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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
Identifying the Parts and the Whole
Parallel Lines and Transversals
Similar Triangles
Reducing Fractions
2. 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
Counting the Possibilities
The 5-12-13 Triangle
Identifying the Parts and the Whole
Multiplying and Dividing Roots
3. Add the exponents and keep the same base
Counting the Possibilities
Multiplying and Dividing Roots
Multiplying and Dividing Powers
Finding the Original Whole
4. To find the reciprocal of a fraction switch the numerator and the denominator
The 3-4-5 Triangle
Prime Factorization
Length of an Arc
Reciprocal
5. Combine equations in such a way that one of the variables cancel out
Number Categories
Multiplying/Dividing Signed Numbers
Intersection of sets
Solving a System of Equations
6. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Finding the Original Whole
Solving a System of Equations
Raising Powers to Powers
Average Formula -
7. Part = Percent x Whole
Percent Formula
Average Formula -
Finding the midpoint
Interior and Exterior Angles of a Triangle
8. 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
Finding the Distance Between Two Points
Part-to-Part Ratios and Part-to-Whole Ratios
Isosceles and Equilateral triangles
Finding the Original Whole
9. Sum=(Average) x (Number of Terms)
Average Formula -
Surface Area of a Rectangular Solid
Using the Average to Find the Sum
Adding and Subtracting Roots
10. Multiply the exponents
Length of an Arc
Isosceles and Equilateral triangles
Raising Powers to Powers
Tangency
11. 2pr
Adding/Subtracting Signed Numbers
Area of a Circle
Circumference of a Circle
Adding/Subtracting Fractions
12. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Using the Average to Find the Sum
Multiplying and Dividing Powers
Similar Triangles
Setting up a Ratio
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 monomials
Volume of a Cylinder
Multiplying and Dividing Powers
Finding the Distance Between Two Points
14. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Comparing Fractions
Average Rate
Area of a Sector
Using Two Points to Find the Slope
15. 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
Rate
Pythagorean Theorem
Mixed Numbers and Improper Fractions
Volume of a Rectangular Solid
16. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Isosceles and Equilateral triangles
The 5-12-13 Triangle
Rate
Multiples of 3 and 9
17. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Finding the midpoint
Determining Absolute Value
Function - Notation - and Evaulation
Percent Formula
18. 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
Domain and Range of a Function
Surface Area of a Rectangular Solid
Multiplying/Dividing Signed Numbers
19. 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
Multiplying and Dividing Roots
Comparing Fractions
Negative Exponent and Rational Exponent
Intersecting Lines
20. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Factor/Multiple
Multiplying Monomials
PEMDAS
Characteristics of a Rectangle
21. 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
Median and Mode
Area of a Triangle
Parallel Lines and Transversals
Mixed Numbers and Improper Fractions
22. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Characteristics of a Square
Average Formula -
Setting up a Ratio
23. To solve a proportion - cross multiply
Using an Equation to Find the Slope
Solving a Proportion
Multiples of 2 and 4
Using the Average to Find the Sum
24. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Finding the midpoint
Raising Powers to Powers
Finding the Missing Number
25. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Finding the midpoint
Multiplying and Dividing Roots
Evaluating an Expression
Using the Average to Find the Sum
26. A square is a rectangle with four equal sides; Area of Square = side*side
Using the Average to Find the Sum
Dividing Fractions
Characteristics of a Square
Identifying the Parts and the Whole
27. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Volume of a Rectangular Solid
Combined Percent Increase and Decrease
Rate
Finding the Distance Between Two Points
28. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Percent Increase and Decrease
Union of Sets
Exponential Growth
Characteristics of a Square
29. 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
Intersecting Lines
Multiples of 2 and 4
Isosceles and Equilateral triangles
Direct and Inverse Variation
30. 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
Intersecting Lines
Interior and Exterior Angles of a Triangle
Volume of a Cylinder
31. 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
Multiplying and Dividing Powers
Prime Factorization
Triangle Inequality Theorem
Exponential Growth
32. 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
Multiples of 3 and 9
Even/Odd
Reciprocal
Solving a Proportion
33. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Determining Absolute Value
Median and Mode
Multiplying and Dividing Roots
Mixed Numbers and Improper Fractions
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
Characteristics of a Rectangle
Using an Equation to Find the Slope
Finding the Original Whole
Part-to-Part Ratios and Part-to-Whole Ratios
35. For all right triangles: a^2+b^2=c^2
Area of a Sector
Evaluating an Expression
Pythagorean Theorem
Finding the Original Whole
36. 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
Average of Evenly Spaced Numbers
Average Formula -
Counting the Possibilities
37. 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
Relative Primes
Dividing Fractions
Using an Equation to Find an Intercept
Intersecting Lines
38. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Multiplying and Dividing Powers
Interior and Exterior Angles of a Triangle
Tangency
Characteristics of a Parallelogram
39. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Factor/Multiple
Probability
Volume of a Rectangular Solid
Evaluating an Expression
40. 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
Function - Notation - and Evaulation
Adding/Subtracting Fractions
Interior and Exterior Angles of a Triangle
Multiplying/Dividing Signed Numbers
41. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Characteristics of a Rectangle
Adding/Subtracting Fractions
Volume of a Cylinder
The 5-12-13 Triangle
42. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Counting Consecutive Integers
Factor/Multiple
Pythagorean Theorem
Area of a Sector
43. 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
Union of Sets
Prime Factorization
Adding/Subtracting Fractions
Percent Increase and Decrease
44. 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
Domain and Range of a Function
Using an Equation to Find an Intercept
Simplifying Square Roots
Relative Primes
45. 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
Finding the midpoint
Multiples of 2 and 4
Parallel Lines and Transversals
Solving an Inequality
46. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Greatest Common Factor
Using an Equation to Find the Slope
Exponential Growth
Dividing Fractions
47. you can add/subtract when the part under the radical is the same
Remainders
Adding and Subtracting Roots
Pythagorean Theorem
Circumference of a Circle
48. 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
Isosceles and Equilateral triangles
The 5-12-13 Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a Proportion
49. 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
Prime Factorization
Average of Evenly Spaced Numbers
Median and Mode
Combined Percent Increase and Decrease
50. Surface Area = 2lw + 2wh + 2lh
Probability
Rate
Surface Area of a Rectangular Solid
The 3-4-5 Triangle