Algebra 2: Quadratics & Factoring Challenge for Grade 10

A rectangle has a length that is 3 meters longer than its width. If the area of the rectangle is 40 square meters, find the dimensions of the rectangle by setting up and solving a quadratic equation.

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

• Width: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

The product of two consecutive integers is 72. Set up an equation to find the integers and solve it using factoring.

• 10 and 11

• -10 and -9

• 8 and 9 or -9 and -8

• 7 and 8

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 10 meters per second. The height of the ball can be modeled by the equation h(t) = -4.9t^2 + 10t + 1.5. Find the time when the ball hits the ground using the quadratic formula.

• 4.20 seconds

• 2.56 seconds

• 1.75 seconds

• 3.10 seconds

The sum of the ages of a father and his son is 50 years. If the father is 4 times as old as the son, find their ages by forming and solving a system of equations.

• Father: 36 years, Son: 14 years

• Father: 40 years, Son: 10 years

• Father: 30 years, Son: 20 years

• Father: 50 years, Son: 0 years

A garden is in the shape of a triangle with a base that is 5 meters longer than its height. If the area of the garden is 30 square meters, find the dimensions of the garden using a quadratic equation.

• Height: 3 meters, Base: 8 meters

• Height: 6 meters, Base: 11 meters

• Height: 4 meters, Base: 9 meters

• Height: 5 meters, Base: 10 meters

A car's value decreases according to the equation V(t) = -2000t^2 + 12000t + 3000, where V is the value in dollars and t is the time in years. Determine when the car's value will be zero using the quadratic formula.

• t = 20

• t = 10

• t = 15 or t = -0.1 (discard negative time)

• t = 5

The difference between two numbers is 6, and their product is 45. Set up a quadratic equation to find the two numbers and solve it by factoring.

• The two numbers are 11 and 5.

• 12 and 6

• 9 and 3

• 10 and 4

A rectangular pool is 4 meters longer than it is wide. If the perimeter of the pool is 48 meters, find the dimensions of the pool using algebraic equations.

• Width: 10 meters, Length: 14 meters

• Width: 6 meters, Length: 10 meters

• Width: 8 meters, Length: 12 meters

• Width: 12 meters, Length: 16 meters

A company produces a certain number of gadgets, and the profit P (in dollars) can be modeled by the equation P(x) = -5x^2 + 150x - 200, where x is the number of gadgets produced. Find the number of gadgets that maximizes the profit using the quadratic formula.

• 20

• 15

• 10

• 25

The height of a projectile is modeled by the equation h(t) = -16t^2 + 64t + 80. Determine the time at which the projectile reaches its maximum height using the vertex formula for quadratics.

• 1

• 3

• 4

• 2