Gr 9 MATH: November Hard

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Which of the following operations is not closed under the system of natural numbers?

Multiplication
Division (correct)
Subtraction (correct)
Addition

What is the purpose of the number 0 in the system of whole numbers?

To represent the presence of quantity
To write fractions
To represent the absence of quantity (correct)
To make subtraction possible

Which of the following statements is true about the system of integers?

The system of integers is closed under subtraction
The sum of two integers can be zero (correct)
The sum of two integers is always an integer
Each integer does not have an additive inverse

What is the definition of a rational number?

A number that can be expressed as the quotient of two integers (A) Signup and view all the answers

Which of the following is an example of an irrational number?

√2 (A) Signup and view all the answers

What is the set of real numbers composed of?

Rational and irrational numbers (A) Signup and view all the answers

What is the identity element for addition in the system of whole numbers?

0 (C) Signup and view all the answers

Which of the following is a property of natural numbers?

When you add two or more natural numbers, you get a natural number again (D) Signup and view all the answers

What is the result of subtracting a larger number from a smaller number?

A negative number (B) Signup and view all the answers

What is the additive inverse of a positive number?

Its corresponding negative number (C) Signup and view all the answers

What is the result of adding a positive and a negative number?

Depends on the magnitudes of the numbers involved (B) Signup and view all the answers

What is the product of two negative numbers?

Positive (D) Signup and view all the answers

What is the distributive property of multiplication over addition?

a(b + c) = ab + ac (A) Signup and view all the answers

What is the result of dividing a positive number by a negative number?

Negative (C) Signup and view all the answers

What is the square root of a number?

The positive or negative number that, when multiplied by itself, gives the original number (B) Signup and view all the answers

What is the result of adding a negative number to its additive inverse?

Zero (C) Signup and view all the answers

What is the result of subtracting an additive inverse from a number?

The additive inverse of the number (D) Signup and view all the answers

What is the purpose of negative numbers in real-world applications?

Both a and b (B) Signup and view all the answers

What is the primary purpose of estimating in calculations?

To get close to an answer without performing precise calculations (C) Signup and view all the answers

When performing addition in columns, what is the correct order of operation?

Add each digit starting from the rightmost digit (D) Signup and view all the answers

What is the process of expressing a number as a product of its prime factors called?

Prime factorization (A) Signup and view all the answers

What is the formula to calculate the average speed of an object?

Average speed = Distance / Time (D) Signup and view all the answers

What is the term for the largest number that divides each of two or more numbers without leaving a remainder?

Highest common factor (C) Signup and view all the answers

What is the purpose of compensating for errors in calculations?

To correct errors introduced by rounding (B) Signup and view all the answers

What is the formula to calculate the distance traveled by an object?

Distance = Average speed × Time (B) Signup and view all the answers

What is the term for the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

Long division (C) Signup and view all the answers

What is the formula to calculate the time taken to travel a certain distance?

Time = Distance / Average speed (D) Signup and view all the answers

What is the term for the process of paying a deposit and then making monthly instalments?

Hire purchase (B) Signup and view all the answers

What is the result of subtracting a larger number from a smaller number?

A negative number (D) Signup and view all the answers

What is the equivalent of adding a negative number?

Subtracting a positive number (C) Signup and view all the answers

What is the result of the product of a positive and a negative number?

A negative number (C) Signup and view all the answers

What is the order of operations when calculating expressions involving exponents?

Parentheses, exponents, multiplication, division, addition, subtraction (C) Signup and view all the answers

What is the value of a^-n in exponential notation?

1/a^n (A) Signup and view all the answers

What is the purpose of scientific notation?

To express very large or very small numbers (C) Signup and view all the answers

What is the result of adding an integer to its additive inverse?

Zero (D) Signup and view all the answers

What is the product of a negative and a negative integer?

A positive number (C) Signup and view all the answers

What is the purpose of the laws of exponents?

To simplify exponential expressions (C) Signup and view all the answers

What is the purpose of investigating and extending geometric patterns?

To analyze arrangements consisting of different shapes and colors (D) Signup and view all the answers

What is the primary purpose of an algebraic expression?

To indicate a sequence of operations that can be described in words or diagrams. (C) Signup and view all the answers

Which of the following is a convention for writing algebraic expressions?

Write a known number first in a product. (B) Signup and view all the answers

What is the correct order of operations in an algebraic expression without brackets?

Multiplication and division, then addition and subtraction. (C) Signup and view all the answers

What is an expression with one term only?

Monomial (A) Signup and view all the answers

What is the symbol often used to represent the variable in an algebraic expression?

x (C) Signup and view all the answers

What is the purpose of brackets in an algebraic expression?

To indicate that the expression should be evaluated first. (A) Signup and view all the answers

What is an equivalent expression?

An expression with the same numerical value for any given value of the variable. (A) Signup and view all the answers

What is the term for the number multiplying the variable in an algebraic expression?

Coefficient (D) Signup and view all the answers

What is the purpose of forming sequences and identifying patterns?

To extend sequences and describe how they are formed. (B) Signup and view all the answers

What is the term for a fixed value in an algebraic expression?

Constant (A) Signup and view all the answers

What is the term for the sum of interior angles of a polygon?

Dependent on the number of sides (C) Signup and view all the answers

What is the primary purpose of a flow diagram in representing a function?

To determine the output value for a given input (C) Signup and view all the answers

What is the condition for two lines to be perpendicular?

They intersect at a right angle (C) Signup and view all the answers

What is the key feature of a graph that indicates the rate of change between variables?

Slope/Gradient (C) Signup and view all the answers

What is the result of multiplying the polynomial 2x^2 + 3x - 1 by the monomial 5x?

10x^3 + 15x^2 - 5x^2 (C) Signup and view all the answers

What is the term for a polygon with all sides and angles equal?

Regular polygon (D) Signup and view all the answers

Which of the following representations of a function shows the values of input and corresponding output?

Table (B) Signup and view all the answers

What is the formula to calculate the area of a rectangle?

A = l × w (D) Signup and view all the answers

What is the result of simplifying the expression (3x + 2)^2?

9x^2 + 12x + 4 (B) Signup and view all the answers

What is the term for the line that intersects two or more other lines?

Transversal (D) Signup and view all the answers

What is the result of evaluating the expression 2x^2 + 5x - 1 when x = 3?

25 (C) Signup and view all the answers

What is the formula to calculate the gradient of a line passing through two points?

Gradient = (y2 - y1) / (x2 - x1) (D) Signup and view all the answers

What is the sum of the interior angles of a triangle?

180° (D) Signup and view all the answers

What is the result of dividing the polynomial 4x^2 + 2x - 3 by the monomial 2x?

2x + 1 - 3/2x (C) Signup and view all the answers

What is the definition of a function in terms of variables?

A relationship between two variables where each input has exactly one output (A) Signup and view all the answers

What is the primary purpose of a graph in representing a function?

To provide a visual representation of the relationship (A) Signup and view all the answers

What is the term for the angles formed when two lines intersect?

Vertically opposite angles (C) Signup and view all the answers

What is the result of applying the rule 2n + 1 to the even number 4?

9 (B) Signup and view all the answers

What are the key features to consider when interpreting graphs?

Slope/Gradient, Intercepts, and Continuity (C) Signup and view all the answers

What is the result of simplifying the expression (x + 2)(x - 3)?

x^2 - x - 6 (D) Signup and view all the answers

What is the formula to calculate the perimeter of a square?

P = 4s (A) Signup and view all the answers

What is the term for the angles formed when a transversal intersects parallel lines?

Corresponding angles (D) Signup and view all the answers

What is the purpose of a formula in representing a function?

To describe the algebraic expression that defines the function (A) Signup and view all the answers

What is the result of evaluating the expression x^2 + 2x - 5 when x = -2?

-1 (D) Signup and view all the answers

What is the result of multiplying the polynomial x^2 - 2x + 1 by the monomial 3x?

3x^3 - 6x^2 + 3x (C) Signup and view all the answers

What is the term for the process of drawing and interpreting graphs of angles and lines?

Drawing and interpreting graphs of angles and lines (D) Signup and view all the answers

What is the relationship between the input and output values in a function?

Each input has exactly one output (D) Signup and view all the answers

What is the purpose of a table in representing a function?

To display values of input and corresponding output (B) Signup and view all the answers

What is the result of simplifying the expression (x + 1)(x - 2) + 3x?

x^2 - x + 1 (C) Signup and view all the answers

What is the result of applying the rule x - 1000 to the natural number 800?

-200 (B) Signup and view all the answers

What is the primary purpose of using tables to represent functions?

To identify the input and output values (C) Signup and view all the answers

What is the sum of the angles on a straight line?

180° (A) Signup and view all the answers

What is the term for angles whose sum is 180°?

Supplementary angles (A) Signup and view all the answers

What is the purpose of drawing graphs of functions?

To visualize the relationship between variables (C) Signup and view all the answers

What is the result of subtracting a larger number from a smaller number in the context of functions?

A negative number (B) Signup and view all the answers

What is the term for lines that intersect to form equal angles of 90°?

Perpendicular lines (D) Signup and view all the answers

What is the purpose of identifying the gradient of a line?

To identify the slope of a line (D) Signup and view all the answers

What is the term for a line that intersects two or more other lines?

Transversal (A) Signup and view all the answers

What is the term for angles formed when two straight lines intersect?

Vertically opposite angles (D) Signup and view all the answers

What is the purpose of measuring angles in degrees?

To describe the size of angles (A) Signup and view all the answers

What is the formula for the surface area of a cylinder?

SA = 2πr(h + r) (B) Signup and view all the answers

What is the formula for the volume of a rectangular prism?

V = lwh (C) Signup and view all the answers

What is the formula for the area of a trapezium?

A = 1/2 × (side1 + side2) × height (D) Signup and view all the answers

What is the formula for the perimeter of a rectangle?

P = 2l + 2w (D) Signup and view all the answers

What is the formula for the surface area of a sphere?

SA = 4πr^2 (A) Signup and view all the answers

What is the formula for the volume of a cone?

V = 1/3πr^2h (D) Signup and view all the answers

What is the formula for the area of a rhombus?

A = 1/2 × d1 × d2 (A) Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2πr (D) Signup and view all the answers

What is the formula to calculate the area of a sector?

A = (θ/360) × πr^2 (D) Signup and view all the answers

What is the formula to calculate the sum of interior angles in a polygon?

(n - 2) × 180° (C) Signup and view all the answers

What is the formula to calculate the perimeter of a polygon?

P = ns (C) Signup and view all the answers

What is the method to construct a perpendicular line through a point on a line segment?

Draw a circle with the point as the center and the radius smaller than the distance to one end of the segment. (D) Signup and view all the answers

What is the formula to calculate the arc length of a sector?

L = (θ/360) × 2πr (D) Signup and view all the answers

What is the method to bisect an angle?

Draw a circle with the vertex of the angle as the center and marking off equal lengths on both arms of the angle. (D) Signup and view all the answers

What is the property of the angle bisectors of a triangle?

The three angle bisectors of a triangle intersect at one point, equidistant from each side of the triangle. (A) Signup and view all the answers

What is the formula to calculate the area of a regular polygon?

A = 1/4ns^2cot(π/n) (D) Signup and view all the answers

What is the method to construct a 45° angle?

Draw a 90° angle using the method for constructing perpendicular lines and then bisect it. (C) Signup and view all the answers

What is the property of the exterior angle of a triangle?

The exterior angle of a triangle is equal to the sum of the interior opposite angles. (C) Signup and view all the answers

What is the formula to translate a point by a vector (a, b)?

(x, y) -> (x + a, y + b) (B) Signup and view all the answers

What is the formula to rotate a point 90 degrees counterclockwise about the origin?

(x, y) -> (-y, x) (A) Signup and view all the answers

What is the formula to reflect a point over the line y = x?

(x, y) -> (y, x) (B) Signup and view all the answers

What is the formula to dilate a point from the origin by a scale factor k?

(x, y) -> (kx, ky) (D) Signup and view all the answers

What is the formula for the area of a parallelogram?

A = base * height (A) Signup and view all the answers

What is the formula for the perimeter of a kite?

P = 2a + 2b (A) Signup and view all the answers

What is the effect of doubling the dimensions of a shape on its perimeter?

The perimeter doubles (C) Signup and view all the answers

What is the effect of doubling the dimensions of a shape on its area?

The area quadruples (B) Signup and view all the answers

What is the conversion factor from meters to kilometers?

1 km = 1000 m (A) Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2pi r (B) Signup and view all the answers

What is the minimum condition required to prove congruency of two triangles using the SAS method?

Two sides and the included angle (A) Signup and view all the answers

What is the formula to calculate the area of a triangle using Heron's Formula?

A = √(s(s - a)(s - b)(s - c)) (D) Signup and view all the answers

What is the formula to calculate the perimeter of a rectangle?

P = 2(l + w) (B) Signup and view all the answers

What is the formula to calculate the area of a circle?

A = πr^2 (C) Signup and view all the answers

What is the formula to calculate the sum of interior angles of a regular polygon?

Sum = (n - 2) × 180° (D) Signup and view all the answers

What is the method of constructing a triangle using the SSS method?

Use a compass to draw arcs from each endpoint of the base to intersect and form the other vertices (B) Signup and view all the answers

What is the type of transformation that moves every point of a shape the same distance in the same direction?

Translation (C) Signup and view all the answers

What is the formula to calculate the arc length of a circle?

L = θ/360 × 2πr (B) Signup and view all the answers

What is the method of constructing a parallelogram?

Draw the base, use a set square to draw the height, and then draw the parallel opposite sides (A) Signup and view all the answers

What is the formula to calculate the area of a sector of a circle?

A = θ/360 × πr^2 (A) Signup and view all the answers

Which property of natural numbers is also true for integers?

When you multiply two or more, you get an integer again. (A), When you add two or more, you get an integer again. (C) Signup and view all the answers

What is a characteristic of rational numbers that distinguishes them from integers?

They can be expressed as the quotient of two integers. (A) Signup and view all the answers

What is the primary reason for extending whole numbers to integers?

To include negative numbers. (D) Signup and view all the answers

Which set of numbers includes both rational and irrational numbers?

Real numbers. (A) Signup and view all the answers

What is the result of adding the additive inverse of a number to itself?

Zero. (A) Signup and view all the answers

What is a characteristic of natural numbers under subtraction?

The answer is not always a natural number. (B) Signup and view all the answers

Which property of natural numbers is not true for whole numbers?

Closed under division. (A) Signup and view all the answers

What is a characteristic of irrational numbers?

They cannot be expressed as a fraction of two integers. (A) Signup and view all the answers

What is the result of subtracting a negative number from a positive number?

Always positive (C) Signup and view all the answers

What is the purpose of the laws of exponents?

To simplify exponential expressions (D) Signup and view all the answers

What is the value of a^0 in exponential notation?

1 (A) Signup and view all the answers

What is the correct order of operations when calculating expressions involving exponents?

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction (D) Signup and view all the answers

What is the purpose of scientific notation?

To express very large or very small numbers in a compact form (A) Signup and view all the answers

What is the result of adding a positive and a negative number?

Sometimes positive, sometimes negative (D) Signup and view all the answers

What is the product of a positive and a negative integer?

Always negative (D) Signup and view all the answers

What is the purpose of investigating and extending geometric patterns?

To identify and extend patterns in shapes and arrangements (C) Signup and view all the answers

What is the value of a^-n in exponential notation?

1/a^n (B) Signup and view all the answers

What is the major difference between estimating and rounding off numbers?

Rounding off is used for precise calculations, while estimating is used for approximate calculations. (C) Signup and view all the answers

What is the purpose of negative numbers in real-world applications?

To represent debts or losses (C) Signup and view all the answers

What is the purpose of finding the lowest common multiple of two numbers?

To find the common denominator of two fractions. (C) Signup and view all the answers

What is the formula to calculate the average speed of an object?

Average speed = Distance / Time (D) Signup and view all the answers

What is the term for the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

Long division (C) Signup and view all the answers

What is the purpose of calculating the highest common factor of two numbers?

To simplify fractions. (B) Signup and view all the answers

What is the formula to calculate the distance traveled by an object?

Distance = Average speed × Time (B) Signup and view all the answers

What is the term for the process of paying a deposit and then making monthly instalments?

Hire purchase (B) Signup and view all the answers

What is the purpose of calculating the ratio of two numbers?

To compare the rates of two people collecting apples. (C) Signup and view all the answers

What is the formula to calculate the time taken to travel a certain distance?

Time = Distance / Average speed (A) Signup and view all the answers

What is the purpose of finding the prime factorization of a number?

To find the highest common factor of two numbers. (D) Signup and view all the answers

What is the result of adding a positive and a negative number with the same magnitude?

Zero (D) Signup and view all the answers

What is the additive inverse of a negative number?

A positive number with the same magnitude (A) Signup and view all the answers

What is the result of subtracting a negative number from a positive number?

A positive number (B) Signup and view all the answers

What is the product of a positive and a negative integer?

A negative integer (A) Signup and view all the answers

What is the distributive property of multiplication over addition?

a(b + c) = ab + ac (B) Signup and view all the answers

What is the result of dividing a positive number by a negative number?

A negative number (B) Signup and view all the answers

What is the purpose of negative numbers in real-world applications?

All of the above (D) Signup and view all the answers

What is the result of adding a negative number to its additive inverse?

Zero (D) Signup and view all the answers

What is the product of two negative numbers?

A positive number (B) Signup and view all the answers

What is the result of subtracting an additive inverse from a number?

The original number (B) Signup and view all the answers

What is the primary purpose of algebraic expressions?

To describe a sequence of operations (C) Signup and view all the answers

What is the correct order of operations in an algebraic expression without brackets?

Multiplication and division first, then addition and subtraction (A) Signup and view all the answers

What is the term for an expression with one term only?

Monomial (A) Signup and view all the answers

What is the purpose of brackets in an algebraic expression?

To indicate the order of operations (A) Signup and view all the answers

What is the term for a fixed value in an algebraic expression?

Constant (B) Signup and view all the answers

What is the symbol often used to represent the variable in an algebraic expression?

x (A) Signup and view all the answers

What is an equivalent expression?

An expression with different sequences of operations but the same numerical value (B) Signup and view all the answers

What is the term for the number multiplying the variable in an algebraic expression?

Coefficient (A) Signup and view all the answers

What is the purpose of forming sequences and identifying patterns?

To describe the relationship between terms and their positions in sequences (B) Signup and view all the answers

What is the convention for writing algebraic expressions?

Write the known number first in a product (B) Signup and view all the answers

What is the result of squaring the binomial (a + b)?

a^2 + 2ab + b (D) Signup and view all the answers

Which of the following expressions is equivalent to 2x^2 + 5x + 3?

2(x^2 + 2.5x + 1.5) (C) Signup and view all the answers

What is the result of dividing the polynomial x^2 + 4x + 4 by the monomial x + 2?

x + 2 (A) Signup and view all the answers

What is the result of applying the rule 2n + 1 to the even number 4?

9 (B) Signup and view all the answers

What is the result of evaluating the expression (x + 1)^2 when x = 2?

13 (D) Signup and view all the answers

What is the result of multiplying the polynomial 2x^2 + 3x - 1 by the monomial 3x?

6x^3 + 9x^2 - 3x (A) Signup and view all the answers

What is the result of simplifying the expression (3x + 2)(x - 1)?

3x^2 - x - 2 (D) Signup and view all the answers

What is the result of dividing the polynomial 2x^2 + 5x + 3 by the integer 2?

x^2 + 2.5x + 1.5 (C) Signup and view all the answers

What is the result of applying the rule x - 1000 to the natural number 800?

-200 (A) Signup and view all the answers

What is the result of evaluating the expression (2x + 1)^2 when x = 3?

50 (B) Signup and view all the answers

What is the minimum condition for congruency in a triangle with three sides given?

SSS (D) Signup and view all the answers

What is the formula to calculate the area of a triangle given the base and height?

A = 1/2 * base * height (D) Signup and view all the answers

What is the condition for two triangles to be congruent by SAS?

Two sides and an included angle (B) Signup and view all the answers

What is the formula to calculate the perimeter of a rectangle?

P = 2(l + w) (A) Signup and view all the answers

What is the condition for constructing a triangle with two sides and an included angle?

SAS (D) Signup and view all the answers

What is the formula to calculate the area of a circle?

A = π * r^2 (C) Signup and view all the answers

What is the type of transformation that moves every point of a shape the same distance in the same direction?

Translation (C) Signup and view all the answers

What is the primary characteristic of a function that distinguishes it from other relationships between variables?

Each input has exactly one output (D) Signup and view all the answers

What is the advantage of using a flow diagram to represent a function?

It clearly shows the calculations needed to determine the output value (D) Signup and view all the answers

What is the formula to calculate the sum of interior angles of a polygon?

Sum = (n - 2) * 180° (D) Signup and view all the answers

What is the condition for constructing a parallelogram?

All of the above (D) Signup and view all the answers

What is the formula used to calculate the gradient of a line passing through two points (x1, y1) and (x2, y2)?

Gradient = (y2 - y1) / (x2 - x1) (D) Signup and view all the answers

What is the formula to calculate the area of a regular polygon?

A = 1/2 * n * s^2 * cot(π/n) (D) Signup and view all the answers

What is the purpose of interpreting graphs in the context of functions?

To visualize the relationship between variables and identify key features (A) Signup and view all the answers

What is the term for a quantity that can change in a function?

Variable (A) Signup and view all the answers

What is the purpose of tables in the context of functions?

To display the input values and their corresponding output values (D) Signup and view all the answers

What is the term for the result of applying a function to an input value?

Function value (A) Signup and view all the answers

What is the purpose of formulas in the context of functions?

To describe the calculations needed to determine the output value (B) Signup and view all the answers

What is the term for the rate of change between variables in a graph?

Gradient (C) Signup and view all the answers

What is the purpose of drawing graphs in the context of functions?

To visualize the relationship between variables and identify key features (B) Signup and view all the answers

What is the sum of interior angles of a quadrilateral?

360° (D) Signup and view all the answers

Which of the following angles are equal when two lines intersect?

Vertically opposite angles (A) Signup and view all the answers

What is the term for a polygon with all sides and angles equal?

Regular polygon (C) Signup and view all the answers

What is the formula to calculate the area of a rhombus?

A = ½ × d1 × d2 (C) Signup and view all the answers

Which of the following is a property of parallel lines and transversals?

All of the above (D) Signup and view all the answers

What is the term for a triangle with two sides and two angles equal?

Isosceles triangle (A) Signup and view all the answers

What is the sum of interior angles of a triangle?

180° (C) Signup and view all the answers

Which of the following is a property of a circle?

All points are equidistant from the center (D) Signup and view all the answers

What is the formula to calculate the perimeter of a rectangle?

P = 2(l + w) (C) Signup and view all the answers

Which of the following angles are equal when a transversal intersects parallel lines?

All of the above (D) Signup and view all the answers

What is the formula to calculate the gradient of a line passing through two points (x_1, y_1) and (x_2, y_2)?

Gradient = (y_2 - y_1) / (x_2 - x_1) (C) Signup and view all the answers

What is the term for the relationship between two variables where each input corresponds to exactly one output?

Function (D) Signup and view all the answers

When interpreting graphs, what does the slope/gradient indicate?

How rapidly the output changes with respect to the input (C) Signup and view all the answers

What is the formula to calculate the surface area of a rectangular prism?

SA = 2lw + 2lh + 2wh (B) Signup and view all the answers

What is the sum of angles on a straight line?

180° (A) Signup and view all the answers

What is the formula to calculate the volume of a cylinder?

V = πr^2h (B) Signup and view all the answers

What is the term for two angles whose sum is 180°?

Supplementary angles (D) Signup and view all the answers

What is the formula to calculate the surface area of a sphere?

SA = 4πr^2 (B) Signup and view all the answers

When two lines intersect, what is the relationship between the vertically opposite angles?

They are equal (B) Signup and view all the answers

What is the term for a line that intersects two or more other lines?

Transversal (D) Signup and view all the answers

What is the formula to calculate the volume of a cone?

V = (1/3)πr^2h (D) Signup and view all the answers

What is the term for the angles on opposite sides of the transversal but inside the two intersected lines?

Alternate angles (A) Signup and view all the answers

What is the formula to calculate the perimeter of a rectangle?

P = 2(l + w) (B) Signup and view all the answers

When drawing graphs of functions, what is the first step?

Identify the function (C) Signup and view all the answers

What is the formula to calculate the area of a triangle?

A = (1/2)base × height (A) Signup and view all the answers

What is the formula to calculate the surface area of a cube?

SA = 6s^2 (A) Signup and view all the answers

What is the term for the output value corresponding to a given input?

Function value (A) Signup and view all the answers

What is the formula to calculate the volume of a rectangular pyramid?

V = (1/3)lwh (A) Signup and view all the answers

What is the formula to calculate the area of a sector?

A = θ/360 × πr^2 (B) Signup and view all the answers

What is the formula to calculate the arc length of a sector?

L = θ/360 × 2πr (C) Signup and view all the answers

What is the sum of interior angles of a regular polygon with n sides?

(n - 2) × 180° (A) Signup and view all the answers

What is the formula to calculate the area of a regular polygon with n sides and side length s?

A = (1/4) × n × s^2 × cot(π/n) (C) Signup and view all the answers

What is the method to construct a perpendicular line through a point not on the line segment?

Draw a circle with one end point of the line segment as the center and passing through the given point. (D) Signup and view all the answers

What is the method to bisect an angle using circles?

Draw a circle with the vertex of the angle as the center and marking off equal lengths on both arms of the angle. (C) Signup and view all the answers

What is the method to construct a 45° angle?

Draw a 90° angle using the method for constructing perpendicular lines and then bisect it. (D) Signup and view all the answers

What is the property of angle bisectors in a triangle?

They intersect at one point, equidistant from each side of the triangle. (C) Signup and view all the answers

What is the relationship between an exterior angle and its interior opposite angles?

The exterior angle is equal to the sum of its interior opposite angles. (C) Signup and view all the answers

What is the formula for the reflection of a point over the line y = x?

(x, y) → (y, x) (D) Signup and view all the answers

What is the result of a 90° counterclockwise rotation about the origin of a point (x, y)?

(x, y) → (y, -x) (A) Signup and view all the answers

What is the formula for the area of a parallelogram?

A = base × height (A) Signup and view all the answers

What is the result of doubling the dimensions of a rectangle?

The area is quadrupled and the perimeter is doubled. (A) Signup and view all the answers

What is the formula for the circumference of a circle?

C = 2 × π × radius (D) Signup and view all the answers

What is the effect of a 180° rotation about the origin of a point (x, y)?

The point is reflected over the x-axis. (A) Signup and view all the answers

Gr 9 MATH: November Hard

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Questions and Answers

Which of the following operations is not closed under the system of natural numbers?

What is the purpose of the number 0 in the system of whole numbers?

Which of the following statements is true about the system of integers?

What is the definition of a rational number?

Which of the following is an example of an irrational number?

What is the set of real numbers composed of?

What is the identity element for addition in the system of whole numbers?

Which of the following is a property of natural numbers?

What is the result of subtracting a larger number from a smaller number?

What is the additive inverse of a positive number?

What is the result of adding a positive and a negative number?

What is the product of two negative numbers?

What is the distributive property of multiplication over addition?

What is the result of dividing a positive number by a negative number?

What is the square root of a number?

What is the result of adding a negative number to its additive inverse?

What is the result of subtracting an additive inverse from a number?

What is the purpose of negative numbers in real-world applications?

What is the primary purpose of estimating in calculations?

When performing addition in columns, what is the correct order of operation?

What is the process of expressing a number as a product of its prime factors called?

What is the formula to calculate the average speed of an object?

What is the term for the largest number that divides each of two or more numbers without leaving a remainder?

What is the purpose of compensating for errors in calculations?

What is the formula to calculate the distance traveled by an object?

What is the term for the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

What is the formula to calculate the time taken to travel a certain distance?

What is the term for the process of paying a deposit and then making monthly instalments?

What is the result of subtracting a larger number from a smaller number?

What is the equivalent of adding a negative number?

What is the result of the product of a positive and a negative number?

What is the order of operations when calculating expressions involving exponents?

What is the value of a^-n in exponential notation?

What is the purpose of scientific notation?

What is the result of adding an integer to its additive inverse?

What is the product of a negative and a negative integer?

What is the purpose of the laws of exponents?

What is the purpose of investigating and extending geometric patterns?

What is the primary purpose of an algebraic expression?

Which of the following is a convention for writing algebraic expressions?

What is the correct order of operations in an algebraic expression without brackets?

What is an expression with one term only?

What is the symbol often used to represent the variable in an algebraic expression?

What is the purpose of brackets in an algebraic expression?

What is an equivalent expression?

What is the term for the number multiplying the variable in an algebraic expression?

What is the purpose of forming sequences and identifying patterns?

What is the term for a fixed value in an algebraic expression?

What is the term for the sum of interior angles of a polygon?

What is the primary purpose of a flow diagram in representing a function?

What is the condition for two lines to be perpendicular?

What is the key feature of a graph that indicates the rate of change between variables?

What is the result of multiplying the polynomial 2x^2 + 3x - 1 by the monomial 5x?

What is the term for a polygon with all sides and angles equal?

Which of the following representations of a function shows the values of input and corresponding output?

What is the formula to calculate the area of a rectangle?

What is the result of simplifying the expression (3x + 2)^2?

What is the term for the line that intersects two or more other lines?

What is the result of evaluating the expression 2x^2 + 5x - 1 when x = 3?

What is the formula to calculate the gradient of a line passing through two points?

What is the sum of the interior angles of a triangle?

What is the result of dividing the polynomial 4x^2 + 2x - 3 by the monomial 2x?

What is the definition of a function in terms of variables?

What is the primary purpose of a graph in representing a function?

What is the term for the angles formed when two lines intersect?

What is the result of applying the rule 2n + 1 to the even number 4?

What are the key features to consider when interpreting graphs?

What is the result of simplifying the expression (x + 2)(x - 3)?

What is the formula to calculate the perimeter of a square?

What is the term for the angles formed when a transversal intersects parallel lines?

What is the purpose of a formula in representing a function?

What is the result of evaluating the expression x^2 + 2x - 5 when x = -2?

What is the result of multiplying the polynomial x^2 - 2x + 1 by the monomial 3x?

What is the term for the process of drawing and interpreting graphs of angles and lines?

What is the relationship between the input and output values in a function?

What is the purpose of a table in representing a function?