Adding/Subtracting Signed Numbers
23. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Union of Sets
Finding the Original Whole
Using an Equation to Find an Intercept
24. 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
The 5-12-13 Triangle
Direct and Inverse Variation
Combined Percent Increase and Decrease
25. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Median and Mode
Area of a Triangle
Reducing Fractions
Rate
26. Combine like terms
Solving an Inequality
Area of a Circle
Using an Equation to Find an Intercept
Adding and Subtraction Polynomials
27. A square is a rectangle with four equal sides; Area of Square = side*side
Rate
Identifying the Parts and the Whole
Interior Angles of a Polygon
Characteristics of a Square
28. Combine equations in such a way that one of the variables cancel out
Using an Equation to Find an Intercept
Triangle Inequality Theorem
Solving a System of Equations
Similar Triangles
29. Part = Percent x Whole
Adding and Subtracting Roots
Percent Formula
Multiplying Monomials
Exponential Growth
30. Surface Area = 2lw + 2wh + 2lh
Characteristics of a Parallelogram
Union of Sets
Solving a Quadratic Equation
Surface Area of a Rectangular Solid
31. 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
Multiplying Monomials
Length of an Arc
Similar Triangles
32. 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
Average Rate
Adding and Subtraction Polynomials
Identifying the Parts and the Whole
(Least) Common Multiple
33. 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
Using Two Points to Find the Slope
Probability
Counting the Possibilities
Mixed Numbers and Improper Fractions
34. 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
Interior Angles of a Polygon
Volume of a Rectangular Solid
Part-to-Part Ratios and Part-to-Whole Ratios
Adding and Subtracting Roots
35. Domain: all possible values of x for a function range: all possible outputs of a function
Volume of a Cylinder
Domain and Range of a Function
Surface Area of a Rectangular Solid
Greatest Common Factor
36. To divide fractions - invert the second one and multiply
Finding the Missing Number
Reciprocal
(Least) Common Multiple
Dividing Fractions
37. 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
Direct and Inverse Variation
Multiplying and Dividing Roots
Volume of a Cylinder
Counting Consecutive Integers
38. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Finding the Original Whole
Setting up a Ratio
Using Two Points to Find the Slope
Characteristics of a Square
39. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Using the Average to Find the Sum
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Rectangle
40. 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
Percent Formula
Exponential Growth
Isosceles and Equilateral triangles
Direct and Inverse Variation
41. 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
Exponential Growth
Multiplying/Dividing Signed Numbers
Direct and Inverse Variation
42. 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
Pythagorean Theorem
Percent Increase and Decrease
Multiplying Monomials
Finding the Original Whole
43. 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
Reducing Fractions
Combined Percent Increase and Decrease
Adding and Subtraction Polynomials
Finding the Original Whole
44. (average of the x coordinates - average of the y coordinates)
Simplifying Square Roots
Counting the Possibilities
Area of a Sector
Finding the midpoint
45. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Factor/Multiple
Adding/Subtracting Fractions
Median and Mode
Remainders
46. 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
Reducing Fractions
Using Two Points to Find the Slope
Finding the Original Whole
Adding/Subtracting Signed Numbers
47. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Solving a Proportion
Using an Equation to Find the Slope
Characteristics of a Rectangle
Exponential Growth
48. 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
Adding and Subtracting Roots
Characteristics of a Rectangle
Factor/Multiple
Isosceles and Equilateral triangles
49. 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
Parallel Lines and Transversals
Area of a Triangle
Average Rate
Solving a System of Equations
50. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
The 5-12-13 Triangle
Percent Formula
Setting up a Ratio