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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. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Percent Formula
Interior and Exterior Angles of a Triangle
PEMDAS
2. 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
Percent Formula
Direct and Inverse Variation
Using an Equation to Find an Intercept
Adding/Subtracting Fractions
3. Factor out the perfect squares
Simplifying Square Roots
Using the Average to Find the Sum
Comparing Fractions
Mixed Numbers and Improper Fractions
4. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Tangency
Percent Formula
Evaluating an Expression
Number Categories
5. To multiply fractions - multiply the numerators and multiply the denominators
Domain and Range of a Function
Multiplying Fractions
Multiplying and Dividing Roots
Dividing Fractions
6. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Adding and Subtracting Roots
Union of Sets
Median and Mode
Mixed Numbers and Improper Fractions
7. 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
Using an Equation to Find an Intercept
Mixed Numbers and Improper Fractions
Similar Triangles
Average Formula -
8. For all right triangles: a^2+b^2=c^2
Multiplying Monomials
Characteristics of a Rectangle
Pythagorean Theorem
Tangency
9. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Finding the Distance Between Two Points
Similar Triangles
Dividing Fractions
Solving a System of Equations
10. 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
Using the Average to Find the Sum
Relative Primes
Multiplying Monomials
Part-to-Part Ratios and Part-to-Whole Ratios
11. 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
Finding the Missing Number
Repeating Decimal
Multiplying/Dividing Signed Numbers
Circumference of a Circle
12. 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.
Characteristics of a Square
Simplifying Square Roots
Triangle Inequality Theorem
Number Categories
13. 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
Multiplying Fractions
Adding and Subtracting Roots
Adding/Subtracting Signed Numbers
14. Multiply the exponents
Reducing Fractions
Adding and Subtracting Roots
Raising Powers to Powers
Multiples of 3 and 9
15. Domain: all possible values of x for a function range: all possible outputs of a function
Reciprocal
Identifying the Parts and the Whole
Domain and Range of a Function
Intersection of sets
16. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Area of a Triangle
Length of an Arc
Function - Notation - and Evaulation
Prime Factorization
17. Part = Percent x Whole
Solving a Quadratic Equation
Comparing Fractions
Percent Formula
Direct and Inverse Variation
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
Interior Angles of a Polygon
Rate
Length of an Arc
Interior and Exterior Angles of a Triangle
19. 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
Negative Exponent and Rational Exponent
Solving an Inequality
Counting Consecutive Integers
Simplifying Square Roots
20. 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 midpoint
PEMDAS
Exponential Growth
Intersection of sets
21. 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
Evaluating an Expression
Counting the Possibilities
Rate
22. To divide fractions - invert the second one and multiply
Area of a Circle
Dividing Fractions
Finding the midpoint
Probability
23. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Dividing Fractions
The 3-4-5 Triangle
Mixed Numbers and Improper Fractions
Volume of a Rectangular Solid
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
Similar Triangles
Repeating Decimal
Adding/Subtracting Fractions
Interior and Exterior Angles of a Triangle
25. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Even/Odd
Length of an Arc
Union of Sets
Similar Triangles
26. 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
Raising Powers to Powers
Reciprocal
Solving an Inequality
Adding/Subtracting Signed Numbers
27. Volume of a Cylinder = pr^2h
Intersecting Lines
Volume of a Cylinder
Solving an Inequality
Characteristics of a Rectangle
28. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Intersecting Lines
Multiplying Monomials
Part-to-Part Ratios and Part-to-Whole Ratios
Multiples of 3 and 9
29. 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
Function - Notation - and Evaulation
Identifying the Parts and the Whole
Using the Average to Find the Sum
Dividing Fractions
30. 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
Reciprocal
Intersection of sets
Tangency
31. 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
Finding the Original Whole
Intersection of sets
Circumference of a Circle
Reciprocal
32. 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
Length of an Arc
Characteristics of a Parallelogram
Mixed Numbers and Improper Fractions
Combined Percent Increase and Decrease
33. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Rate
Characteristics of a Rectangle
Finding the midpoint
Domain and Range of a Function
34. 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
Volume of a Rectangular Solid
Factor/Multiple
Using an Equation to Find an Intercept
Area of a Sector
35. 2pr
Multiplying and Dividing Powers
Circumference of a Circle
Adding/Subtracting Fractions
Adding and Subtraction Polynomials
36. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Intersection of sets
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying and Dividing Roots
Function - Notation - and Evaulation
37. 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)
Length of an Arc
Average Formula -
Interior and Exterior Angles of a Triangle
Solving a Proportion
38. Probability= Favorable Outcomes/Total Possible Outcomes
Isosceles and Equilateral triangles
Reducing Fractions
Average of Evenly Spaced Numbers
Probability
39. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Multiplying Monomials
Average Formula -
Tangency
40. 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
Intersecting Lines
Finding the Missing Number
Multiplying and Dividing Roots
Even/Odd
41. The largest factor that two or more numbers have in common.
Percent Increase and Decrease
Finding the midpoint
Negative Exponent and Rational Exponent
Greatest Common Factor
42. 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
Adding and Subtracting Roots
Remainders
The 3-4-5 Triangle
43. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
The 5-12-13 Triangle
Identifying the Parts and the Whole
Determining Absolute Value
44. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Exponential Growth
Solving a Quadratic Equation
Solving a Proportion
Average of Evenly Spaced Numbers
45. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Pythagorean Theorem
Interior Angles of a Polygon
Median and Mode
Rate
46. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Percent Increase and Decrease
Adding and Subtracting Roots
Raising Powers to Powers
Average Formula -
47. Combine equations in such a way that one of the variables cancel out
Median and Mode
Adding and Subtracting Roots
Solving a System of Equations
Volume of a Rectangular Solid
48. 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
Isosceles and Equilateral triangles
Pythagorean Theorem
Percent Increase and Decrease
Solving a System of Equations
49. To find the reciprocal of a fraction switch the numerator and the denominator
Using the Average to Find the Sum
Relative Primes
Reciprocal
(Least) Common Multiple
50. 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
Multiples of 2 and 4
Characteristics of a Square
Using Two Points to Find the Slope
Triangle Inequality Theorem