End Of Years 2025 Flashcards
What should you be able to do by the end of the unit on Reasoning with Algebra?
Solve inequalities with negative numbers, solve equations with unknowns on both sides, solve inequalities with unknowns on both sides, substitute into formulas and equations, rearrange formulae.
What is an inequality?
An inequality compares two values, showing if one is greater than, less than, or equal to another.
What is a variable?
A quantity that may change within the context of the problem.
What does it mean to rearrange?
To change the order.
What is an inverse operation?
The operation that reverses the action.
What does it mean to substitute?
To replace a variable with a numerical value.
What does it mean to solve?
To find a numerical value that satisfies an equation.
How do you solve equations with brackets?
Expand the brackets.
How do you form and solve inequalities?
Translate the statement into an inequality and solve for the variable.
What is the method for solving inequalities with negatives?
Make x positive first, then solve the inequality.
What is the first step in solving the inequality 2 - 3x > 17?
Add 3x to both sides.
What is the result of solving the inequality 2 - 3x > 17?
x < -5.
What is the method for solving equations with unknowns on both sides?
Use the same method as solving inequalities.
What is a formula?
An expression in symbols.
What happens when you multiply or divide x by a negative?
You need to reverse the inequality.
How do you rearrange the formula x = y + z to make y the subject?
y = x - z.
How do you rearrange the equation 4x - 3 = 9 to find x?
Add 3 to both sides and then divide by 4.
What is the gradient of the line 2y - 4x - 9?
First, make y the subject: y = 2x + 4. The gradient is 2.
What should you be able to do by the end of the unit on Straight Line Graphs?
Compare gradients, compare intercepts, understand and use y = mx + c, find the equation of a line from a graph, interpret gradient and intercepts of real-life graphs.
What is the gradient?
The steepness of a line.
What is an intercept?
Where two lines cross.
What is the y-intercept?
Where the line meets the y-axis.
What are parallel lines?
Two lines that never meet with the same gradient.
What is a coordinate?
A set of values that show an exact position on a graph.
What does linear mean?
Linear graphs (straight line) have a linear common difference by addition/subtraction.
What is an asymptote?
A straight line that a graph will never meet.
What is a reciprocal?
A pair of numbers that multiply together to give 1.
What does perpendicular mean?
Two lines that meet at a right angle.
What is the form of lines parallel to the y-axis?
x = a and are vertical.
What is the form of lines parallel to the x-axis?
y = a and are horizontal.
How many points do you need to form a straight line?
You only need two points.
What does a greater gradient indicate?
The steeper the line.
What do positive gradients look like?
They increase as x increases.
What do negative gradients indicate?
They decrease as x increases.
What is the y-intercept in the equation y = mx + c?
The value of c is the point at which the line crosses the y-axis.
What does the coefficient of x tell us?
It tells us the gradient of the line.
How can the equation of a line be rearranged?
For example, y = c + mx or c = y - mx.
What does the gradient represent in real-life graphs?
It represents the price per unit.
What does a direct proportion graph look like?
It must start at the origin.
What does the gradient show in a direct proportion graph?
The price per unit.
