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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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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. 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
Comparing Fractions
Parallel Lines and Transversals
Area of a Triangle
Identifying the Parts and the Whole
2. Subtract the smallest from the largest and add 1
Multiplying/Dividing Signed Numbers
Counting Consecutive Integers
Tangency
Interior and Exterior Angles of a Triangle
3. 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
Pythagorean Theorem
Tangency
Relative Primes
Exponential Growth
4. To find the reciprocal of a fraction switch the numerator and the denominator
Mixed Numbers and Improper Fractions
Area of a Circle
Reciprocal
Length of an Arc
5. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Pythagorean Theorem
Combined Percent Increase and Decrease
Similar Triangles
Tangency
6. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Multiplying/Dividing Signed Numbers
Union of Sets
Repeating Decimal
Surface Area of a Rectangular Solid
7. Factor out the perfect squares
Volume of a Rectangular Solid
Simplifying Square Roots
Interior and Exterior Angles of a Triangle
Average Rate
8. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Part-to-Part Ratios and Part-to-Whole Ratios
Evaluating an Expression
Intersection of sets
Using an Equation to Find an Intercept
9. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Parallel Lines and Transversals
Repeating Decimal
Using the Average to Find the Sum
10. Domain: all possible values of x for a function range: all possible outputs of a function
Using the Average to Find the Sum
Union of Sets
Average Formula -
Domain and Range of a Function
11. 2pr
Surface Area of a Rectangular Solid
Prime Factorization
Even/Odd
Circumference of a Circle
12. 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
Identifying the Parts and the Whole
The 3-4-5 Triangle
Evaluating an Expression
Area of a Sector
13. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiplying and Dividing Powers
Percent Formula
Mixed Numbers and Improper Fractions
Multiples of 2 and 4
14. 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
Interior Angles of a Polygon
Length of an Arc
Identifying the Parts and the Whole
15. To solve a proportion - cross multiply
Union of Sets
Adding and Subtraction Polynomials
Finding the Distance Between Two Points
Solving a Proportion
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)
Union of Sets
Solving a Proportion
Area of a Sector
Tangency
17. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Triangle Inequality Theorem
Pythagorean Theorem
Similar Triangles
18. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Average Rate
Probability
Intersecting Lines
Percent Increase and Decrease
19. 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 midpoint
Number Categories
Multiplying/Dividing Signed Numbers
Combined Percent Increase and Decrease
20. 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)
Number Categories
Even/Odd
Length of an Arc
Counting Consecutive Integers
21. 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
Repeating Decimal
Using the Average to Find the Sum
Determining Absolute Value
22. 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
Greatest Common Factor
PEMDAS
Multiplying Monomials
23. 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
Direct and Inverse Variation
The 3-4-5 Triangle
Surface Area of a Rectangular Solid
Finding the Original Whole
24. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Area of a Circle
The 3-4-5 Triangle
Simplifying Square Roots
25. A square is a rectangle with four equal sides; Area of Square = side*side
Dividing Fractions
Interior Angles of a Polygon
Adding and Subtraction Polynomials
Characteristics of a Square
26. 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
Area of a Sector
Using an Equation to Find the Slope
The 5-12-13 Triangle
Adding and Subtraction Polynomials
27. To divide fractions - invert the second one and multiply
Multiples of 3 and 9
Multiplying Fractions
Length of an Arc
Dividing Fractions
28. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Isosceles and Equilateral triangles
Solving a Quadratic Equation
Simplifying Square Roots
Volume of a Rectangular Solid
29. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Finding the Original Whole
Surface Area of a Rectangular Solid
Even/Odd
30. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Characteristics of a Parallelogram
Finding the Original Whole
Median and Mode
Multiplying and Dividing Powers
31. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Similar Triangles
Tangency
Using the Average to Find the Sum
32. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Factor/Multiple
Adding and Subtracting monomials
Area of a Sector
Multiplying/Dividing Signed Numbers
33. 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
Average of Evenly Spaced Numbers
Volume of a Cylinder
Combined Percent Increase and Decrease
Raising Powers to Powers
34. The whole # left over after division
Multiplying/Dividing Signed Numbers
Percent Increase and Decrease
Comparing Fractions
Remainders
35. 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
Multiples of 3 and 9
Adding/Subtracting Signed Numbers
Multiplying and Dividing Powers
Finding the midpoint
36. 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
Even/Odd
Interior and Exterior Angles of a Triangle
Using an Equation to Find an Intercept
Determining Absolute Value
37. 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
Function - Notation - and Evaulation
Repeating Decimal
Average Formula -
The 5-12-13 Triangle
38. Sum=(Average) x (Number of Terms)
Multiples of 2 and 4
Finding the Original Whole
Using the Average to Find the Sum
Characteristics of a Parallelogram
39. To multiply fractions - multiply the numerators and multiply the denominators
Probability
Multiplying Fractions
PEMDAS
Median and Mode
40. Combine like terms
Percent Formula
Using Two Points to Find the Slope
Number Categories
Adding and Subtraction Polynomials
41. Combine equations in such a way that one of the variables cancel out
Combined Percent Increase and Decrease
Pythagorean Theorem
Average of Evenly Spaced Numbers
Solving a System of Equations
42. 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
Multiplying and Dividing Powers
Adding and Subtraction Polynomials
Solving an Inequality
Finding the Missing Number
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
Characteristics of a Square
Reciprocal
Area of a Circle
44. pr^2
Solving a Proportion
Finding the midpoint
Area of a Circle
Using an Equation to Find the Slope
45. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Multiplying/Dividing Signed Numbers
Multiplying Fractions
Determining Absolute Value
46. Volume of a Cylinder = pr^2h
Surface Area of a Rectangular Solid
Evaluating an Expression
Volume of a Cylinder
Probability
47. 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
Interior Angles of a Polygon
Part-to-Part Ratios and Part-to-Whole Ratios
Domain and Range of a Function
Circumference of a Circle
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
Using an Equation to Find the Slope
Parallel Lines and Transversals
Using the Average to Find the Sum
The 3-4-5 Triangle
49. Multiply the exponents
Raising Powers to Powers
Multiplying and Dividing Roots
Adding and Subtracting Roots
Greatest Common Factor
50. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Determining Absolute Value
Reciprocal
Area of a Sector