Trigonometric Functions & Geometric Series

False (B)

Determinant

<p>element</p> Signup and view all the answers

<p>A = [[2, 3], [4, 5]] = −2 B = [[−2, −√5], [−√5, 3]] = −11 C = [[x, 4], [x, x^2]] = x^2</p> Signup and view all the answers

<p>[[-2, -√5], [-√5, 3]] (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>The diagonal elements from the top left to the bottom right.</p> Signup and view all the answers

<p>10 (A)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>-1 &lt; y &lt; 1 (D)</p> Signup and view all the answers

<p>(-3, 0)</p> Signup and view all the answers

<p>x = -1, x = -2</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>p = 14x + 16y = 3x + 2y ≤ 12; 7x + 5y ≤ 28 z = 6x + 10y + 20 = 3x + 5y ≤ 15; 5x + 2y ≤ 10 F = 6x + 5y = x + y ≤ 6; x - y ≥ -2 Q = 3x + 2y = x + y ≥ 0; x - y ≤ 0</p> Signup and view all the answers

<p>36</p> Signup and view all the answers

<p>3</p> Signup and view all the answers

<p>Both A and B (C)</p> Signup and view all the answers

<p>cosx = Range: -1 &lt; y &lt; 1 tanx = Asymptotes at odd multiples of 90° sinx = Period: 2π y = ax + by + c = Linear inequality in two variables</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>0</p> Signup and view all the answers

<p>-90° (A), 90° (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>Unlimited terms until a certain limit is defined</p> Signup and view all the answers

<p>x = 1 (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>3</p> Signup and view all the answers

<p>2</p> Signup and view all the answers

<p>y = x + 2 (A), y = sqrt(x) (C)</p> Signup and view all the answers

<p>right</p> Signup and view all the answers

<p>3</p> Signup and view all the answers

<p>y = x + 2 = Continuous y = x² = Continuous y = 1/(x - 1) = Discontinuous y = cos(x) = Continuous</p> Signup and view all the answers

<p>60° (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>1/3</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>√3𝑥 – 𝑦 + 8 = 0 = √3 y + 10 = 0 = 0 2x – y + 3 = 0 = -2 x – 3y + 2 = 0 = 1/3</p> Signup and view all the answers

<p>-2 (B)</p> Signup and view all the answers

<p>True (A)</p> Signup and view all the answers

<p>60°</p> Signup and view all the answers

<p>It opens upwards and is a parabola. (C)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>x = -1</p> Signup and view all the answers

<p>-2, 3</p> Signup and view all the answers

<p>$y = -x^3$ = Cubic function $y = 3x^2$ = Parabola opening upwards $y = -2x^2$ = Parabola opening downwards $y = x^2$ = Standard parabola</p> Signup and view all the answers

<p>y = -3x^2 + 5 (A)</p> Signup and view all the answers

<p>False (B)</p> Signup and view all the answers

<p>-1, -6</p> Signup and view all the answers

The highest power of the variable in an equation.

A value of the variable that makes the equation true.

An equation that involves a variable raised to the power of 2.

The shape of the graph of a quadratic equation. It is a symmetrical U-shaped curve.

The process of finding the roots or solutions of a quadratic equation.

A way to represent a quadratic equation visually. It shows the relationship between the variable and the value of the equation.

The points where the graph of a quadratic equation intersects the x-axis.

The highest or lowest point on the graph of a quadratic equation. The point where the curve changes direction.

The highest or lowest point on the graph of a quadratic function. It is also the point where the graph changes direction.

A vertical line that divides the parabola into two symmetrical halves. Its equation is x = the x-coordinate of the vertex.

The graph of a quadratic function opens upwards if the coefficient of x² is positive and downwards if it is negative.

A method used to find the intersection points of two graphs by solving the equations algebraically.

Finding the solutions of an equation by interpreting the points where the graph intersects the x-axis.

A way to solve quadratic equations by factoring the quadratic expression and setting each factor equal to zero.

The domain of the function y=cosx is the set of all possible input values for x, which ranges from -360° to 360° or equivalently in radians, from -2π to 2π.

The range of the function y=cosx is the set of all possible output values for y, which ranges from -1 to 1. This means the cosine of any angle will always fall between -1 and 1.

The period of a trigonometric function is the horizontal distance over which the function's graph repeats itself. For y=cosx, the period is 2π, meaning the graph repeats itself every 2π units.

An asymptote is a line that a curve approaches but never touches as it extends infinitely. In the graph of y=tanx, there are vertical asymptotes at odd multiples of 90° (π/2) because the tangent function becomes infinitely large or small at these points.

A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant factor called the common ratio.

The sum of a finite geometric series is found by using the formula Sn= a(1-r^n)/1-r, where a is the first term, r is the common ratio, and n is the number of terms.

A linear inequality in two variables involves variables x and y, and it typically includes the inequality symbols <, >, ≤, or ≥. It defines a region on the coordinate plane.

The general form of a linear inequality in two variables is ax + by + c < 0, ax + by + c > 0, ax + by + c ≤ 0, or ax + by + c ≥ 0. It's a way to represent the relationship between x and y.

A matrix whose determinant is equal to zero.

A matrix whose determinant is not equal to zero.

A function that associates a number to a square matrix.

The product of the elements on the leading diagonal minus the product of the elements on the secondary diagonal.

The diagonal from the top left to the bottom right of a matrix.

The diagonal from the top right to the bottom left of a matrix.

The number associated with a square matrix.

The order of a matrix is a pair of numbers representing the number of rows and columns respectively.

A function is continuous at a point if there's no gap, jump, or hole in the graph. This means the function's value at that point is the same as its value from the left and right sides.

A function is discontinuous at a point if there is a break or jump in its graph. At this point, the function's value might not exist or differ from either side.

The value of f(x) as x approaches a from the left side. It indicates the function's behavior just before reaching 'a'.

The value of f(x) as x approaches 'a' from the right side. This represents the function's behavior just after passing 'a'.

A function is continuous at 'a' if its left-hand limit, right-hand limit, and the function value at 'a' are all equal.

The value of the function when x is equal to 'a'. This tells you where the point is plotted on the graph.

The process of examining the behavior of a function as x gets closer and closer to a certain point 'a'. This doesn't necessarily involve the function being defined at 'a'.

A function that's continuous over an entire domain or a specific interval. The graph is smooth and unbroken.

The angle between two lines is the angle formed by the intersection of the two lines.

The slope of a line is a measure of its steepness. It represents the change in the y-coordinate divided by the change in the x-coordinate.

The angle between two lines can be calculated using the formula: tan(θ) = ±(m1 - m2) / (1 + m1*m2), where θ is the angle, and m1 and m2 are the slopes of the two lines.

The acute angle between two lines is the smaller of the two possible angles formed by their intersection.

The obtuse angle between two lines is the larger of the two possible angles formed by their intersection. It is greater than 90 degrees.

Two lines are perpendicular if the product of their slopes is -1. This means the angle between them is 90 degrees.

The slope of a line can be found by rearranging the equation of the line into slope-intercept form (y = mx + c), where 'm' represents the slope.