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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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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 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
Multiples of 2 and 4
Circumference of a Circle
The 3-4-5 Triangle
2. 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
Finding the Original Whole
Evaluating an Expression
Counting Consecutive Integers
Exponential Growth
3. The whole # left over after division
Adding and Subtracting monomials
Adding and Subtracting Roots
Remainders
Finding the Distance Between Two Points
4. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Area of a Triangle
Pythagorean Theorem
Interior Angles of a Polygon
Similar Triangles
5. 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
Parallel Lines and Transversals
Intersecting Lines
Adding/Subtracting Signed Numbers
Dividing Fractions
6. The largest factor that two or more numbers have in common.
Area of a Sector
Greatest Common Factor
Average Rate
Number Categories
7. 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
Median and Mode
Combined Percent Increase and Decrease
Number Categories
Prime Factorization
8. pr^2
Area of a Circle
Characteristics of a Square
Solving a Quadratic Equation
Area of a Sector
9. 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
Simplifying Square Roots
Using an Equation to Find the Slope
Characteristics of a Parallelogram
10. 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
Percent Increase and Decrease
Isosceles and Equilateral triangles
Evaluating an Expression
Characteristics of a Rectangle
11. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Solving a Quadratic Equation
Identifying the Parts and the Whole
Determining Absolute Value
Union of Sets
12. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Using Two Points to Find the Slope
Comparing Fractions
Interior and Exterior Angles of a Triangle
Interior Angles of a Polygon
13. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Domain and Range of a Function
Average Formula -
The 3-4-5 Triangle
Factor/Multiple
14. 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
Length of an Arc
Determining Absolute Value
Counting the Possibilities
Simplifying Square Roots
15. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Similar Triangles
Relative Primes
Solving a Quadratic Equation
Characteristics of a Square
16. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Even/Odd
Factor/Multiple
Adding/Subtracting Fractions
Using an Equation to Find the Slope
17. 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
Circumference of a Circle
Multiplying/Dividing Signed Numbers
(Least) Common Multiple
Finding the Missing Number
18. 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 and Subtracting monomials
Even/Odd
Intersection of sets
Interior and Exterior Angles of a Triangle
19. 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
Adding and Subtracting monomials
Domain and Range of a Function
Identifying the Parts and the Whole
Solving a Proportion
20. 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
Evaluating an Expression
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the midpoint
Triangle Inequality Theorem
21. Add the exponents and keep the same base
Using an Equation to Find an Intercept
Percent Increase and Decrease
Multiplying and Dividing Powers
Intersecting Lines
22. 2pr
Circumference of a Circle
Mixed Numbers and Improper Fractions
Factor/Multiple
Intersecting Lines
23. To find the reciprocal of a fraction switch the numerator and the denominator
Intersection of sets
Even/Odd
Reciprocal
Number Categories
24. 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
Using an Equation to Find the Slope
Interior Angles of a Polygon
Percent Increase and Decrease
Even/Odd
25. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Identifying the Parts and the Whole
The 3-4-5 Triangle
Finding the Missing Number
Characteristics of a Rectangle
26. 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.
Number Categories
Surface Area of a Rectangular Solid
Reciprocal
Multiplying and Dividing Powers
27. To divide fractions - invert the second one and multiply
Percent Formula
Dividing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
PEMDAS
28. 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)
Solving a Proportion
Adding and Subtraction Polynomials
PEMDAS
Area of a Sector
29. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Multiplying Fractions
Intersecting Lines
Interior and Exterior Angles of a Triangle
Direct and Inverse Variation
30. 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
Multiplying Monomials
Using an Equation to Find an Intercept
Simplifying Square Roots
Multiples of 2 and 4
31. Volume of a Cylinder = pr^2h
Part-to-Part Ratios and Part-to-Whole Ratios
Volume of a Cylinder
(Least) Common Multiple
Exponential Growth
32. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Setting up a Ratio
Volume of a Rectangular Solid
Solving a Quadratic Equation
Solving an Inequality
33. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Similar Triangles
Reducing Fractions
Negative Exponent and Rational Exponent
Greatest Common Factor
34. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Mixed Numbers and Improper Fractions
Prime Factorization
Multiplying Monomials
Finding the Missing Number
35. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Multiplying/Dividing Signed Numbers
Finding the midpoint
Evaluating an Expression
Average Formula -
36. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Prime Factorization
Volume of a Cylinder
Intersection of sets
37. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Finding the Original Whole
Mixed Numbers and Improper Fractions
Raising Powers to Powers
Using an Equation to Find the Slope
38. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Multiples of 3 and 9
Parallel Lines and Transversals
Comparing Fractions
Tangency
39. 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
Multiplying Fractions
Relative Primes
Area of a Triangle
Solving a Quadratic Equation
40. 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
Function - Notation - and Evaulation
Negative Exponent and Rational Exponent
Using an Equation to Find the Slope
Triangle Inequality Theorem
41. 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
The 3-4-5 Triangle
Volume of a Cylinder
Characteristics of a Parallelogram
Counting the Possibilities
42. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Number Categories
Finding the Distance Between Two Points
Using an Equation to Find an Intercept
Multiples of 3 and 9
43. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Similar Triangles
Characteristics of a Rectangle
Interior Angles of a Polygon
44. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Adding and Subtraction Polynomials
Multiplying and Dividing Roots
Rate
45. Part = Percent x Whole
The 3-4-5 Triangle
Simplifying Square Roots
Percent Formula
Solving a System of Equations
46. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Relative Primes
Length of an Arc
Characteristics of a Square
47. Surface Area = 2lw + 2wh + 2lh
Percent Formula
Percent Increase and Decrease
Solving a Quadratic Equation
Surface Area of a Rectangular Solid
48. Sum=(Average) x (Number of Terms)
Comparing Fractions
Isosceles and Equilateral triangles
Using the Average to Find the Sum
Percent Formula
49. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Relative Primes
Solving a Quadratic Equation
Exponential Growth
Parallel Lines and Transversals
50. 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
Reciprocal
Negative Exponent and Rational Exponent
Surface Area of a Rectangular Solid
Average Rate