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Mathematics Basics: Integers, Operations, and Geometry, Exams of Mathematics

University of LincolnMathematics

Various mathematical concepts including integers, order of operations, properties, factors, fractions, percentages, angles, polygons, quadrilaterals, triangles, similarity, theorems, area and volume formulas, probability, permutations, addition and multiplication rules, expected value, and data types.

Typology: Exams

2023/2024

Available from 04/09/2024

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Integers -
✔️Positive and Negative Whole Numbers; Includes 0
Prime Number -
✔️A whole number greater than 1 that only has two factors (itself and 1)
Composite Number -
✔️A whole number greater than 1 that has more than two different factors
Rational Numbers -
✔️All integers, decimals and fractions; any terminating or repeating decimal number
Irrational Numbers -
✔️Cannot be written as fractions or decimals because the number of decimal places
is infinite and there is no recurring pattern of digits within the number (e.g. pi)
Real Numbers -
✔️Set of all rational and irrational numbers
Order of Operations -
✔️PEMDAS
M/D and A/S are worked left to right in order
Commutative Property -
✔️The order of two numbers may be switched around and the answer is the same
*THINK COMMUTE = move
Associative Property -
✔️Grouping numbers together does not change the value *THINK ASSOCIATE =
group
Distributive Property -
✔️a(b + c) = ab + ac
Additive Identity Property -
✔️a + 0 = a
Additive Inverse Property -
✔️Any (+) number added to its opposite (-) is equal to zero
Multiplicative Identity Property -
✔️1 is the multiplicative identity such that a x 1=a
Multiplicative Inverse Property -
✔️"Reciprocal"
Law of Exponents -
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Integers - ✔️Positive and Negative Whole Numbers; Includes 0 Prime Number - ✔️A whole number greater than 1 that only has two factors (itself and 1) Composite Number - ✔️A whole number greater than 1 that has more than two different factors Rational Numbers - ✔️All integers, decimals and fractions; any terminating or repeating decimal number Irrational Numbers - ✔️Cannot be written as fractions or decimals because the number of decimal places is infinite and there is no recurring pattern of digits within the number (e.g. pi) Real Numbers - ✔️Set of all rational and irrational numbers Order of Operations - ✔️PEMDAS M/D and A/S are worked left to right in order Commutative Property - ✔️The order of two numbers may be switched around and the answer is the same *THINK COMMUTE = move Associative Property - ✔️Grouping numbers together does not change the value *THINK ASSOCIATE = group Distributive Property - ✔️a(b + c) = ab + ac Additive Identity Property - ✔️a + 0 = a Additive Inverse Property - ✔️Any (+) number added to its opposite (-) is equal to zero Multiplicative Identity Property - ✔️1 is the multiplicative identity such that a x 1=a Multiplicative Inverse Property - ✔️"Reciprocal" Law of Exponents -

✔️1) Any number raised to the power of 1 is equal to itself

  1. The number 1 raised to any power is equal to 1
  2. Any number raised to the power of 0 is equal to 1
  3. Add exponents to multiply powers of the same base number
  4. Subtract exponents to divide powers of the same number
  5. Multiply exponents to raise a power to a power
  6. If multiplied or divided numbers inside parentheses are raised to a power it is the same as each individual term raised to that power Factors - ✔️Numbers that are multiplied together to obtain a product Common Factor - ✔️Number that divides exactly into two or more other numbers Greatest Common Factor (GCF) - ✔️The largest number that is a factor of two or more numbers Least Common Multiple (LCM) - ✔️The smallest number that is a multiple of two or more numbers Dividing Fractions - ✔️Flip the numerator and denominator of the second fraction and then multiply Solving Percentage Problems - ✔️P=W x % or %=P/W or W=P/% Bisector - ✔️A line/line segment that divides another line segment into two equal lengths Intersecting Lines - ✔️Lines that have exactly one point in common Transversal Line - ✔️A line that intersects at least two other lines that may or may not be parallel Vertex - ✔️The point where two segments or rays meet to form an angle Angles - ✔️Acute: less than 90 degrees Right: exactly 90 degrees Obtuse: between 90 and 180 Straight: exactly 180 degrees (line) Reflex: between 180 and 360 Full: exactly 360 Complementary -

Square: 4 equal sides and 4 congruent (right) angles Triangles - ✔️Acute: 3 angles are all less than 90 degrees Right: one angle equals 90 degrees (Pythagorean Theorem) Obtuse: one angle is greater than 90 degrees Equilateral: 3 congruent sides/angles each at 60 degrees Isosceles: two congruent sides and two congruent angles opposite the two congruent sides Scalene: no congruent sides with 3 angles of different measures; angle with largest measure is opposite the longest side and angle with the smallest measure is opposite the shortest side Triangle Inequality Theorem - ✔️The sum of the measures of any two sides of a triangle is always greater than the measure of the third side Similar Triangles - ✔️Triangles whose corresponding angles are congruent to one another; proportional Side-Side-Side - ✔️If all three sides of one triangle are equal to all three sides of another triangle, they are congruent Side-Angle-Side - ✔️If two sides and the adjoining angle in one triangle are equal to two sides and the adjoining angle of another triangle, they are congruent Pythagorean Theorem - ✔️a^2 (side) + b^2 (side) = c^2 (hypotenuse) Law of Sines - ✔️sinA/a = sinB/b = sinC/c Law of Cosines - ✔️c^2 = a^2 + b^2 - 2ab(cosC) Area Formulas - ✔️Rectangle: A=wl Square: A=s^ Triangle: A=1/2bh Parallelogram: A=bh Trapezoid: A=1/2 (b1 + b2)h Circle: A=pi(r^2) Volume Formulas - ✔️Pyramid: V=1/3Bh Prism: V=Bh Cube: V=s^ Sphere: V=4/3pi(r)^

Probability - ✔️Desired Outcomes/Total Outcomes Theoretical Probability - ✔️What should happen P(A) = Number of Acceptable Outcomes/Number of Possible Outcomes Permutations - ✔️ Complement of an Event - ✔️The possibility of something not happening Addition Rule - ✔️Used to find the probability of a Compound Event Conditional Probability - ✔️The probability of an event occurring once another event has already occurred Multiplication Rule - ✔️Used to find the probability of two independent events occurring using the formula P (A and B) = P (A) x P (B) Expected Value - ✔️A method of determining expected outcome in a random situation; sum of the weighted probabilities of the possible outcomes Empirical Probability - ✔️The number of times an outcome occurs in a particular experiment or a certain number of observed events (what has happened) Quantitative Data - ✔️Measurements Qualitative Data - ✔️Information Discrete Data - ✔️Info that can be expressed only by a specific value

Praxis II: Math (5003) Study Guide

Continuous Data - ✔️Info that can be expressed by any value within a given range Primary Data - ✔️Info that has been collected directly from a survey/experiment Secondary Data -