Free BPP Mathematics Questions and Answers — Questions and Answers

Question 1: Increase in Y above decrease in X

Formula for slope (Correct answer)
Completing the square
Point slope form
Formula for midpoint

Correct answer: Formula for slope

The formula for slope (m) is defined as the change in the y-coordinates divided by the change in the x-coordinates, often expressed as 'rise over run.' An 'increase in Y above decrease in X' directly describes this ratio of vertical change to horizontal change. This fundamental concept quantifies the steepness and direction of a line on a coordinate plane.

Question 2: To the right side of the equation, move all Constants. To both sides of the equation, add ((B/2)2). Calculate the square roots of the left side factor.

Taking Square Roots
Formula for Slope
Quadratic Formula
Completing the Square (Correct answer)

Correct answer: Completing the Square

The steps described—moving constants to one side, adding (B/2)^2 to both sides, and taking square roots—are the precise sequence used in the algebraic method of completing the square. This technique transforms a quadratic equation into a perfect square trinomial. This makes it easier to solve for the variable by isolating it and taking the square root.

Question 3: Y=mx*b

Slope Intercept Form (Correct answer)
Animal Form
Standard Form
Math Form

Correct answer: Slope Intercept Form

The equation Y=mx+b (assuming the asterisk is a typo and should be a plus sign) is the standard slope-intercept form of a linear equation. In this form, 'm' represents the slope of the line, indicating its steepness and direction. 'b' represents the y-intercept, which is the point where the line crosses the y-axis, making it particularly useful for graphing.

Question 4: Square root Both sides

Formula For slope
Completing The square
Zeros of quadratic equation
Taking Square roots (Correct answer)

Correct answer: Taking Square roots

The action of 'taking square roots' on both sides is a fundamental algebraic operation used to solve equations where a variable is squared. By applying the square root to both sides of an equation, one can isolate the variable and find its possible values. This method is crucial for solving quadratic equations or equations involving perfect squares.

Question 5: (y-y1)=m(x-x1)

Graph Form
Point Slope Form (Correct answer)
Formula For Slope
Standard Form

Correct answer: Point Slope Form

The equation (y-y1)=m(x-x1) is known as the point-slope form of a linear equation. This form is particularly useful when you know the slope (m) of a line and a single point (x1, y1) that the line passes through. It allows for direct construction of the line's equation without first needing to find the y-intercept.

Question 6: He produced important advances in partition theory, combinatorics, number theory, invariant theory, matrix theory, and invariant theory.

James Joseph Sylvester (Correct answer)
Arthur Cayley
William Thomas Tutte
Leonhard Euler

Correct answer: James Joseph Sylvester

James Joseph Sylvester was a prominent English mathematician who made significant contributions across various fields of pure mathematics in the 19th century. His extensive work indeed encompassed partition theory, combinatorics, number theory, and notably, invariant theory and matrix theory. These contributions solidified his legacy as a foundational figure in these areas.

Question 7: Graph the opposites, factor them, and use a test point to see if they hold.

Graphing Absolute Value Inequalities
Discriminant
Graphing absolute value inequalities
Graphing Quadratic Inequalities on a number line (Correct answer)

Correct answer: Graphing Quadratic Inequalities on a number line

The described steps—finding the 'opposites' (roots or zeros of the quadratic), factoring the quadratic expression, and using test points—are standard procedures for solving and graphing quadratic inequalities. These steps help determine the intervals on a number line where the inequality is true. This process effectively identifies the solution set for the quadratic inequality.

Question 8: Factors of AC that add up to get B

Formula for slope
Point Slope Form
How to factor (Correct answer)
Taking Square roots

Correct answer: How to factor

The phrase 'factors of AC that add up to get B' refers to a common method used to factor quadratic trinomials of the form ax^2 + bx + c. This technique, often called the 'AC method,' involves finding two numbers that multiply to the product of 'a' and 'c' (AC) and simultaneously add up to 'b.' This allows the trinomial to be rewritten and factored by grouping.

Question 9: Negative Reciprocal of the slope

Graphing Absolute Value Inequalities
Graphing Quadratic Inequalities on a number line
How to solve Absolute value equations?
Slope of a line perpendicular to another line? (Correct answer)

Correct answer: Slope of a line perpendicular to another line?

The slope of a line perpendicular to another line is always the negative reciprocal of the original line's slope. This mathematical relationship is fundamental in geometry and algebra for determining perpendicularity between lines. If one line has a slope 'm', a line perpendicular to it will have a slope of -1/m.

Question 10: Take the Absolute Value by itself, Make two issues and consequently two solutions by changing everything to the right to plus or minus.

How to solve Absolute value equations? (Correct answer)
Graphing Absolute Value Inequalities
Slope of a line perpendicular to another line?
How to Convert standard form to Vertex Form

Correct answer: How to solve Absolute value equations?

The described process outlines the standard method for solving absolute value equations. First, isolate the absolute value expression on one side of the equation. Then, because the quantity inside the absolute value can be either positive or negative, set up two separate equations: one where the expression equals the positive value, and one where it equals the negative value. Solving both equations yields the two potential solutions.

Question 11: Bring the constant back over after finishing the square, and don't forget to add the slope before the parenthesis.

Graphing Absolute Value Inequalities
Slope of a line perpendicular to another line?
How to solve Absolute value equations?
How to Convert standard form to Vertex Form (Correct answer)

Correct answer: How to Convert standard form to Vertex Form

The steps described are part of the process for converting a quadratic equation from standard form (ax^2 + bx + c) to vertex form (a(x-h)^2 + k). 'Finishing the square' is used to create the (x-h)^2 term, and the 'slope before the parenthesis' refers to the 'a' coefficient, which must be factored out before completing the square if a ≠ 1. Adjusting the constant then yields the 'k' value.

Free BPP Mathematics Questions and Answers

Increase in Y above decrease in X