CHSPE math(questions and answers)2022/2023

3ft= ? Yards 1 5,280 ft= ? Miles 1 00:04 01:36 1,760 yards = ? Mile 1 16 oz = ? Lb 1 1 ton= ? Lbs 2,000 1 pint = ? Fl oz 16 1 quart= ? Pints 2 1 pint = ? Cups 2 1 gallon = ? quarts 4 1 quart = ? Pints 2 1 peck = ? Quarts 8 1 bushel = ? Pecks 4 39.37 inches = ? Meter 1 1 km = ? Mile 5/8 1 litre = ? Quarts 1.1 1 kilogram = ? Lbs 2.2 Pythagorean formula how to find the length of the hypotenuse of a right triangle a squared + b squared = c squared Area of a circle pi r squared radius of a circle ..., the length of a line segment between the center and circumference of a circle or sphere diameter of a circle ..., the length of a straight line passing through the center of a circle and connecting two points on the circumference median ..., relating to or constituting the middle value of an ordered set of values (or the average of the middle two in an even-numbered set) mode .the value that occurs most often. If no number is repeated, then there is no mode for the list.. hypotenuse the longest side of a triangle area of a square, rectangle or parallelogram ...length of side x length of side; A= w x h order of operations ...The rules of which calculation comes first in an expression They are: . do everything inside parentheses first: () . then do exponents, like x2 . then do multiplies and divides from left to right . lastly do the adds and subtracts from left to right obtuse angle ...An obtuse angle is one which is more than 90° but less than 180° irrational number A real number that cannot be written as a simple fraction - the decimal goes on forever without repeating. Example: Pi is an irrational number. slope formula ...y = mx = b where m is the slope of the line, and b is the y-coordinate where the line intercepts the y-axis Y intercept Where a straight line crosses the Y axis of a graph. complex numbers ...A combination of a real and an imaginary number in the form a + bi, where a and b are real, and i is imaginary. isosceles triangle (of a triangle) having two sides of equal length equilateral triangle having all sides or faces equal perimeter The total length of the sides of a plane figure area the measure of a 2-dimensional surface enclosed within a boundary area of a triangle A= 1/2 w x h right triangle one of its angles is a right angle complementary angles angles whose sum is 90 degrees circumference distance around a circle; pi x diameter volume measurement of the content of a 3-dimensional figure perpendicular intersecting at or forming right angles volume of a rectangular solid V = w x h x d volume of a cylinder V = pi x r squared x d volume of a triangular prism V = area of the triangular base x depth of triangular prism; bh/2 x d volume of a sphere V = pi x r cubed slope the measure of how steep a line is If two lines intersect... opposite angles are equal If a line intersects two parallel lines... alternate interior angles are equal The sum of the interior angles of a triangle is 180 degrees Each angle of an equilateral triangle equals 60 degrees The angles opposite the equal sides of an isosceles triangle are equal In any triangle, the largest side is opposite the largest angle and the smallest side is opposite the smallest angle In a right triangle, c squared = a squared x b squared (Pythagorean theorem) The slope-intercept form of a linear equation y = mx = b where m is the slope of the line, and b is the y-coordinate where the line intercepts the y-axis obtuse triangle a triangle that contains an obtuse interior angle 1/4 .25 2/3 .67 2/5 .40 6/7 .86 3/4 .75 1/8 .125 2/25 .8 3/5 .60 x-3 Three less than a number 1/2a Half as large as area A 2x+5 Five more than twice a number 5x-1=14 One less than five times a number is 14 .25x 25% of a number vertical angles angles that are opposites of each other; have equal measurements (congruent) alternate interior angles angles that have equal measurements (congruent) supplementary angles angles that add to 180 degrees l+w+l+w perimeter of a parallelogram l x w area of a parallelogram sum of all side lengths perimeter of a triangle A = hb/2 area of a triangle diameter distance across the centre of a circle radius the distance from the centre of the circle to the perimeter C = pi(d) circumference; the distance around a circle A = pi(r^2) area of a circle A^2 + B^2 = C^2 Pythagorean Theorem geometric transformation image is reflected across the x or y axis scientific notation 1. Move decimal point to the left until it stops before the last digit 2. Count how many decimal places it has been moved 3. Multiply the new number by 10 raised to the power of the number of places the decimal point was moved 4! = 4 x 3 x 2 x 1 factorial order of operations P- parenthesis E- exponents M- multiplication D- division A- addition S- subtraction addition/ subtraction of fractions find the lowest common denominator multiplication of fractions multiply the top number by the top number, and the bottom number by the bottom number division of fractions multiply the first fraction by the reciprocal of the second fraction (copy, dot, flip) similar figures have the same shape (corresponding sides/ angles) but not the same size absolute value how far a given number is from zero on a number line ratio expresses a comparison of two quantities by division proportions a way of comparing two ratios in fraction form rise/run slope; the amount of change in y, for each one unit change in x y = mx + b x = slope, b = y-intercept; linear relationships greater than less than open dot the point is not part of the solution closed dot the point is part of the solution V = l x w x h formula for volume for a box or cube V = pi (r^2) h formula for volume for a cylinder distance = rate x time formula for distance F = 9/5C + 32 Celsius converted to Fahrenheit C = 5/9 (F-32) Fahrenheit converted to Celsius 16 ounces in a pound How many ounces in a pound? frequency distribution Two columns: the first column is comprised of scores, and the second column is comprised of frequencies* (Frequency= how often something occurs on a graph or chart) mean the average score median the score in the middle mode the most frequently occurring score range highest score minus lowest score; measure of variability correlation statistical technique that tell whether two measurements go together along a straight line; displayed on a scatter plot zero correlation two measurements are not related to each other along a straight line negative correlation as one measurement increases, the other measurement tends to decrease permutation the number of ways a set of elements can be arranged when order is important combinations the number of ways a set of element can be arranged when order is not important probability theory a number between 0 and 1 If outcome or event has... 1. Probability 0, it never happens 2. Probability 1, it always happens 3. Probability .5, it happens 1/2 of the time random chance the unknowable effects on the outcome of every experiment compound events when two events occur at the same time Congruent Exactly the same Corresponding If the lines are parallel then corresponding angles are congruent. Alternate Interior Angles (AIA) If lines are parallel then they are congruent. Alternate Exterior Angles (AEA) If lines are parallel then congruent Single Side Interior Angles (SSIA) Supplementary only if lines are parallel. Single Side Exterior Angles (SSEA) Supplementary only if lines are parallel. Parallel lines Same slope different y-intercept Complementary Angles Adds to exactly 90* Supplementary Angles Adds to exactly 180* 30-60-90 Angles Triangles always = 180* area of a circle πr2 Circumference 2πr