Algebra 1 Regents June 2022: Key Concepts and Problem Solving

What does it mean for a number to be rational?

• It cannot be expressed as a fraction.

• It can be expressed as a fraction a/b where a and b are integers and b is not zero.

• It is a square root of a non-perfect square.

• It is always a whole number.

What is the result of multiplying a rational number by an irrational number?

• Always an irrational number.

• Can be either rational or irrational, depending on the numbers.

• Always a rational number.

• Undefined.

How does the graph of a function change when it is shifted three units to the right?

• It moves three units to the right.

• It moves three units down.

• It moves three units to the left.

• It moves three units up.

What does the graph of y = x^2 look like after it has been shifted 3 units to the right and 4 units down?

• A parabola opening upwards, shifted right and down.

• A straight line.

• A parabola opening downwards.

• A circle.

How do you calculate the average rate of change from a graph?

• By finding the slope of the tangent line at a point.

• By finding the highest and lowest points and dividing by two.

• By dividing the change in y-values by the change in x-values over an interval.

• By adding all the y-values and dividing by the number of points.

What is the average rate of change of a function on the interval from x=1 to x=4 if the function values are 40 and 100 respectively?

• 30

• 15

• 60

• 20

What is the purpose of completing the square in a quadratic equation?

• To transform the equation into a perfect square trinomial.

• To simplify the equation into a single variable.

• To eliminate the x-term.

• To make the equation easier to graph.

Which method can be used to solve any quadratic equation?

• Quadratic formula

• Factoring

• Graphing

• Completing the square

What does the solution set of a system of inequalities represent graphically?

• The highest and lowest points of the graphs.

• The points where the graphs of the inequalities cross.

• The points where the graphs of the inequalities touch the x-axis.

• The area where the graphs of the inequalities intersect.

In a word problem involving ticket prices, what is the first step to formulating equations?

• Identify the total cost.

• Determine the number of tickets sold.

• Calculate the tax.

• Assign variables to unknown quantities.