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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. 1. Re-express them with common denominators 2. Convert them to decimals
Part-to-Part Ratios and Part-to-Whole Ratios
Surface Area of a Rectangular Solid
Characteristics of a Rectangle
Comparing Fractions
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
Comparing Fractions
Solving a System of Equations
The 3-4-5 Triangle
Using Two Points to Find the Slope
3. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Prime Factorization
Multiples of 3 and 9
Characteristics of a Square
Using an Equation to Find the Slope
4. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Using an Equation to Find the Slope
Similar Triangles
Evaluating an Expression
Characteristics of a Rectangle
5. 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
Multiples of 2 and 4
Characteristics of a Parallelogram
Interior and Exterior Angles of a Triangle
6. 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
Counting the Possibilities
Percent Increase and Decrease
PEMDAS
Average Formula -
7. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Interior and Exterior Angles of a Triangle
Adding and Subtracting monomials
Using an Equation to Find the Slope
Similar Triangles
8. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Multiplying and Dividing Roots
Tangency
Percent Formula
9. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Multiplying Fractions
Domain and Range of a Function
Finding the Original Whole
10. 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
Union of Sets
Characteristics of a Square
Area of a Sector
11. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Surface Area of a Rectangular Solid
Adding/Subtracting Signed Numbers
Characteristics of a Square
12. Part = Percent x Whole
Negative Exponent and Rational Exponent
Percent Formula
Interior Angles of a Polygon
Intersecting Lines
13. 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
Pythagorean Theorem
Solving an Inequality
Finding the Original Whole
Multiplying and Dividing Roots
14. Subtract the smallest from the largest and add 1
Intersection of sets
Finding the Original Whole
Counting Consecutive Integers
Volume of a Rectangular Solid
15. 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
Prime Factorization
Characteristics of a Square
Identifying the Parts and the Whole
Area of a Sector
16. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
Average Rate
The 3-4-5 Triangle
Multiplying Fractions
17. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Intersecting Lines
Factor/Multiple
Comparing Fractions
Finding the Original Whole
18. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen
Counting the Possibilities
Negative Exponent and Rational Exponent
Adding and Subtraction Polynomials
Repeating Decimal
19. To multiply fractions - multiply the numerators and multiply the denominators
Adding and Subtracting Roots
Adding/Subtracting Fractions
Combined Percent Increase and Decrease
Multiplying Fractions
20. 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
Reciprocal
Combined Percent Increase and Decrease
Finding the Missing Number
Multiples of 3 and 9
21. 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
Counting the Possibilities
Direct and Inverse Variation
Rate
Simplifying Square Roots
22. 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
Multiplying/Dividing Signed Numbers
Multiplying Fractions
Raising Powers to Powers
Characteristics of a Square
23. Surface Area = 2lw + 2wh + 2lh
Intersecting Lines
Surface Area of a Rectangular Solid
Multiplying Monomials
Interior and Exterior Angles of a Triangle
24. To divide fractions - invert the second one and multiply
Dividing Fractions
Interior and Exterior Angles of a Triangle
Adding and Subtracting monomials
Volume of a Rectangular Solid
25. 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)
Volume of a Rectangular Solid
Using an Equation to Find an Intercept
Length of an Arc
Exponential Growth
26. 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
Identifying the Parts and the Whole
Interior Angles of a Polygon
Relative Primes
Volume of a Cylinder
27. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
The 3-4-5 Triangle
Parallel Lines and Transversals
Average Formula -
Adding and Subtracting monomials
28. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Identifying the Parts and the Whole
Using an Equation to Find the Slope
Triangle Inequality Theorem
29. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
(Least) Common Multiple
Adding/Subtracting Fractions
Finding the Distance Between Two Points
Characteristics of a Parallelogram
30. 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
Raising Powers to Powers
Part-to-Part Ratios and Part-to-Whole Ratios
PEMDAS
31. 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
Factor/Multiple
Negative Exponent and Rational Exponent
Multiples of 3 and 9
Union of Sets
32. Add the exponents and keep the same base
Multiplying and Dividing Powers
Interior and Exterior Angles of a Triangle
Adding and Subtracting monomials
Surface Area of a Rectangular Solid
33. 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
Domain and Range of a Function
(Least) Common Multiple
Adding and Subtracting Roots
34. 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
Repeating Decimal
Reducing Fractions
Counting Consecutive Integers
35. 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
Multiplying Monomials
Part-to-Part Ratios and Part-to-Whole Ratios
Direct and Inverse Variation
Interior Angles of a Polygon
36. 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
Average Rate
PEMDAS
Even/Odd
37. 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)
Finding the Missing Number
Intersecting Lines
Isosceles and Equilateral triangles
Area of a Sector
38. Combine like terms
Adding and Subtraction Polynomials
Union of Sets
Characteristics of a Rectangle
Volume of a Cylinder
39. The largest factor that two or more numbers have in common.
Finding the midpoint
Intersection of sets
Counting Consecutive Integers
Greatest Common Factor
40. 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
Finding the Missing Number
Negative Exponent and Rational Exponent
Surface Area of a Rectangular Solid
41. 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
Reciprocal
Part-to-Part Ratios and Part-to-Whole Ratios
Comparing Fractions
Multiplying Monomials
42. 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
Using Two Points to Find the Slope
Even/Odd
Similar Triangles
Characteristics of a Square
43. 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
Using the Average to Find the Sum
Percent Increase and Decrease
Setting up a Ratio
44. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Using an Equation to Find the Slope
Comparing Fractions
Remainders
Reducing Fractions
45. you can add/subtract when the part under the radical is the same
Area of a Circle
Similar Triangles
Characteristics of a Parallelogram
Adding and Subtracting Roots
46. Multiply the exponents
Raising Powers to Powers
Characteristics of a Square
(Least) Common Multiple
The 5-12-13 Triangle
47. To solve a proportion - cross multiply
Number Categories
Solving a Proportion
Interior and Exterior Angles of a Triangle
Parallel Lines and Transversals
48. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Dividing Fractions
Intersecting Lines
Surface Area of a Rectangular Solid
Intersection of sets
49. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Finding the Distance Between Two Points
Multiplying Fractions
Adding/Subtracting Fractions
Even/Odd
50. Sum=(Average) x (Number of Terms)
Area of a Circle
The 5-12-13 Triangle
Percent Increase and Decrease
Using the Average to Find the Sum