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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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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. 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
Percent Formula
Solving a System of Equations
Exponential Growth
Area of a Triangle
2. The whole # left over after division
Remainders
Reducing Fractions
Solving an Inequality
PEMDAS
3. 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
Average of Evenly Spaced Numbers
Remainders
Probability
Direct and Inverse Variation
4. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Finding the Original Whole
PEMDAS
Volume of a Rectangular Solid
Setting up a Ratio
5. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Solving a System of Equations
Comparing Fractions
Determining Absolute Value
6. 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)
Average Rate
Setting up a Ratio
Area of a Sector
Length of an Arc
7. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Percent Formula
Domain and Range of a Function
Characteristics of a Rectangle
Interior Angles of a Polygon
8. Multiply the exponents
Finding the Distance Between Two Points
Raising Powers to Powers
Surface Area of a Rectangular Solid
Simplifying Square Roots
9. (average of the x coordinates - average of the y coordinates)
Area of a Sector
Solving a System of Equations
Finding the midpoint
The 5-12-13 Triangle
10. 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
Adding/Subtracting Fractions
Using an Equation to Find an Intercept
Remainders
Reducing Fractions
11. 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
Combined Percent Increase and Decrease
Percent Formula
Repeating Decimal
Counting Consecutive Integers
12. 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
Reducing Fractions
Probability
Characteristics of a Parallelogram
Multiplying/Dividing Signed Numbers
13. The largest factor that two or more numbers have in common.
Greatest Common Factor
Simplifying Square Roots
Similar Triangles
Interior Angles of a Polygon
14. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Triangle Inequality Theorem
Finding the Original Whole
Interior Angles of a Polygon
Percent Increase and Decrease
15. you can add/subtract when the part under the radical is the same
Percent Formula
Even/Odd
Multiples of 2 and 4
Adding and Subtracting Roots
16. 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
Interior and Exterior Angles of a Triangle
The 5-12-13 Triangle
Adding and Subtraction Polynomials
Repeating Decimal
17. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Finding the midpoint
Number Categories
Exponential Growth
18. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Multiplying Monomials
Tangency
Average Formula -
19. Subtract the smallest from the largest and add 1
Repeating Decimal
Counting Consecutive Integers
Multiples of 3 and 9
Volume of a Rectangular Solid
20. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Domain and Range of a Function
Multiplying/Dividing Signed Numbers
Interior Angles of a Polygon
Adding and Subtracting monomials
21. 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
Comparing Fractions
Probability
Interior and Exterior Angles of a Triangle
Number Categories
22. 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
Comparing Fractions
Rate
Isosceles and Equilateral triangles
Mixed Numbers and Improper Fractions
23. To solve a proportion - cross multiply
Solving a Proportion
Multiples of 2 and 4
Simplifying Square Roots
Multiplying/Dividing Signed Numbers
24. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Part-to-Part Ratios and Part-to-Whole Ratios
Parallel Lines and Transversals
Triangle Inequality Theorem
Solving a Quadratic Equation
25. 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
Adding and Subtracting monomials
Setting up a Ratio
Finding the midpoint
Negative Exponent and Rational Exponent
26. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Parallel Lines and Transversals
Direct and Inverse Variation
Factor/Multiple
Using Two Points to Find the Slope
27. Add the exponents and keep the same base
Combined Percent Increase and Decrease
Mixed Numbers and Improper Fractions
Multiplying and Dividing Powers
Using Two Points to Find the Slope
28. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Multiples of 2 and 4
Prime Factorization
Intersection of sets
Solving an Inequality
29. 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
Volume of a Rectangular Solid
Reciprocal
PEMDAS
Finding the Original Whole
30. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Using the Average to Find the Sum
Mixed Numbers and Improper Fractions
Identifying the Parts and the Whole
31. 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
Volume of a Rectangular Solid
Percent Increase and Decrease
Adding/Subtracting Fractions
Intersecting Lines
32. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Solving a Quadratic Equation
Solving a Proportion
Similar Triangles
Direct and Inverse Variation
33. 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
Triangle Inequality Theorem
Tangency
Adding/Subtracting Fractions
Counting the Possibilities
34. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Intersection of sets
Using an Equation to Find an Intercept
Multiples of 2 and 4
Adding/Subtracting Signed Numbers
35. 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
Interior and Exterior Angles of a Triangle
Parallel Lines and Transversals
Solving an Inequality
Mixed Numbers and Improper Fractions
36. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Sector
Negative Exponent and Rational Exponent
Evaluating an Expression
37. Combine equations in such a way that one of the variables cancel out
Multiplying and Dividing Powers
Evaluating an Expression
Adding and Subtracting Roots
Solving a System of Equations
38. 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
Using an Equation to Find the Slope
Even/Odd
Area of a Triangle
Reciprocal
39. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Finding the midpoint
Adding/Subtracting Signed Numbers
Interior and Exterior Angles of a Triangle
Multiplying Monomials
40. 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
Pythagorean Theorem
Finding the Distance Between Two Points
Parallel Lines and Transversals
Adding/Subtracting Signed Numbers
41. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Area of a Triangle
Using Two Points to Find the Slope
The 5-12-13 Triangle
Average Rate
42. 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)
Characteristics of a Square
Area of a Sector
Mixed Numbers and Improper Fractions
Counting the Possibilities
43. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Finding the midpoint
Evaluating an Expression
Repeating Decimal
Mixed Numbers and Improper Fractions
44. Part = Percent x Whole
Function - Notation - and Evaulation
Using an Equation to Find an Intercept
Percent Formula
Probability
45. Volume of a Cylinder = pr^2h
Finding the Missing Number
Volume of a Cylinder
Characteristics of a Rectangle
Finding the Distance Between Two Points
46. Probability= Favorable Outcomes/Total Possible Outcomes
Parallel Lines and Transversals
Probability
Intersection of sets
Reciprocal
47. 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
Multiplying/Dividing Signed Numbers
Solving a System of Equations
Determining Absolute Value
Exponential Growth
48. A square is a rectangle with four equal sides; Area of Square = side*side
Exponential Growth
Multiplying Fractions
Characteristics of a Square
Area of a Sector
49. Factor out the perfect squares
Simplifying Square Roots
Area of a Triangle
Volume of a Rectangular Solid
Exponential Growth
50. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Multiples of 2 and 4
Relative Primes
Prime Factorization
Intersection of sets