265 Questions
What is the gradient of a line passing through points (2, 3) and (4, 5)?
1
Which of the following is NOT a way to represent relationships between variables?
Pictures
What does the slope of a graph indicate?
The rate of change between variables
What is a function?
A relationship between two variables where each input has exactly one output
What is the term for the value substituted into a function?
Input number
What is the purpose of flow diagrams?
To show the calculations needed to transform input into output
What is the term for the result after applying a function to an input?
Output number
What does the shape of a graph provide insights into?
The nature of the relationship between variables
What is the sum of interior angles of a triangle?
180°
What type of triangle has all sides and angles equal?
Equilateral Triangle
What is the name of the theorem that relates to right triangles?
Pythagorean Theorem
What is the sum of co-interior angles?
180°
What type of angle is formed when two lines intersect?
Vertically Opposite Angle
What is the name of the shape with all sides and angles equal?
Regular Polygon
What is the formula for the area of a rectangle?
A = l × w
What type of angle is formed when a transversal intersects parallel lines?
Corresponding Angle
What is the name of the shape with opposite sides equal and parallel?
Parallelogram
What is the formula for the perimeter of a square?
P = 4s
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)
What is the purpose of a flow diagram in understanding functions?
To illustrate the steps to compute outputs from inputs
What does the slope of a graph indicate?
How rapidly the output changes with respect to the input
What is the sum of angles on a straight line?
180°
What are the angles called when two lines intersect to form equal angles of 90°?
Perpendicular angles
What is the term for angles on opposite sides of a transversal but inside the two intersected lines?
Alternate angles
What is the purpose of measuring angles in a graph?
To check the equality of corresponding and alternate angles
What is a function?
A relationship between two variables where each input corresponds to exactly one output
What is the term for the value substituted into a function?
Input number
What is the term for the specific output corresponding to a given input?
Function value
How many interior opposite angles does an exterior angle of a triangle have?
Two
What is the minimum condition for congruency of two triangles when given one side and two angles?
SAA
What is the formula for the area of a triangle?
A = 1/2 × base × height
What is the condition for congruency of two triangles when given a right angle, the hypotenuse, and one other side?
RHS
What is the formula for the perimeter of a triangle?
P = a + b + c
How many minimum conditions are there for congruency of two triangles?
6
What is the formula for the area of a circle?
A = πr^2
What is the formula for the circumference of a circle?
C = 2πr
What is the formula for the area of a sector?
A = (θ/360) × πr^2
What is the formula for the sum of interior angles of a regular polygon?
Sum = (n - 2) × 180°
What is the essential tool used to draw a circle with a given radius?
Compass
How do you ensure all angles are equal when constructing a square or rectangle?
Using a set square
What is the key to constructing a rhombus?
Using a compass to draw four equal sides from a single vertex
How do you determine the angle between vertices when constructing a regular polygon?
Dividing 360° by the number of sides
What is the primary tool used to construct parallel lines in a parallelogram?
Set square
What is the formula to find the area of a trapezium?
A = 1/2 × (a + b) × h
What is the formula to find the circumference of a circle?
C = 2πr
What is the formula to find the area of a sector?
A = θ/360 × πr^2
What is the sum of interior angles in a polygon with n sides?
(n - 2) × 180°
What is the formula to find the area of a regular polygon?
A = 1/4 × n × s^2 × cot(π/n)
How do you 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 draw another circle with the other end point as the center.
What is the property of interior angles in a triangle?
The sum of the interior angles is 180°.
What is the property of angle bisectors in a triangle?
The three angle bisectors intersect at one point, equidistant from each side of the triangle.
What is the definition of an exterior angle in a triangle?
An angle between a side of the triangle and an extended adjacent side.
How do you construct a 45° angle?
Draw a 90° angle using the method for constructing perpendicular lines, and then bisect the 90° angle.
What is the primary way to represent the relationship between variables in a graph?
Visual representation on a coordinate plane
What does the gradient of a line indicate?
The rate of change between variables
What is the key feature to consider when interpreting graphs?
The slope/gradient
What type of representation shows the calculations needed to transform input into output?
Flow diagram
What is the importance of continuity in interpreting graphs?
It determines whether the graph is a continuous line or has breaks/discontinuities
What is the purpose of a graph in understanding functions?
To provide a visual representation of the relationship between variables
What is the relationship between the input and output in a function?
Each input has exactly one output
What is the term for the point where the graph crosses the axes?
Intercept
What is the formula for the area of a kite?
A = 1/2 × d1 × d2
What is the formula for the circumference of a circle?
C = 2 × π × r
What is the formula for the area of a sector?
A = (θ/360) × π × r^2
What is the formula for the area of a trapezium?
A = 1/2 × (a + b) × h
What is the sum of interior angles of a regular polygon with n sides?
(n - 2) × 180°
What is the construction method to bisect an angle?
Using a compass to draw a circle with the vertex as the center
What is the property of the three angle bisectors of a triangle?
They intersect at one point, equidistant from each side of the triangle
What is the formula for the perimeter of a polygon with n sides and side length s?
P = n × s
What is the purpose of constructing perpendicular lines?
To construct a square or rectangle
What is the tool used to construct a circle with a given radius?
Compass
What is the sum of angles on a straight line?
180°
What is the name of the shape with all sides and angles equal?
Regular Polygon
What is the term for angles on opposite sides of a transversal but inside the two intersected lines?
Alternate Angles
What is the property of corresponding angles when a transversal intersects parallel lines?
They are equal
What is the sum of co-interior angles?
180°
What is the name of the theorem that relates to right triangles?
Pythagorean Theorem
What is the condition for congruency of two triangles when given a right angle, the hypotenuse, and one other side?
RHS
What is the formula for the area of a parallelogram?
A = bh
What is the name of the shape with opposite sides equal and parallel?
Parallelogram
What is the purpose of measuring angles in a graph?
To determine the properties of parallel lines and transversals
What is the minimum condition for congruency of two triangles when given two sides and an included angle?
SAS
What is the formula for the area of a triangle?
A = 1/2 × base × height
How many interior opposite angles does an exterior angle of a triangle have?
2
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
What is the condition for congruency of two triangles when given a right angle, the hypotenuse, and one other side?
RHS
What is the formula for the area of a sector?
A = (θ/360) × πr^2
What is the sum of interior angles in a polygon with n sides?
(n - 2) × 180º
What is the formula for the area of a rhombus?
A = 1/2 × d1 × d2
What is the formula for the circumference of a circle?
C = 2πr
What is the minimum number of conditions required for congruency of two triangles?
6
What is the essential tool used to draw a circle with a given radius?
Compass
When constructing a parallelogram, what is used to ensure opposite angles are equal?
Set square
What is the key to constructing a rhombus?
Using a compass to draw four equal sides from a single vertex
How do you determine the angle between vertices when constructing a regular polygon?
Divide 360° by the number of sides
What is the primary tool used to construct a square or rectangle?
Ruler
What is the purpose of creating a table of values when drawing graphs of functions?
To plot the input-output pairs on a coordinate plane
What is the relationship between the angles on a straight line?
The sum of the angles is 180°
What is the term for the angles formed when two lines intersect to form equal angles of 90°?
Perpendicular angles
What is the purpose of identifying the parallel lines and transversal when drawing graphs of angles and lines?
To determine the corresponding angles
What is the term for the angles on opposite sides of a transversal but inside the two intersected lines?
Alternate angles
What is the formula for calculating 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)
What is the purpose of drawing graphs of functions?
To visualize the relationship between variables
What is the sum of co-interior angles when a transversal intersects parallel lines?
180°
What is the term for the value substituted into a function to get the output value?
Input number
What is the purpose of using a protractor when drawing graphs of angles and lines?
To measure the angles formed by the lines
What is the primary purpose of a graph in understanding relationships between variables?
To visualize the relationship between variables
Which of the following represents a relationship between two variables where each input has exactly one output?
Function
What is the key feature to consider when interpreting a graph that indicates the rate of change between variables?
Slope/Gradient
What is the term for the points where a graph crosses the axes?
Intercepts
Which of the following is a way to represent relationships between variables?
All of the above
What does the continuity of a graph indicate?
Whether the graph is a continuous line or has breaks/discontinuities
What is the term for a quantity that can change?
Variable
What is the term for the result after applying a function to an input?
Output number
What is the formula for the area of a trapezium?
A = (a + b) / 2h
What is the formula for the circumference of a circle?
C = 2πr
What is the sum of angles on a straight line?
180°
What is the property of a regular polygon?
A polygon with all sides and angles equal
What is the formula for the area of a sector?
A = θ/360 × πr^2
What type of angles are formed when two lines intersect?
Vertically Opposite Angles
What is the term for angles on the same side of the transversal and inside the parallel lines?
Co-Interior Angles
What is the formula for the sum of interior angles of a regular polygon?
(n - 2) × 180°
How do you 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
What is the formula to find the area of a square?
A = s^2
What is the term for a polygon with all sides and angles equal?
Regular Polygon
What is the formula for the area of a circle?
A = πr^2
What is the formula for the perimeter of a polygon?
P = sum of all side lengths
What is the primary tool used to construct a circle with a given radius?
Compass
What is the sum of interior angles of a triangle?
180°
How do you ensure all angles are equal when constructing a square or rectangle?
Use a set square to ensure all angles are 90°
What is the name of the theorem that relates to right triangles?
Pythagorean Theorem
What is the formula for the diagonal of a rectangle?
d = √(l^2 + w^2)
What is the key to constructing a rhombus?
Use a ruler to draw equal sides
What is the property of interior angles of a triangle?
The sum of interior angles is 180°
What type of angle is formed when a transversal intersects parallel lines?
Corresponding Angles
How do you determine the angle between vertices when constructing a regular polygon?
Divide 360° by the number of sides
What is the formula to find the perimeter of a rectangle?
P = 2(l + w)
What is the name of the shape with opposite sides equal and parallel?
Parallelogram
What is the primary tool used to construct parallel lines in a parallelogram?
Set square
What is the minimum condition for congruency of two triangles when given two sides and an included angle?
Two Sides and an Included Angle (SAS)
What is the formula for the area of a triangle?
A = 1/2 × base × height
What is the condition for congruency of two triangles when given a right angle, the hypotenuse, and one other side?
Right Angle, Hypotenuse, and a Side (RHS)
What is the sum of interior angles in a polygon with n sides?
(n - 2) × 180°
What is the formula for the area of a circle?
A = πr^2
What is the formula for the perimeter of a triangle?
P = a + b + c
How many interior opposite angles does an exterior angle of a triangle have?
2
What is the minimum condition for congruency of two triangles when given one side and two angles?
One Side and Two Angles (SAA)
What is the formula for the area of a sector?
A = θ/360 × πr^2
What is the formula for the circumference of a circle?
C = 2πr
What is the purpose of creating a table of values when drawing graphs of functions?
To identify the input and output values
What is the relationship between the gradients of two perpendicular lines?
The gradients are negative reciprocals
What is the term for the point where the graph crosses the x-axis?
Intercept
What is the condition for two lines to be perpendicular?
The sum of the angles is 90°
What is the term for the angle formed when two lines intersect?
Vertically opposite angle
What is the purpose of identifying supplementary angles in geometry?
To find the sum of the angles on a straight line
What is the relationship between the angles formed when a transversal intersects two parallel lines?
The angles are equal
What is the term for the angle formed when two lines intersect to form equal angles of 90°?
Perpendicular angle
What is the purpose of measuring angles in a graph?
To check the properties of parallel lines and transversals
What is the term for the angles formed on opposite sides of a transversal but inside the two intersected lines?
Co-interior angles
What is the primary purpose of representing relationships between variables in multiple ways?
To provide a comprehensive understanding of the relationship
What is the key feature to consider when interpreting the graph of a function?
All of the above
What is the primary purpose of flow diagrams in understanding functions?
To visualize the calculations needed to transform input into output
What is the term for the quantity that can change in a function?
Variable
What is the formula for calculating the gradient of a line passing through two points?
(y_2 - y_1) / (x_2 - x_1)
What is the primary purpose of drawing graphs in functions?
To visualize the relationship between variables
What is the term for the result after applying a function to an input?
Output number
What is the relationship between the gradient of a line and the ratio of the vertical change to the horizontal change between two points on the line?
The gradient is equal to the ratio of the vertical change to the horizontal change.
What is the term for the specific output corresponding to a given input in a function?
Function value
Which of the following representations is most suitable for showing the relationship between two variables when the input values are not uniformly spaced?
Graph
What is the term for the angles formed when two lines intersect, and the sum of these angles is 180°?
Supplementary angles
A function has an input value of 2 and an output value of 5. What is the output value when the input value is 4?
Cannot be determined from the given information
What is the essential tool used to construct a regular polygon with a given number of sides?
Protractor
What is the relationship between the gradients of two perpendicular lines?
The gradients are negative reciprocals of each other.
What is the key to constructing a square or rectangle?
Using a ruler to draw four equal sides for a square or two pairs of equal sides for a rectangle
What is the term for the angle formed when a transversal intersects two parallel lines, and the angle is inside the two lines?
Co-interior angle
What is the primary tool used to construct a circle with a given radius?
Compass
What is the key to constructing a parallelogram?
Using a compass to draw parallel opposite sides
What is the purpose of creating a table of values when drawing a graph of a function?
To choose a range of input values to plot on the graph.
What is the formula used to determine the angle between vertices when constructing a regular polygon?
360° / number of sides
What is the term for the value of a function when the input value is zero?
y-intercept
What is the relationship between the number of angles formed when two lines intersect, and the number of lines?
The number of angles is twice the number of lines.
What is the term for the process of measuring angles to check their properties when drawing a graph of angles and lines?
Measurement
What is the relationship between the angles formed when two lines intersect?
They are equal.
What is the sum of the interior angles of a quadrilateral?
360°
What is the name of the theorem that relates to the sum of squares of the lengths of the legs of a right triangle?
Pythagorean theorem
What is the condition for two angles to be supplementary?
Their sum is 180°.
What is the name of the shape with opposite sides equal and parallel, and all angles equal to 90°?
Square
What is the formula for the area of a parallelogram?
A = b × h
What is the name of the angle formed when two lines intersect to form equal angles of 90°?
Right angle
What is the relationship between the corresponding angles formed when a transversal intersects parallel lines?
They are equal.
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
What is the name of the shape with all sides and angles equal?
Regular polygon
What is the minimum condition for congruency of two triangles when given two sides and an angle that is not included?
Two sides and an angle not included
What is the formula for the area of a triangle when given the base and height?
A = 1/2 × base × height
What is the relationship between an exterior angle and its interior opposite angles in a triangle?
The exterior angle is equal to the sum of the interior opposite angles
What is the condition for congruency of two triangles when given a right angle, the hypotenuse, and one other side?
RHS
What is the formula for the perimeter of a triangle?
P = a + b + c
What is the formula for the area of a circle?
A = πr^2
What is the formula for the arc length of a circle?
L = θ/360 × 2πr
What is the formula for the area of a sector of a circle?
A = θ/360 × πr^2
What is the formula for the sum of interior angles of a regular polygon?
Sum = (n - 2) × 180°
What is the formula for the area of a regular polygon?
A = 1/4 n s^2 cot(π/n)
What is the formula for the area of a trapezium?
A = 1/2 × (a + b) × h
What is the formula for the sum of interior angles of a regular polygon?
(n - 2) × 180°
What is the formula for the area of a sector?
A = θ/360 × π × r^2
What is the formula for the arc length of a sector?
L = θ/360 × 2 × π × r
What is the formula for the circumference of a circle?
C = 2 × π × r
What is the formula for the area of a circle?
A = π × r^2
What is the property of a regular polygon?
All sides and angles are equal
What is the method for constructing 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
What is the formula for the area of a triangle?
A = 1/2 × base × height
What is the property of interior and exterior angles of a triangle?
The exterior angle is equal to the sum of the two interior angles
What is the primary method used to draw a circle with a given radius?
Using a compass to draw a circle from a central point
When constructing a parallelogram, how do you ensure opposite angles are equal?
By drawing the parallel opposite sides and using a protractor to measure angles
What is the key to constructing a rhombus?
Using a compass to draw four equal sides from a single vertex
When constructing a regular polygon, how do you determine the angle between vertices?
By dividing 360° by the number of sides
What is the essential tool used to construct a square or rectangle?
A ruler
What is the primary purpose of a graph in understanding functions?
To visualize the rate of change between variables
What is the key concept in understanding the relationship between input and output values in a function?
Determining the formula
What does the continuity of a graph indicate?
The graph has no breaks or discontinuities
Which of the following representations of relationships is most suitable for visualizing patterns?
Graphs
Which of the following representations is most useful for identifying the input-output relationship?
Table of values
What is the key feature of a graph that indicates the rate of change between variables?
Slope/Gradient
When interpreting graphs, what does the shape of the graph indicate?
The type of relationship
What is the term for angles whose sum is 180°?
Supplementary angles
What is the purpose of a formula in representing relationships between variables?
To algebraically express the relationship between variables
What is represented by a point on a graph?
A specific input and corresponding output value
When two lines intersect, what is the relationship between the vertically opposite angles?
They are equal
What is the role of a table in understanding functions?
To display values of input and corresponding output
What is the term for the angles formed when a transversal intersects two or more parallel lines?
Corresponding angles
What is the primary difference between a table and a graph in representing relationships between variables?
A table displays numerical values, while a graph provides a visual representation
What is the sum of co-interior angles when a transversal intersects two parallel lines?
180°
What is the purpose of drawing a graph of a function?
To visualize the relationship between variables
What is the key concept in understanding the geometry of straight lines?
Angle relationships
What is the term for the lines that intersect to form equal angles of 90°?
Perpendicular lines
What is the sum of co-interior angles when two lines intersect?
180°
What is the name of the method used to construct a perpendicular line through a point on the line segment?
Case 2: Using Circles
What is the formula for the area of a sector of a circle?
A = (θ/360) × πr²
What is the property of a regular polygon?
All sides and angles are equal
What is the formula for the perimeter of a polygon?
P = n × s
What is the name of the angle formed when two lines intersect to form equal angles of 90°?
Right Angle
What is the formula for the area of a trapezium?
A = (1/2) × (a + b) × h
What is the property of the diagonal of a rectangle?
d = √(l² + w²)
What is the formula for the sum of interior angles of a regular polygon?
(n - 2) × 180°
What is the method used to construct a 45° angle?
Bisecting a 90° angle
What is the sum of angles on a straight line formed by two lines intersecting at a point?
180°
Which of the following types of angles are formed when a transversal intersects parallel lines?
Alternate angles
What is the sum of interior angles of a regular polygon with 8 sides?
720°
What is the name of the theorem that relates to the area of a triangle?
Heron's Formula
What is the term for a polygon with all sides and angles equal?
Regular Polygon
What is the name of the shape with opposite sides equal and parallel?
Parallelogram
What is the sum of co-interior angles formed by a transversal intersecting two parallel lines?
180°
What is the name of the shape with all sides equal?
Rhombus
What is the purpose of measuring angles in a graph?
To check the properties of parallel lines and transversals
What is the minimum condition for congruency of two triangles when given two sides and an angle not included?
Two sides and an angle not included
What is the term for angles formed when two lines intersect to form equal angles of 90°?
Perpendicular Angles
What is the formula for the area of a triangle using Heron's formula?
A = sqrt(s(s - a)(s - b)(s - c))
How many interior opposite angles does an exterior angle of a triangle have?
Two
What is the condition for congruency of two triangles when given a right angle, the hypotenuse, and one other side?
RHS
What is the formula for the area of a sector?
A = 1/2 * θ/360 * 2πr
What is the formula for the perimeter of a triangle?
P = a + b + c
How do you construct a rhombus?
Using a ruler to draw the diagonals and ensure they are perpendicular
What is the formula for the area of a parallelogram?
A = b * h
What is the sum of interior angles of a regular polygon?
(n - 2) * 180°
What is the tool used to construct a circle with a given radius?
Compass
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