FALL ACP 2024 REVIEW DAY 1

Front

What is the result of the multiplication \( (5-2i\sqrt{6})(5-4i\sqrt{6}) \)?

Back

The result is \( -23 - 30i\sqrt{6} \).

Front

What are the equations represented by the graph: \( y=\frac{3}{5}x-4 \) and \( y=2(x+3)^2-7 \)?

Back

The system of equations is \( y=\frac{3}{5}x-4 \) and \( y=2(x+3)^2-7 \).

Front

Solve the system of equations: What is the solution?

Back

The solution is (2, -5, -9).

Front

What is the graph of the equation \( y=-x^2+4 \) and \( y=-\frac{1}{2}x+1 \)?

Back

The graph represents a downward-opening parabola and a line with a negative slope.

Front

How can you express the average price of skis being $750 with a variation of $250?

Back

The equation is \( |x - 750| = 250 \).

Front

What is the definition of a complex number?

Back

A complex number is a number that can be expressed in the form \( a + bi \), where \( a \) and \( b \) are real numbers and \( i \) is the imaginary unit.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the solutions of a quadratic equation in the form \( ax^2 + bx + c = 0 \) and is given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Front

What does the absolute value equation \( |x - a| = b \) represent?

Back

It represents two possible equations: \( x - a = b \) and \( x - a = -b \).

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is \( y = a(x-h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant \( b^2 - 4ac \) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.