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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. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle
Finding the Missing Number
Multiplying and Dividing Powers
Percent Formula
The 5-12-13 Triangle
2. 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
The 3-4-5 Triangle
Multiplying and Dividing Powers
Adding/Subtracting Signed Numbers
3. 2pr
Median and Mode
Circumference of a Circle
Multiples of 2 and 4
Average Formula -
4. A square is a rectangle with four equal sides; Area of Square = side*side
Raising Powers to Powers
Characteristics of a Rectangle
Determining Absolute Value
Characteristics of a Square
5. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 3 and 9
Multiplying Monomials
Percent Formula
Adding/Subtracting Signed Numbers
6. 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
Percent Formula
Combined Percent Increase and Decrease
Using an Equation to Find an Intercept
Finding the midpoint
7. 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
Circumference of a Circle
Exponential Growth
Probability
Evaluating an Expression
8. To solve a proportion - cross multiply
Counting Consecutive Integers
Solving a Proportion
Comparing Fractions
Even/Odd
9. Combine equations in such a way that one of the variables cancel out
Comparing Fractions
Solving a Quadratic Equation
Solving a System of Equations
The 5-12-13 Triangle
10. 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
Surface Area of a Rectangular Solid
Prime Factorization
Reducing Fractions
11. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Union of Sets
Multiplying and Dividing Roots
Multiplying Fractions
Comparing Fractions
12. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Determining Absolute Value
Intersection of sets
Similar Triangles
Simplifying Square Roots
13. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Intersecting Lines
Percent Increase and Decrease
Part-to-Part Ratios and Part-to-Whole Ratios
14. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Finding the Missing Number
Parallel Lines and Transversals
(Least) Common Multiple
Solving a System of Equations
15. The smallest multiple (other than zero) that two or more numbers have in common.
Adding/Subtracting Signed Numbers
(Least) Common Multiple
Volume of a Rectangular Solid
Intersection of sets
16. 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)
Multiplying/Dividing Signed Numbers
Finding the Original Whole
Parallel Lines and Transversals
Area of a Sector
17. you can add/subtract when the part under the radical is the same
Exponential Growth
Adding and Subtracting Roots
Identifying the Parts and the Whole
Adding/Subtracting Fractions
18. 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.
Finding the Original Whole
Repeating Decimal
Counting the Possibilities
Number Categories
19. pr^2
Remainders
Area of a Circle
Greatest Common Factor
Interior Angles of a Polygon
20. 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
Number Categories
Solving a Proportion
Greatest Common Factor
Characteristics of a Parallelogram
21. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Reciprocal
Setting up a Ratio
Average of Evenly Spaced Numbers
Characteristics of a Square
22. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Function - Notation - and Evaulation
Identifying the Parts and the Whole
Adding/Subtracting Signed Numbers
23. 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
Length of an Arc
Rate
Characteristics of a Rectangle
Even/Odd
24. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Characteristics of a Square
Adding and Subtraction Polynomials
Circumference of a Circle
Determining Absolute Value
25. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)
Multiples of 3 and 9
Interior and Exterior Angles of a Triangle
Probability
Length of an Arc
26. 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
Solving a Quadratic Equation
Adding and Subtraction Polynomials
Repeating Decimal
Multiplying/Dividing Signed Numbers
27. The whole # left over after division
Area of a Triangle
Mixed Numbers and Improper Fractions
Reducing Fractions
Remainders
28. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Percent Increase and Decrease
Part-to-Part Ratios and Part-to-Whole Ratios
Probability
29. 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
Average Rate
Remainders
Area of a Triangle
Intersection of sets
30. 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
Union of Sets
Prime Factorization
Direct and Inverse Variation
Solving a Quadratic Equation
31. 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
Even/Odd
Using an Equation to Find the Slope
Using the Average to Find the Sum
Part-to-Part Ratios and Part-to-Whole Ratios
32. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Similar Triangles
Solving a System of Equations
Percent Formula
33. Combine like terms
Adding and Subtraction Polynomials
Reducing Fractions
Area of a Circle
Multiplying Monomials
34. 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
Multiples of 2 and 4
Isosceles and Equilateral triangles
Surface Area of a Rectangular Solid
Finding the Distance Between Two Points
35. 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
Part-to-Part Ratios and Part-to-Whole Ratios
(Least) Common Multiple
Characteristics of a Square
The 3-4-5 Triangle
36. To find the reciprocal of a fraction switch the numerator and the denominator
Surface Area of a Rectangular Solid
Solving a Proportion
Adding and Subtracting monomials
Reciprocal
37. To multiply fractions - multiply the numerators and multiply the denominators
Solving a Quadratic Equation
The 3-4-5 Triangle
Multiplying Fractions
Identifying the Parts and the Whole
38. Volume of a Cylinder = pr^2h
Reciprocal
Volume of a Cylinder
Adding and Subtracting monomials
Reducing Fractions
39. 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
Using the Average to Find the Sum
Greatest Common Factor
Triangle Inequality Theorem
Part-to-Part Ratios and Part-to-Whole Ratios
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
Multiplying Fractions
Raising Powers to Powers
Multiplying/Dividing Signed Numbers
Interior and Exterior Angles of a Triangle
41. 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
Parallel Lines and Transversals
Domain and Range of a Function
Solving a Quadratic Equation
Using an Equation to Find an Intercept
42. Part = Percent x Whole
Domain and Range of a Function
Percent Increase and Decrease
Percent Formula
Area of a Triangle
43. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Reducing Fractions
Interior and Exterior Angles of a Triangle
Volume of a Cylinder
44. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Multiplying/Dividing Signed Numbers
Reducing Fractions
Function - Notation - and Evaulation
Adding and Subtracting monomials
45. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Tangency
Using an Equation to Find the Slope
Setting up a Ratio
Adding and Subtraction Polynomials
46. Subtract the smallest from the largest and add 1
The 5-12-13 Triangle
Counting Consecutive Integers
Percent Increase and Decrease
Tangency
47. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Using the Average to Find the Sum
Remainders
Adding and Subtracting monomials
48. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Direct and Inverse Variation
Average Rate
Pythagorean Theorem
Adding and Subtracting monomials
49. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Solving a System of Equations
Factor/Multiple
Repeating Decimal
Volume of a Rectangular Solid
50. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Finding the midpoint
Length of an Arc
Interior Angles of a Polygon
Number Categories