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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. 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.
Multiplying Monomials
Number Categories
Adding/Subtracting Signed Numbers
Greatest Common Factor
2. Combine equations in such a way that one of the variables cancel out
Solving a Proportion
Using Two Points to Find the Slope
Percent Increase and Decrease
Solving a System of Equations
3. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Finding the Missing Number
Using an Equation to Find an Intercept
Adding/Subtracting Fractions
Average of Evenly Spaced Numbers
4. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Area of a Sector
Interior and Exterior Angles of a Triangle
Volume of a Cylinder
5. 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
Volume of a Cylinder
Adding and Subtraction Polynomials
Multiplying/Dividing Signed Numbers
(Least) Common Multiple
6. Factor out the perfect squares
Average Formula -
Probability
Prime Factorization
Simplifying Square Roots
7. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 3 and 9
Identifying the Parts and the Whole
Circumference of a Circle
Evaluating an Expression
8. 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
Characteristics of a Rectangle
Solving an Inequality
Interior Angles of a Polygon
Evaluating an Expression
9. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Reciprocal
Intersecting Lines
Adding and Subtraction Polynomials
Using an Equation to Find an Intercept
10. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Adding/Subtracting Fractions
Similar Triangles
Using Two Points to Find the Slope
Finding the Distance Between Two Points
11. 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
Union of Sets
Relative Primes
Negative Exponent and Rational Exponent
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
Repeating Decimal
The 3-4-5 Triangle
Evaluating an Expression
Length of an Arc
13. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Area of a Triangle
The 5-12-13 Triangle
Finding the Missing Number
14. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Average Rate
Finding the Distance Between Two Points
Circumference of a Circle
Setting up a Ratio
15. 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
Solving a Proportion
Adding/Subtracting Fractions
Exponential Growth
Even/Odd
16. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Area of a Sector
Prime Factorization
(Least) Common Multiple
Area of a Circle
17. Volume of a Cylinder = pr^2h
Multiplying and Dividing Roots
Adding and Subtraction Polynomials
Volume of a Cylinder
Using an Equation to Find the Slope
18. 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
Intersection of sets
Area of a Triangle
Using an Equation to Find an Intercept
Adding/Subtracting Signed Numbers
19. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Determining Absolute Value
Rate
Adding/Subtracting Fractions
20. To find the reciprocal of a fraction switch the numerator and the denominator
Average Formula -
Reciprocal
Counting Consecutive Integers
Multiplying and Dividing Powers
21. 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
Percent Formula
Characteristics of a Parallelogram
Multiplying and Dividing Powers
Setting up a Ratio
22. To solve a proportion - cross multiply
Multiplying Monomials
Interior Angles of a Polygon
Determining Absolute Value
Solving a Proportion
23. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Parallel Lines and Transversals
Counting the Possibilities
PEMDAS
Multiplying Monomials
24. 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
Area of a Circle
Remainders
Adding and Subtracting monomials
25. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Median and Mode
Interior Angles of a Polygon
Reducing Fractions
Characteristics of a Square
26. 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
Relative Primes
Interior and Exterior Angles of a Triangle
Circumference of a Circle
27. 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
Multiplying Fractions
Triangle Inequality Theorem
Counting the Possibilities
Average Formula -
28. The whole # left over after division
Remainders
Interior and Exterior Angles of a Triangle
Domain and Range of a Function
Direct and Inverse Variation
29. Probability= Favorable Outcomes/Total Possible Outcomes
Isosceles and Equilateral triangles
Probability
Multiplying and Dividing Roots
Volume of a Rectangular Solid
30. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Area of a Circle
Even/Odd
Multiples of 2 and 4
Finding the Missing Number
31. Surface Area = 2lw + 2wh + 2lh
Reducing Fractions
Volume of a Rectangular Solid
Surface Area of a Rectangular Solid
PEMDAS
32. 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
Greatest Common Factor
Solving an Inequality
Pythagorean Theorem
Part-to-Part Ratios and Part-to-Whole Ratios
33. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Using an Equation to Find an Intercept
Using an Equation to Find the Slope
Average Formula -
Factor/Multiple
34. 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
Median and Mode
Using an Equation to Find an Intercept
Interior and Exterior Angles of a Triangle
Area of a Sector
35. 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
Volume of a Cylinder
Repeating Decimal
Setting up a Ratio
Percent Formula
36. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Average Formula -
Pythagorean Theorem
Solving a Quadratic Equation
Volume of a Cylinder
37. 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
Using the Average to Find the Sum
Function - Notation - and Evaulation
Intersecting Lines
Percent Formula
38. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Probability
Combined Percent Increase and Decrease
Circumference of a Circle
Union of Sets
39. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Comparing Fractions
Length of an Arc
Multiplying Fractions
40. 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
Finding the Original Whole
The 5-12-13 Triangle
Negative Exponent and Rational Exponent
Length of an Arc
41. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Simplifying Square Roots
Volume of a Rectangular Solid
Characteristics of a Rectangle
Intersection of sets
42. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Adding and Subtracting Roots
Using the Average to Find the Sum
Reducing Fractions
Area of a Triangle
43. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Evaluating an Expression
Setting up a Ratio
Average Rate
Solving a Quadratic Equation
44. For all right triangles: a^2+b^2=c^2
Prime Factorization
Pythagorean Theorem
Percent Increase and Decrease
Counting the Possibilities
45. 1. Re-express them with common denominators 2. Convert them to decimals
Average Formula -
Comparing Fractions
Percent Increase and Decrease
Finding the Distance Between Two Points
46. Multiply the exponents
Raising Powers to Powers
Average Formula -
Multiplying/Dividing Signed Numbers
Reciprocal
47. 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)
Using an Equation to Find the Slope
Length of an Arc
The 3-4-5 Triangle
Percent Increase and Decrease
48. 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
Median and Mode
Finding the midpoint
Rate
49. 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
Volume of a Cylinder
Exponential Growth
PEMDAS
Characteristics of a Rectangle
50. # 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
Raising Powers to Powers
Solving a Quadratic Equation
Intersecting Lines