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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 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
Multiples of 2 and 4
Even/Odd
Counting Consecutive Integers
Setting up a Ratio
2. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Finding the midpoint
Surface Area of a Rectangular Solid
Adding and Subtraction Polynomials
3. 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
Using an Equation to Find an Intercept
Solving a Proportion
Reciprocal
Combined Percent Increase and Decrease
4. Part = Percent x Whole
Percent Formula
Function - Notation - and Evaulation
Isosceles and Equilateral triangles
PEMDAS
5. Multiply the exponents
Raising Powers to Powers
Interior and Exterior Angles of a Triangle
Characteristics of a Parallelogram
Reducing Fractions
6. 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
The 3-4-5 Triangle
Length of an Arc
Finding the Missing Number
Solving a System of Equations
7. 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
Using an Equation to Find an Intercept
Using an Equation to Find the Slope
Multiplying/Dividing Signed Numbers
Solving a Proportion
8. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Median and Mode
Part-to-Part Ratios and Part-to-Whole Ratios
Determining Absolute Value
Adding and Subtracting monomials
9. 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
Triangle Inequality Theorem
Comparing Fractions
Solving a System of Equations
Counting the Possibilities
10. 2pr
Circumference of a Circle
Union of Sets
Negative Exponent and Rational Exponent
Even/Odd
11. 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
Multiplying and Dividing Roots
Percent Increase and Decrease
Surface Area of a Rectangular Solid
12. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Length of an Arc
Triangle Inequality Theorem
Multiplying Monomials
Area of a Triangle
13. Change in y/ change in x rise/run
Relative Primes
Interior Angles of a Polygon
Using Two Points to Find the Slope
The 5-12-13 Triangle
14. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Circumference of a Circle
Determining Absolute Value
Union of Sets
15. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Mixed Numbers and Improper Fractions
Multiplying/Dividing Signed Numbers
Setting up a Ratio
Counting the Possibilities
16. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Union of Sets
Finding the Distance Between Two Points
Multiplying and Dividing Roots
Tangency
17. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Exponential Growth
Direct and Inverse Variation
Intersecting Lines
Counting the Possibilities
18. Sum=(Average) x (Number of Terms)
Adding and Subtraction Polynomials
Finding the midpoint
Using the Average to Find the Sum
Number Categories
19. 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.
Number Categories
Pythagorean Theorem
Reducing Fractions
Multiplying Monomials
20. (average of the x coordinates - average of the y coordinates)
Using an Equation to Find the Slope
Finding the midpoint
Area of a Sector
Surface Area of a Rectangular Solid
21. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Counting the Possibilities
Solving a Quadratic Equation
Circumference of a Circle
Number Categories
22. Probability= Favorable Outcomes/Total Possible Outcomes
Reducing Fractions
Tangency
Area of a Triangle
Probability
23. Factor out the perfect squares
Simplifying Square Roots
Adding and Subtraction Polynomials
Rate
Exponential Growth
24. 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
Comparing Fractions
Exponential Growth
Volume of a Cylinder
25. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Multiplying Fractions
Intersection of sets
Union of Sets
Circumference of a Circle
26. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Length of an Arc
Multiplying and Dividing Roots
Comparing Fractions
Characteristics of a Square
27. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Area of a Triangle
Tangency
Using the Average to Find the Sum
Reducing Fractions
28. 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
Area of a Triangle
Adding/Subtracting Fractions
Using an Equation to Find an Intercept
Part-to-Part Ratios and Part-to-Whole Ratios
29. 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
Percent Increase and Decrease
Finding the Missing Number
Pythagorean Theorem
Similar Triangles
30. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Percent Formula
Using an Equation to Find the Slope
Reciprocal
Finding the Original Whole
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
Percent Formula
Finding the Original Whole
Length of an Arc
The 3-4-5 Triangle
32. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Isosceles and Equilateral triangles
Percent Formula
Negative Exponent and Rational Exponent
33. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Using an Equation to Find the Slope
Determining Absolute Value
Multiplying and Dividing Powers
Intersection of sets
34. Add the exponents and keep the same base
Direct and Inverse Variation
Evaluating an Expression
Multiplying and Dividing Powers
Adding and Subtracting monomials
35. The smallest multiple (other than zero) that two or more numbers have in common.
Rate
Characteristics of a Rectangle
(Least) Common Multiple
Pythagorean Theorem
36. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Interior Angles of a Polygon
Adding and Subtracting monomials
Adding/Subtracting Signed Numbers
Adding and Subtraction Polynomials
37. 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
Solving a Proportion
Multiplying/Dividing Signed Numbers
Area of a Triangle
Evaluating an Expression
38. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
The 5-12-13 Triangle
Area of a Sector
Characteristics of a Rectangle
Area of a Triangle
39. 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
Solving a System of Equations
Parallel Lines and Transversals
Negative Exponent and Rational Exponent
Multiplying and Dividing Roots
40. 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
Setting up a Ratio
Multiplying Fractions
Identifying the Parts and the Whole
Solving an Inequality
41. 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
Counting Consecutive Integers
Comparing Fractions
Repeating Decimal
Triangle Inequality Theorem
42. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Parallel Lines and Transversals
Volume of a Rectangular Solid
Solving a Proportion
Characteristics of a Rectangle
43. The largest factor that two or more numbers have in common.
Greatest Common Factor
Prime Factorization
Multiplying and Dividing Powers
Area of a Circle
44. 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
Repeating Decimal
Rate
Interior Angles of a Polygon
Isosceles and Equilateral triangles
45. 1. Re-express them with common denominators 2. Convert them to decimals
Multiplying Monomials
Volume of a Rectangular Solid
Comparing Fractions
Similar Triangles
46. 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
Characteristics of a Square
Direct and Inverse Variation
Pythagorean Theorem
Circumference of a Circle
47. 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
Repeating Decimal
Multiplying and Dividing Powers
Relative Primes
Area of a Circle
48. 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)
Volume of a Rectangular Solid
Area of a Sector
Prime Factorization
The 3-4-5 Triangle
49. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Finding the Original Whole
Parallel Lines and Transversals
Prime Factorization
Median and Mode
50. 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
Determining Absolute Value
Adding/Subtracting Fractions
Adding/Subtracting Signed Numbers
Using Two Points to Find the Slope