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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 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 Monomials
Multiplying/Dividing Signed Numbers
(Least) Common Multiple
Adding and Subtraction Polynomials
2. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
The 5-12-13 Triangle
Simplifying Square Roots
Area of a Triangle
Adding and Subtracting monomials
3. 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
Counting Consecutive Integers
Repeating Decimal
Intersecting Lines
Solving an Inequality
4. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Area of a Circle
Finding the Distance Between Two Points
Area of a Sector
5. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Raising Powers to Powers
Evaluating an Expression
Characteristics of a Square
Characteristics of a Parallelogram
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
Number Categories
Negative Exponent and Rational Exponent
Combined Percent Increase and Decrease
Mixed Numbers and Improper Fractions
7. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Dividing Fractions
Negative Exponent and Rational Exponent
Part-to-Part Ratios and Part-to-Whole Ratios
Determining Absolute Value
8. you can add/subtract when the part under the radical is the same
The 3-4-5 Triangle
Function - Notation - and Evaulation
Similar Triangles
Adding and Subtracting Roots
9. Add the exponents and keep the same base
Multiplying and Dividing Powers
Mixed Numbers and Improper Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Volume of a Cylinder
10. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Similar Triangles
Dividing Fractions
Parallel Lines and Transversals
Median and Mode
11. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Using an Equation to Find the Slope
Multiples of 3 and 9
The 5-12-13 Triangle
Characteristics of a Parallelogram
12. 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
Similar Triangles
Triangle Inequality Theorem
Solving a System of Equations
Prime Factorization
13. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Prime Factorization
Simplifying Square Roots
Greatest Common Factor
Tangency
14. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Combined Percent Increase and Decrease
Finding the Distance Between Two Points
15. 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
Adding/Subtracting Signed Numbers
Counting the Possibilities
Average of Evenly Spaced Numbers
Finding the midpoint
16. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Circumference of a Circle
Simplifying Square Roots
Length of an Arc
17. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Function - Notation - and Evaulation
Adding/Subtracting Fractions
(Least) Common Multiple
Surface Area of a Rectangular Solid
18. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
PEMDAS
Finding the Distance Between Two Points
Probability
Volume of a Cylinder
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
(Least) Common Multiple
Solving a Proportion
The 3-4-5 Triangle
Identifying the Parts and the Whole
20. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Pythagorean Theorem
Using an Equation to Find the Slope
Solving a Quadratic Equation
21. Factor out the perfect squares
Determining Absolute Value
Multiples of 3 and 9
Multiplying and Dividing Powers
Simplifying Square Roots
22. 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
Finding the Missing Number
Repeating Decimal
Relative Primes
Even/Odd
23. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Repeating Decimal
Multiplying Monomials
Finding the Distance Between Two Points
24. 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
Multiplying Fractions
Interior and Exterior Angles of a Triangle
Negative Exponent and Rational Exponent
Repeating Decimal
25. 2pr
Circumference of a Circle
Counting the Possibilities
Isosceles and Equilateral triangles
Adding and Subtracting monomials
26. 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
Using an Equation to Find an Intercept
Using an Equation to Find the Slope
Intersecting Lines
Part-to-Part Ratios and Part-to-Whole Ratios
27. For all right triangles: a^2+b^2=c^2
Percent Formula
Reducing Fractions
Number Categories
Pythagorean Theorem
28. Part = Percent x Whole
Determining Absolute Value
Percent Formula
Finding the Original Whole
Union of Sets
29. 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
Intersection of sets
Interior Angles of a Polygon
Volume of a Rectangular Solid
Isosceles and Equilateral triangles
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
(Least) Common Multiple
Using an Equation to Find an Intercept
Counting the Possibilities
Counting Consecutive Integers
31. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Solving a Quadratic Equation
Even/Odd
Average of Evenly Spaced Numbers
Volume of a Cylinder
32. 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
Percent Increase and Decrease
Raising Powers to Powers
Setting up a Ratio
Adding/Subtracting Signed Numbers
33. The largest factor that two or more numbers have in common.
Solving a Proportion
Combined Percent Increase and Decrease
Using the Average to Find the Sum
Greatest Common Factor
34. Change in y/ change in x rise/run
Multiplying/Dividing Signed Numbers
Characteristics of a Rectangle
Determining Absolute Value
Using Two Points to Find the Slope
35. Volume of a Cylinder = pr^2h
Rate
Similar Triangles
Volume of a Cylinder
Finding the Original Whole
36. 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
Circumference of a Circle
Function - Notation - and Evaulation
Multiplying and Dividing Powers
Finding the midpoint
37. (average of the x coordinates - average of the y coordinates)
Tangency
Finding the midpoint
Reciprocal
Counting Consecutive Integers
38. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Identifying the Parts and the Whole
Intersection of sets
Multiplying/Dividing Signed Numbers
39. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
PEMDAS
Setting up a Ratio
Finding the midpoint
Characteristics of a Rectangle
40. 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
Negative Exponent and Rational Exponent
Direct and Inverse Variation
Area of a Triangle
Multiples of 2 and 4
41. 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
Domain and Range of a Function
Comparing Fractions
Combined Percent Increase and Decrease
Adding/Subtracting Fractions
42. 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
Setting up a Ratio
Adding/Subtracting Signed Numbers
Prime Factorization
Exponential Growth
43. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Area of a Circle
Average Formula -
(Least) Common Multiple
44. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Adding and Subtracting Roots
Direct and Inverse Variation
Mixed Numbers and Improper Fractions
45. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Parallel Lines and Transversals
Volume of a Cylinder
Reducing Fractions
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
Setting up a Ratio
Solving a Quadratic Equation
Using an Equation to Find the Slope
Intersection of sets
47. 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
Adding/Subtracting Fractions
Tangency
Interior Angles of a Polygon
48. Domain: all possible values of x for a function range: all possible outputs of a function
Median and Mode
Volume of a Rectangular Solid
Domain and Range of a Function
Using the Average to Find the Sum
49. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Length of an Arc
Prime Factorization
Using an Equation to Find an Intercept
50. To solve a proportion - cross multiply
Solving a Proportion
The 3-4-5 Triangle
Percent Formula
Adding and Subtraction Polynomials