GRE Quant Foundation Assessment Test (Algebra)

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This is an assessment designed to assess your GRE Quant Foundation knowledge. None of the questions are tricky. None of the questions are puzzles. They solely test knowledge.

Calculators: You can use a calculator but it has to be one of those crappy ones like the one on your phone when you turn it vertically. Or the one on the ETS website in the PowerPrep exams. Or https://www.gregmat.com/tools/calculator

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In the expression below, the variable x can take any real value.

1 point

True

False

Clear selection

In the expression below, the variable x can take any real value.

1 point

True

False

Clear selection

After simplification, how many terms does the algebraic expression below have?

1 point

What is the degree of an algebraic expression that contains only a constant?

1 point

Clear selection

What is the degree of the polynomial below?

1 point

The algebraic identity below can be written in what other form?

1 point

The algebraic identity below can be written in what other form?

1 point

A linear equation contains at most two variables.

1 point

True

False

Clear selection

What is the degree of a quadratic equation?

1 point

Clear selection

1 point

True

False

Clear selection

1 point

True

False

Clear selection

Using the system of equations below, calculate the product of x and y.

1 point

Using the system of equations below, calculate the sum of x and y.

1 point

If we have three non-equivalent linear equations, each containing the same three variables (and no other variables), we can solve for the value of each variable.

1 point

True

False

Clear selection

What is the formula for the discriminant of the quadratic formula?

1 point

Option 1

Option 2

Option 3

Option 4

Clear selection

If a quadratic equation has only one solution, what is the value of its discriminant?

1 point

If we were to factor the quadratic expression below into the form (x+a)(x+b), how would we write the expression?

1 point

If we were to factor the quadratic expression below into the form (cx+a)(x+b), where a, b, and c are all integers not equal to 1, how would we write the expression?

1 point

If we wanted to complete the square of the quadratic equation below, what number should we add to both sides of the equation?

1 point

The two equations below are equivalent.

1 point

True

False

Clear selection

How many solutions satisfy the equation below?

1 point

Given the inequality below, which of the following is true?

Select all that apply.

1 point

Option 1

Option 2

Option 3

Option 4

Option 5

The two inequalities below are equivalent.

1 point

True

False

Clear selection

If f(x) = f(x+2) and f(4) = 2, what does f(16) equal?

1 point

The domain and range of the function below are equal.

1 point

True

False

Clear selection

The domain and range of the function below are equal.

1 point

True

False

Clear selection

If the below is true, what does f(81) equal?

1 point

Which of the following correctly represents an even function?

1 point

Option 1

Option 2

Option 3

Option 4

Clear selection

Which of the following functions is/are odd?

Select all that apply.

1 point

Option 1

Option 2

Option 3

John is currently three times as old as Alice (in years). In 12 years, Alice will be half as old as John. How old is John (in years) right now?

1 point

Bob invested $50,000 in an account earning simple annual interest of x%, which pays out in equal monthly installments. If he received $500 after the first month, what is x?

1 point

A bank account earns 8% annual interest, compounding quarterly. If John invests $100 in this account for three years, the amount of money the bank account has can be represented by the equation below. What is r + n?

1 point

Solution A contains 30% substance Z by volume and solution B contains 45% substance Z by volume. When a certain amount of solution A is mixed with a certain amount of solution B, the combined solution contains 41% substance Z. In what ratio were the two solutions mixed (A to B)?

1 point

Which of the following scenarios results in a LONGER commute time?

Scenario 1: Sarah drives to her work at a constant speed of 30 mph and drives home from work at a constant speed of 40 mph.

Scenario 2: Sarah drives to her work and back to her home at a constant speed of 35 mph both ways.

1 point

Scenario 1 results in a longer commute.

Scenario 2 results in a longer commute.

The two scenarios result in an equivalent commute time.

Clear selection

Train A is traveling directly east from town R to town T at a constant speed of 74 mph. Train B is traveling directly west from town T to town R at a constant speed of 90 mph. If the two towns are 300 miles apart and if both trains leave at precisely the same time, approximately how many minutes will pass before they meet?

Round your answer to the nearest integer.

1 point

Ahmed and Sanjeet are running on a 2-mile circular track, running at constant speeds of 8 mph and 5 mph respectively, in the same direction. If Ahmed is currently 1 mile behind Sanjeet, how many minutes will pass before Ahmed passes Sanjeet twice?

1 point

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