High School Algebra Practice - Creating Equations

Common Core Math Practice


This quiz illustrates the range of difficulty expected by the following Common Core State (CCS) standards:

QuestionCommon Core Standard #
indicates a modelling standard.

All questions of this quiz illustrate the difficulty of the high school A.CED standards required for all students, including the college and career ready students.

Question 1: The area of a trapezoid is given by:

where a and b are the lengths of the parallel sides, and h is the height.
Write an equation whose solution is the side a of a trapezoid with an area A = 24in2, b = 3in and h = 4in.

Question 2: The total resistance of a set of two resistors in parallel is found by using the relation:

where R1 and R2 are the resistances of the two resistors.

Write an equation whose solution is the resistance R of a resistor in parallel with another resistor with a value of 10 Ohms, if the parallel combination of the two resistors is 2 Ohms.

Question 3: Find the set of real numbers (x,y) which is a solution to both equations x2 + y2 = 4 and (x - 3)2 + y2 = 1.

Question 4: A square S of side l is divided into four identical squares of sides l/2. One of the four squares is divided again into four smaller identical squares and the same process continues until the initial square S is divided n times.
Write the mathematical relation between l, n and A, where A is the area of the smallest square resulted after n divisions.

Questions 5 and 6 : A gas station sells m gallons of gasoline fuel at $3.8 per gallon and n gallons of diesel fuel at $4.25 per gallon.
Write an equation relating m and n if the gas station sells fuel worth $23,250.

If the total number of gallons sold by the gas station is 6,000, the ratio between the volumes of gasoline fuel and diesel fuel sold is .

Question 7: Violet light has a wavelength of λ = 400nm. What is its frequency, if the speed of light is c = 3·108 m/s and the relation between c, frequency f and λ is c = f·λ?

Question 8: What is the mass of a car, function of its speed v and kinetic energy Ec?

Recall that the formula for the kinetic energy of a moving object is:

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