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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. The largest factor that two or more numbers have in common.
Using an Equation to Find an Intercept
Greatest Common Factor
Pythagorean Theorem
Using the Average to Find the Sum
2. 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
Greatest Common Factor
Isosceles and Equilateral triangles
Direct and Inverse Variation
Prime Factorization
3. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Remainders
Adding and Subtracting monomials
Reciprocal
Setting up a Ratio
4. 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
Characteristics of a Parallelogram
Using an Equation to Find the Slope
Counting the Possibilities
Remainders
5. Combine like terms
Multiplying and Dividing Powers
The 3-4-5 Triangle
Direct and Inverse Variation
Adding and Subtraction Polynomials
6. 1. Re-express them with common denominators 2. Convert them to decimals
PEMDAS
Mixed Numbers and Improper Fractions
Comparing Fractions
Volume of a Rectangular Solid
7. 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
Characteristics of a Parallelogram
Using Two Points to Find the Slope
Characteristics of a Square
Greatest Common Factor
8. 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.
Probability
Volume of a Rectangular Solid
Number Categories
Negative Exponent and Rational Exponent
9. 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
Characteristics of a Parallelogram
Number Categories
Characteristics of a Rectangle
Even/Odd
10. 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
The 5-12-13 Triangle
Similar Triangles
Relative Primes
Isosceles and Equilateral triangles
11. 2pr
Counting Consecutive Integers
Function - Notation - and Evaulation
Finding the midpoint
Circumference of a Circle
12. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Raising Powers to Powers
Average Rate
Adding and Subtracting Roots
Using an Equation to Find an Intercept
13. 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
Multiplying/Dividing Signed Numbers
Domain and Range of a Function
Adding/Subtracting Signed Numbers
14. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Reducing Fractions
Combined Percent Increase and Decrease
Factor/Multiple
15. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Direct and Inverse Variation
Probability
Volume of a Cylinder
16. 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
Comparing Fractions
Determining Absolute Value
Solving a Quadratic Equation
Using an Equation to Find an Intercept
17. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Direct and Inverse Variation
Characteristics of a Rectangle
Tangency
Union of Sets
18. To find the reciprocal of a fraction switch the numerator and the denominator
Pythagorean Theorem
Reciprocal
Rate
Adding/Subtracting Fractions
19. 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 Parallelogram
Median and Mode
Length of an Arc
Solving an Inequality
20. 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
Percent Formula
Characteristics of a Rectangle
Average Rate
21. Part = Percent x Whole
Using an Equation to Find an Intercept
Adding and Subtracting monomials
Percent Formula
Reciprocal
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
Intersecting Lines
Using Two Points to Find the Slope
Finding the Distance Between Two Points
Multiplying/Dividing Signed Numbers
23. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Tangency
Setting up a Ratio
Determining Absolute Value
Multiplying and Dividing Powers
24. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Length of an Arc
Dividing Fractions
Intersecting Lines
Determining Absolute Value
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)
Tangency
Reciprocal
Length of an Arc
Isosceles and Equilateral triangles
26. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Parallel Lines and Transversals
Area of a Triangle
Triangle Inequality Theorem
27. 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 and Dividing Roots
Multiplying Monomials
Part-to-Part Ratios and Part-to-Whole Ratios
Exponential Growth
28. 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
Combined Percent Increase and Decrease
Isosceles and Equilateral triangles
Multiplying and Dividing Powers
Mixed Numbers and Improper Fractions
29. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Circumference of a Circle
Greatest Common Factor
Using the Average to Find the Sum
Median and Mode
30. 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
The 5-12-13 Triangle
Solving an Inequality
Finding the midpoint
Mixed Numbers and Improper Fractions
31. 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
Comparing Fractions
Percent Increase and Decrease
Pythagorean Theorem
Adding and Subtracting monomials
32. Surface Area = 2lw + 2wh + 2lh
Area of a Circle
Average Rate
Surface Area of a Rectangular Solid
Solving a Quadratic Equation
33. 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
Negative Exponent and Rational Exponent
Part-to-Part Ratios and Part-to-Whole Ratios
Counting Consecutive Integers
Using an Equation to Find the Slope
34. Factor out the perfect squares
Using an Equation to Find the Slope
Finding the Distance Between Two Points
PEMDAS
Simplifying Square Roots
35. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Percent Increase and Decrease
Characteristics of a Rectangle
Area of a Circle
Intersection of sets
36. 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
PEMDAS
Finding the Missing Number
Function - Notation - and Evaulation
Parallel Lines and Transversals
37. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Negative Exponent and Rational Exponent
Function - Notation - and Evaulation
Length of an Arc
Union of Sets
38. 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
Triangle Inequality Theorem
Solving a Proportion
Area of a Triangle
Similar Triangles
39. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Using the Average to Find the Sum
Circumference of a Circle
Similar Triangles
Multiples of 3 and 9
40. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Union of Sets
Multiplying Fractions
The 3-4-5 Triangle
41. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Mixed Numbers and Improper Fractions
Isosceles and Equilateral triangles
Repeating Decimal
Determining Absolute Value
42. 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
Reducing Fractions
Adding/Subtracting Signed Numbers
Interior and Exterior Angles of a Triangle
Factor/Multiple
43. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Probability
Multiples of 3 and 9
Counting the Possibilities
Length of an Arc
44. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Median and Mode
Circumference of a Circle
Characteristics of a Rectangle
Tangency
45. To multiply fractions - multiply the numerators and multiply the denominators
Setting up a Ratio
Direct and Inverse Variation
Adding/Subtracting Fractions
Multiplying Fractions
46. 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
Comparing Fractions
Finding the midpoint
Volume of a Cylinder
47. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Interior and Exterior Angles of a Triangle
Area of a Triangle
Adding and Subtracting Roots
48. 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)
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Sector
Interior Angles of a Polygon
The 5-12-13 Triangle
49. 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
Dividing Fractions
Finding the Missing Number
Using an Equation to Find an Intercept
50. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Characteristics of a Square
Multiples of 2 and 4
Volume of a Cylinder
Reciprocal