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FTCE MIDDLE GRADES MATHS 5-9 EXAM LATEST 2023-2024 ACTUAL EXAM 200 QUESTIONS AND CORRECT DETAILED ANSWERS WITH RATIONALES|ALREADY GRADED A+
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pyramid - ANSWER- A solid shape with a polygon as a base and triangular faces that come to a point (vertex or apex) 6faces 8Edges 5Vertices Volume of a pyramid - ANSWER- V=1/3Bh cone - ANSWER- A three dimensional shape with a circular base and a vertex opposite the base 2 Faces 1 edge 1 vertex
Prism - ANSWER- A solid figure that has two congruent, parallel polygons as its bases. Its sides are parallelograms Volume of a prism - ANSWER- V=Bh circumference - ANSWER- the perimeter of a circle surface area - ANSWER- 1. The sum of all the areas of all the faces or surfaces that enclose a solid. Find area of each shape then add together Surface area of a sphere - ANSWER- 4πr² Surface Area of a Cylinder - ANSWER- 2πrh+2πr² Gram - ANSWER- Mass of a paper clip 1000 g=1 kg Kilogram - ANSWER- Mass of baseball 1 kg=1000 g millimeter - ANSWER- thickness of paper clip
Pint - ANSWER- 1 pt = 2cups Quart - ANSWER- 1 qt=2 pints 1 qt = 4 cups Gallon - ANSWER- 1 G = 4 qt Inch - ANSWER- length of quarter 12 in = 1 ft foot - ANSWER- length of foot 1 ft=12 in yard - ANSWER- Length of guitar 1 yd=36 in 1 yd= 3 ft Mile - ANSWER- length of airport runway 1 mile = 1760 yd to convert a larger unit to a smaller unit - ANSWER- multiply
Covert to smaller unit to larger unit - ANSWER- Divide Line - ANSWER- a straight path that extends without end in opposite directions point - ANSWER- an exact location in space plane - ANSWER- A two-dimensional flat surface that extends in all directions segment - ANSWER- A part of a line consisting of two endpoints and all points between them. ray - ANSWER- A part of a line, with one endpoint, that continues without end in one direction iscosceles triangle - ANSWER- has at least two congruent sides and angles scalene triangle - ANSWER- a triangle with no congruent sides equilateral triangle - ANSWER- A triangle with three congruent sides trigonomic ratio - ANSWER- SOH-CAH-TOA
Line - ANSWER- a straight path that extends without end in opposite directions point - ANSWER- an exact location in space plane - ANSWER- A two-dimensional flat surface that extends in all directions segment - ANSWER- A part of a line consisting of two endpoints and all points between them. ray - ANSWER- A part of a line, with one endpoint, that continues without end in one direction iscosceles triangle - ANSWER- has at least two congruent sides and angles scalene triangle - ANSWER- a triangle with no congruent sides equilateral triangle - ANSWER- A triangle with three congruent sides trigonomic ratio - ANSWER- SOH-CAH-TOA Parrellelogram - ANSWER- A quadrilateral with two pairs of parallel sides
Trapezoid - ANSWER- a quadrilateral with one pair of parallel sides Kite - ANSWER- a quadrilateral with two pairs of adjacent sides congruent and no opposite sides congruent Rhombus - ANSWER- A parallelogram with four congruent sides Distance Formula - ANSWER- d = √[( x₂ - x₁)² + (y₂ - y₁)²] midpoint formula - ANSWER- (x₁+x₂)/2, (y₁+y₂)/ Translation - ANSWER- moving without rotating, resizing, etc. Reflection - ANSWER- A transformation that "flips" a figure over a mirror or reflection line. Rotation - ANSWER- CIRCULAR MOVEMENT AROUND AN AXIS Dialation - ANSWER- A transformation that enlarges or reduces a figure by a scale factor. parallel to the given line - ANSWER- Has the same slope
a specific case (The sun rises every morning; therefore, the sun will rise on Tuesday morning.) inductive reasoning - ANSWER- A type of logic in which generalizations are based on a large number of specific observations. prime number - ANSWER- A whole number greater than 0 that has exactly two different factors, 1 and itself. combination - ANSWER- a selection of a group of objects in which order is not important nCr = n!/r!*(n-r)! Order of operations - ANSWER- PEMDAS Divide & Multiply equal (Left to right) Add & Subtract equal (left to right) Integers - ANSWER- Whole numbers and their opposites (... - 3, - 2, - 1, 0, 1, 2, 3.. .) rational number - ANSWER- Number that can be made dividing 2 integers 1/ 214/
Natural Numbers - ANSWER- The set of numbers 1, 2, 3, 4, ... Also called counting numbers. whole numbers - ANSWER- a number without fractions; an integer. irrational numbers - ANSWER- numbers that cannot be expressed in the form a/b, where a and b are integers and b =0. Pie 3. sphere - ANSWER- A solid shape that is perfectly round like a ball. No faces, edges, or vertices. 1 face 1 edge 0 vertices Volume of a sphere - ANSWER- V=4/3πr³ cylinder - ANSWER- A solid composed of two congruent circles in parallel planes, their interiors, and all the line segments parallel to the axis with endpoints on the two circles. 3 Faces 2 Edges
Probability AND - ANSWER- Independent. Without replacement Multiply the probabilities Probability OR - ANSWER- With replacement. Add replacements face - ANSWER- A flat surface of a polyhedron vertices - ANSWER- The point of intersection of two sides of a polygon. edges - ANSWER- the line segments where the faces intersect Triangle Inequality Theorem - ANSWER- The sum of any two side lengths of a triangle is greater than the third side length gaming lecture - ANSWER- Used in open environment modern structure lectures - ANSWER- Used in controlled environment, high structure Questioning - ANSWER- used in controlled environment, moderate to high structure Group investigations - ANSWER- used in open environment, low structure
Finding interior angle of an angle polygon - ANSWER- S₁=(n-2) Binomial Theorem - ANSWER- a formula for finding any power of a binomial without multiplying at length. lbs to kg - ANSWER- 1 lb = 0.45 kg y is a function of x - ANSWER- The graph will pass vertical line test geometric mean - ANSWER- a/x=x/b disjoint - ANSWER- non over lapping sets. have no element in common Curriculum Principle - ANSWER- Must be coherent, focused on important mathematics, and well articulated across the grades. Teaching Principle - ANSWER- Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. Learning Principles - ANSWER- guidelines to the ways people learn most effectively
standard numerals - ANSWER- "4, 100, 35" pictoral models - ANSWER- "drawings, graphs" counting numbers - ANSWER- "1, 2, 3, 4, 5..." common fraction - ANSWER- a/b integers - ANSWER- "-5, - 4, - 2, 2, 4, 5..." exponential notation - ANSWER- 2^ scientific notation - ANSWER- 3.6 x 10^- 3 ratio notation - ANSWER- "two to five, 2:5, 2/5" factors - ANSWER- "of 12: 1, 2, 3, 4, 6, 12" multiples - ANSWER- "of 7: 7, 14, 21, 28...." identity property - ANSWER- y * 1 = y
reciprocal property - ANSWER- x/1x= additive property of 0 - ANSWER- x + 0 = x commutitive property - ANSWER- x + y = y + x associative property - ANSWER- (x + y) + z = x + (y + z) distributive property - ANSWER- a(b+c)=(ab)+(a*c) rational numbers - ANSWER- "1/4, 2/4, 3/4, 4/4" division by 0 - ANSWER- impossible division by 3 - ANSWER- sum of digits must be divisible by 3 division by 4 - ANSWER- last two digits must be divisible by 4 division by 6 - ANSWER- sum of digits must be divisible by both 2 and 3 division by 8 - ANSWER- last three digits must be divisible by 8
integers - ANSWER- "-3, - 2, - 1, 0, 1, 2, 3, 4" rational - ANSWER- "1/2, 0.5" irrational - ANSWER- "pi" congruent - ANSWER- identical shapes and sizes similar - ANSWER- "same shape, different size" commutative property - ANSWER- a+b=b+a associative property - ANSWER- (a+b)+c=a+(b+c) distributive property - ANSWER- a(b+c)= ab+ac mode - ANSWER- most frequent number median - ANSWER- middle score when arranged in order mean - ANSWER- average range - ANSWER- difference between high score and low score
cooperative or collaborative learning - ANSWER- classroom organized into groups of 2- 5 scaffolding - ANSWER- provides guidance without limiting student's investigation abilities manipulatives - ANSWER- math games and tools - abstract ideas at a concrete level algebra tiles - ANSWER- "factoring, equations, estimation, integers, inequalities, operations, polynomials, similar terms," Attribute blocks - ANSWER- "classifying, congruence, geometry, investigation of attributes (size, shape, color, thickness), logical reasoning, organization of data, patterns, problem solving, sequencing, similarity, sorting, symmetry, thinking skills," Balance scale - ANSWER- "equality, equations, estimation, inequality, measurement, operations, mass, weight, ..." Base-ten blocks - ANSWER- "area, classification, comparing, computation (whole numbers and decimals), decimal-fractional-percent equivalencies, perimeter, metric measurement, number concepts, ordering, place value, square and cubic numbers, polynomials, sorting, ..."
