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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. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
PEMDAS
Characteristics of a Parallelogram
Probability
Volume of a Rectangular Solid
2. 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
Even/Odd
Pythagorean Theorem
Characteristics of a Square
3. 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)
Relative Primes
Percent Increase and Decrease
Solving a System of Equations
Area of a Sector
4. 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
Solving an Inequality
Finding the Missing Number
Circumference of a Circle
Using an Equation to Find the Slope
5. 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
Multiplying Fractions
Adding and Subtracting Roots
PEMDAS
Characteristics of a Parallelogram
6. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Comparing Fractions
Multiplying Monomials
Identifying the Parts and the Whole
7. Factor out the perfect squares
Dividing Fractions
Pythagorean Theorem
Area of a Circle
Simplifying Square Roots
8. To divide fractions - invert the second one and multiply
Triangle Inequality Theorem
Dividing Fractions
Surface Area of a Rectangular Solid
Adding/Subtracting Signed Numbers
9. 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
Raising Powers to Powers
Reciprocal
Rate
10. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Comparing Fractions
Median and Mode
Circumference of a Circle
Interior Angles of a Polygon
11. 2pr
Multiplying Fractions
Negative Exponent and Rational Exponent
Area of a Sector
Circumference of a Circle
12. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Solving an Inequality
Exponential Growth
PEMDAS
13. 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
Volume of a Cylinder
Exponential Growth
Direct and Inverse Variation
14. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Identifying the Parts and the Whole
Multiples of 2 and 4
Multiplying Monomials
Using Two Points to Find the Slope
15. 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
Surface Area of a Rectangular Solid
Triangle Inequality Theorem
Using an Equation to Find an Intercept
Volume of a Cylinder
16. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Even/Odd
Finding the Distance Between Two Points
Adding and Subtraction Polynomials
Simplifying Square Roots
17. To multiply fractions - multiply the numerators and multiply the denominators
Interior and Exterior Angles of a Triangle
The 3-4-5 Triangle
Finding the midpoint
Multiplying Fractions
18. 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
Simplifying Square Roots
Finding the Missing Number
Multiples of 2 and 4
Rate
19. For all right triangles: a^2+b^2=c^2
Finding the midpoint
Adding and Subtracting Roots
Pythagorean Theorem
Finding the Distance Between Two Points
20. To solve a proportion - cross multiply
Solving a Proportion
Number Categories
Exponential Growth
Tangency
21. pr^2
Triangle Inequality Theorem
Determining Absolute Value
The 5-12-13 Triangle
Area of a Circle
22. 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 Formula
Adding and Subtraction Polynomials
Percent Increase and Decrease
Characteristics of a Rectangle
23. 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 Sector
Median and Mode
Multiplying and Dividing Roots
Part-to-Part Ratios and Part-to-Whole Ratios
24. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Dividing Fractions
Union of Sets
Adding/Subtracting Fractions
Area of a Circle
25. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Using Two Points to Find the Slope
Multiplying Monomials
Surface Area of a Rectangular Solid
26. 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
Average Rate
Characteristics of a Parallelogram
Multiplying Monomials
27. you can add/subtract when the part under the radical is the same
Multiplying and Dividing Powers
Setting up a Ratio
Adding and Subtracting Roots
Adding and Subtraction Polynomials
28. 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
Tangency
Identifying the Parts and the Whole
Interior Angles of a Polygon
29. 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
Comparing Fractions
Combined Percent Increase and Decrease
Determining Absolute Value
Interior Angles of a Polygon
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
Function - Notation - and Evaulation
Finding the Distance Between Two Points
Multiples of 3 and 9
Direct and Inverse Variation
31. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds
Identifying the Parts and the Whole
Finding the midpoint
Finding the Distance Between Two Points
Multiplying Fractions
32. 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
Percent Increase and Decrease
Simplifying Square Roots
Median and Mode
33. # 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
Intersecting Lines
Interior Angles of a Polygon
Determining Absolute Value
34. 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)
Multiplying Monomials
Average Formula -
Length of an Arc
Intersecting Lines
35. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Parallel Lines and Transversals
The 5-12-13 Triangle
Reducing Fractions
Solving an Inequality
36. A square is a rectangle with four equal sides; Area of Square = side*side
Interior and Exterior Angles of a Triangle
Solving a Proportion
Finding the Missing Number
Characteristics of a Square
37. Sum=(Average) x (Number of Terms)
Adding/Subtracting Fractions
Setting up a Ratio
Probability
Using the Average to Find the Sum
38. 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
Union of Sets
Interior and Exterior Angles of a Triangle
Greatest Common Factor
Length of an Arc
39. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Interior and Exterior Angles of a Triangle
Adding/Subtracting Fractions
PEMDAS
Intersection of sets
40. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
PEMDAS
Multiples of 2 and 4
Evaluating an Expression
Intersecting Lines
41. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Reducing Fractions
Adding and Subtracting monomials
Finding the Missing Number
42. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Solving a Quadratic Equation
Similar Triangles
Union of Sets
43. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Multiples of 3 and 9
Interior Angles of a Polygon
Evaluating an Expression
Adding and Subtracting monomials
44. 1. Re-express them with common denominators 2. Convert them to decimals
Finding the Original Whole
Solving a System of Equations
Even/Odd
Comparing Fractions
45. Add the exponents and keep the same base
Adding and Subtracting monomials
Multiplying and Dividing Powers
Using an Equation to Find an Intercept
Using an Equation to Find the Slope
46. Combine like terms
Average of Evenly Spaced Numbers
Adding and Subtracting Roots
Adding and Subtraction Polynomials
Using an Equation to Find an Intercept
47. (average of the x coordinates - average of the y coordinates)
Adding/Subtracting Signed Numbers
Isosceles and Equilateral triangles
Multiplying Fractions
Finding the midpoint
48. Change in y/ change in x rise/run
Part-to-Part Ratios and Part-to-Whole Ratios
Length of an Arc
Using Two Points to Find the Slope
Finding the Original Whole
49. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Percent Formula
Number Categories
Prime Factorization
50. 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
Function - Notation - and Evaulation
PEMDAS
Negative Exponent and Rational Exponent
Evaluating an Expression