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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. Change in y/ change in x rise/run
Combined Percent Increase and Decrease
Multiplying Fractions
Adding and Subtracting Roots
Using Two Points to Find the Slope
2. you can add/subtract when the part under the radical is the same
Union of Sets
The 5-12-13 Triangle
Adding and Subtracting Roots
Parallel Lines and Transversals
3. The largest factor that two or more numbers have in common.
Identifying the Parts and the Whole
Adding and Subtracting monomials
Greatest Common Factor
The 3-4-5 Triangle
4. 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
Probability
Average Rate
Finding the Original Whole
Raising Powers to Powers
5. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Raising Powers to Powers
Finding the Missing Number
Solving an Inequality
6. 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
Volume of a Rectangular Solid
Solving an Inequality
Function - Notation - and Evaulation
Raising Powers to Powers
7. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Area of a Circle
Factor/Multiple
Characteristics of a Rectangle
Using an Equation to Find the Slope
8. Multiply the exponents
Triangle Inequality Theorem
Raising Powers to Powers
Multiplying Monomials
Interior Angles of a Polygon
9. 2pr
PEMDAS
Circumference of a Circle
Surface Area of a Rectangular Solid
Area of a Sector
10. 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
Remainders
Area of a Circle
Raising Powers to Powers
Function - Notation - and Evaulation
11. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Interior and Exterior Angles of a Triangle
Multiples of 2 and 4
Average Formula -
12. 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
Multiples of 3 and 9
Adding and Subtraction Polynomials
Area of a Sector
13. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Characteristics of a Square
Length of an Arc
Evaluating an Expression
14. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Pythagorean Theorem
Adding and Subtracting monomials
Area of a Sector
Counting Consecutive Integers
15. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Volume of a Rectangular Solid
Interior Angles of a Polygon
Determining Absolute Value
Remainders
16. 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
Setting up a Ratio
Using the Average to Find the Sum
Negative Exponent and Rational Exponent
Part-to-Part Ratios and Part-to-Whole Ratios
17. 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)
Area of a Sector
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
Combined Percent Increase and Decrease
18. Subtract the smallest from the largest and add 1
Raising Powers to Powers
Counting Consecutive Integers
Evaluating an Expression
The 5-12-13 Triangle
19. 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
Mixed Numbers and Improper Fractions
The 3-4-5 Triangle
Remainders
Solving a System of Equations
20. To multiply fractions - multiply the numerators and multiply the denominators
Domain and Range of a Function
Adding and Subtracting monomials
Multiplying Fractions
Mixed Numbers and Improper Fractions
21. A square is a rectangle with four equal sides; Area of Square = side*side
Multiples of 3 and 9
Multiplying and Dividing Powers
Exponential Growth
Characteristics of a Square
22. 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
Multiplying/Dividing Signed Numbers
Area of a Triangle
Multiples of 3 and 9
Adding/Subtracting Signed Numbers
23. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Average of Evenly Spaced Numbers
Parallel Lines and Transversals
Comparing Fractions
Adding/Subtracting Signed Numbers
24. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Part-to-Part Ratios and Part-to-Whole Ratios
Multiples of 3 and 9
Similar Triangles
Average Formula -
25. 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
Circumference of a Circle
Intersecting Lines
Percent Formula
Direct and Inverse Variation
26. To solve a proportion - cross multiply
Average Formula -
Comparing Fractions
Triangle Inequality Theorem
Solving a Proportion
27. 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
Characteristics of a Square
Multiplying/Dividing Signed Numbers
Simplifying Square Roots
28. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Solving a System of Equations
Similar Triangles
Characteristics of a Parallelogram
29. 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
Comparing Fractions
Surface Area of a Rectangular Solid
Reducing Fractions
Relative Primes
30. 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
Similar Triangles
Remainders
Area of a Triangle
Multiplying and Dividing Powers
31. Combine equations in such a way that one of the variables cancel out
Exponential Growth
Solving a System of Equations
Average Rate
Multiplying Fractions
32. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
PEMDAS
Factor/Multiple
Intersecting Lines
Percent Increase and Decrease
33. 1. Re-express them with common denominators 2. Convert them to decimals
Using Two Points to Find the Slope
Comparing Fractions
Raising Powers to Powers
Relative Primes
34. The smallest multiple (other than zero) that two or more numbers have in common.
Relative Primes
Finding the midpoint
The 5-12-13 Triangle
(Least) Common Multiple
35. Surface Area = 2lw + 2wh + 2lh
Surface Area of a Rectangular Solid
PEMDAS
Characteristics of a Parallelogram
Comparing Fractions
36. 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.
Simplifying Square Roots
Number Categories
Characteristics of a Parallelogram
Using an Equation to Find an Intercept
37. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Solving a Quadratic Equation
Intersecting Lines
Reducing Fractions
38. 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
Combined Percent Increase and Decrease
Isosceles and Equilateral triangles
Adding and Subtracting Roots
39. 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
Interior and Exterior Angles of a Triangle
The 3-4-5 Triangle
Finding the Distance Between Two Points
Similar Triangles
40. pr^2
Area of a Circle
Solving a Quadratic Equation
Characteristics of a Square
Average of Evenly Spaced Numbers
41. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Multiples of 3 and 9
Median and Mode
Repeating Decimal
Setting up a Ratio
42. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Rate
Multiplying/Dividing Signed Numbers
Interior and Exterior Angles of a Triangle
43. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Volume of a Rectangular Solid
Multiplying Monomials
Multiplying and Dividing Roots
44. Add the exponents and keep the same base
Function - Notation - and Evaulation
Multiplying and Dividing Roots
Intersecting Lines
Multiplying and Dividing Powers
45. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Function - Notation - and Evaulation
Finding the Missing Number
Surface Area of a Rectangular Solid
46. Domain: all possible values of x for a function range: all possible outputs of a function
Repeating Decimal
Similar Triangles
Domain and Range of a Function
Solving an Inequality
47. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12
Finding the Missing Number
The 3-4-5 Triangle
Mixed Numbers and Improper Fractions
Median and Mode
48. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Dividing Fractions
Tangency
Using an Equation to Find the Slope
Negative Exponent and Rational Exponent
49. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Remainders
Solving an Inequality
Area of a Triangle
50. 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
Triangle Inequality Theorem
Prime Factorization
Percent Increase and Decrease
Even/Odd