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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
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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. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Using an Equation to Find the Slope
Finding the Original Whole
Determining Absolute Value
Using an Equation to Find an Intercept
2. 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
Adding/Subtracting Fractions
Reducing Fractions
Using an Equation to Find an Intercept
Function - Notation - and Evaulation
3. To solve a proportion - cross multiply
Multiplying/Dividing Signed Numbers
Interior Angles of a Polygon
Solving a Proportion
Multiplying and Dividing Roots
4. 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
Mixed Numbers and Improper Fractions
Direct and Inverse Variation
Multiplying Monomials
Rate
5. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiplying Monomials
Combined Percent Increase and Decrease
Finding the Distance Between Two Points
Finding the midpoint
6. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying and Dividing Powers
Area of a Circle
Multiplying Monomials
Volume of a Rectangular Solid
7. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Percent Formula
Length of an Arc
Using an Equation to Find the Slope
Evaluating an Expression
8. Factor out the perfect squares
Percent Formula
Volume of a Cylinder
Simplifying Square Roots
Reciprocal
9. 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
Comparing Fractions
Solving a Proportion
Identifying the Parts and the Whole
Solving an Inequality
10. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Dividing Fractions
Similar Triangles
Intersecting Lines
Average Formula -
11. Add the exponents and keep the same base
Reciprocal
Combined Percent Increase and Decrease
Multiplying and Dividing Powers
Probability
12. To find the reciprocal of a fraction switch the numerator and the denominator
Volume of a Rectangular Solid
Part-to-Part Ratios and Part-to-Whole Ratios
Pythagorean Theorem
Reciprocal
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)
Using an Equation to Find an Intercept
Area of a Sector
Counting the Possibilities
Direct and Inverse Variation
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
Solving a Quadratic Equation
Average Rate
Function - Notation - and Evaulation
PEMDAS
15. 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 and Exterior Angles of a Triangle
Multiples of 2 and 4
The 3-4-5 Triangle
Using the Average to Find the Sum
16. Change in y/ change in x rise/run
Solving a System of Equations
Using Two Points to Find the Slope
Identifying the Parts and the Whole
Volume of a Rectangular Solid
17. 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
Area of a Triangle
Average Formula -
Using an Equation to Find the Slope
Area of a Sector
18. 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
Area of a Sector
Percent Increase and Decrease
Using an Equation to Find the Slope
19. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Number Categories
Setting up a Ratio
Finding the Missing Number
Probability
20. Subtract the smallest from the largest and add 1
Similar Triangles
Counting Consecutive Integers
Identifying the Parts and the Whole
(Least) Common Multiple
21. The smallest multiple (other than zero) that two or more numbers have in common.
Negative Exponent and Rational Exponent
Multiples of 3 and 9
(Least) Common Multiple
Finding the midpoint
22. 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
Exponential Growth
Remainders
Tangency
Negative Exponent and Rational Exponent
23. 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
Domain and Range of a Function
Characteristics of a Rectangle
Combined Percent Increase and Decrease
Solving a Quadratic Equation
24. 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
Area of a Sector
Solving a Quadratic Equation
Negative Exponent and Rational Exponent
Area of a Circle
25. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Reducing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Percent Formula
26. 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
Percent Increase and Decrease
Intersecting Lines
Median and Mode
27. Multiply the exponents
Adding/Subtracting Signed Numbers
Intersection of sets
Negative Exponent and Rational Exponent
Raising Powers to Powers
28. 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
Area of a Circle
(Least) Common Multiple
Finding the Original Whole
Union of Sets
29. 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
Probability
Function - Notation - and Evaulation
Multiplying/Dividing Signed Numbers
30. 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
Adding and Subtracting Roots
Multiplying Fractions
Even/Odd
Dividing Fractions
31. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Area of a Circle
Setting up a Ratio
Multiples of 2 and 4
Interior Angles of a Polygon
32. To divide fractions - invert the second one and multiply
Evaluating an Expression
Length of an Arc
Counting Consecutive Integers
Dividing Fractions
33. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Greatest Common Factor
Using the Average to Find the Sum
Isosceles and Equilateral triangles
34. 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
Counting the Possibilities
Finding the Missing Number
The 5-12-13 Triangle
35. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Multiplying Monomials
Interior Angles of a Polygon
Average of Evenly Spaced Numbers
Counting the Possibilities
36. 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)
Finding the Missing Number
Length of an Arc
Greatest Common Factor
Repeating Decimal
37. 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
Volume of a Cylinder
PEMDAS
Using Two Points to Find the Slope
Rate
38. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Finding the midpoint
Average Formula -
Finding the Missing Number
Similar Triangles
39. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Interior and Exterior Angles of a Triangle
Median and Mode
Solving a Proportion
Adding/Subtracting Fractions
40. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Square
Counting Consecutive Integers
Using an Equation to Find an Intercept
41. 2pr
Circumference of a Circle
Intersecting Lines
Characteristics of a Square
Multiplying and Dividing Powers
42. 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
Identifying the Parts and the Whole
Multiplying and Dividing Powers
Triangle Inequality Theorem
43. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Rectangle
Average of Evenly Spaced Numbers
Multiplying Monomials
Counting Consecutive Integers
44. 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
Adding/Subtracting Signed Numbers
Part-to-Part Ratios and Part-to-Whole Ratios
Average of Evenly Spaced Numbers
Counting Consecutive Integers
45. 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
Even/Odd
Direct and Inverse Variation
Intersecting Lines
Raising Powers to Powers
46. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Average Formula -
Surface Area of a Rectangular Solid
Factor/Multiple
Multiplying and Dividing Roots
47. Part = Percent x Whole
Probability
Multiplying/Dividing Signed Numbers
Percent Formula
Greatest Common Factor
48. Combine like terms
Even/Odd
Characteristics of a Rectangle
Adding and Subtraction Polynomials
Solving an Inequality
49. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Area of a Sector
Using the Average to Find the Sum
Adding and Subtracting monomials
Finding the Original Whole
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
Triangle Inequality Theorem
Multiples of 2 and 4
PEMDAS
Adding and Subtracting Roots