Can You Pass Algebra?

By: Jouviane Alexandre
Image: Shutterstock

About This Quiz

We've all been there! You might've gotten your first taste of algebra in elementary school and took your last course in high school or college. Test your knowledge and see if you could still pass the course!

How would you write '10 decreased by X?'

When 10 is decreased by amount 'X,' you are subtracting X from the amount.

Simplify: -8 - 1 =

-8-1 = (-8) + (-1) = -9

Combine like terms: 3x^2 + 7x - 4x - 3x^2

The solutions breaks down to (-3x^2) cancelling out (3x^2) which leaves you with 7x - 4x = 3x

Solve this equation: x + 8 = -5

When following the steps for this equation, subtracting 8 from both sides will leave you with the solution x=-13.

Expand: (5x + 2)(3x - 4)

Multiplying the first two terms of each factor will yield 15x^2. Multiplying the last two terms of each factor will yield -8. Multiplying 5x and -4 while yield -20x while the product of 2 and 3x is 6x. When 6x is added to -20x, the sum is -14x.

Factor: x^2 + 11x + 28

Although the product of 14 and 2 equals 28, the numbers used must be 7 and 4 because when added together, you will receive the middle term of 11x.

Simplify: (11x/10) - (x/10)

When the numerator is handles, you get the difference to be 10x. When the numerator (10x) is divided by the denominator (10), the quotient is x.

Find the solution: 2x-4y = 12

When (0,-3) is made to replace x and y, respectively, the equation becomes 0 + 12 = 12.

The sum of two numbers is 22. The larger is two less than twice the smaller number. What is the larger number?

If x equals the smaller number and the larger number is two less than twice the smaller, the larger number can be written as 2x-2. When 2x - 2 + x = 22, the solution for x = 8. When 8 is substituted into the larger number (2x-2), the answer is 14.

What is the square root of 28?

When solving radicals that aren't perfect squares, the first step is to split them up in a fashion where you can solve for a perfect square. Radical 28 can be simplified to radical 4 and radical 7. Since 4 is a perfect square, the radical 4 gets simplified to 2 and the whole answer is written as 2 radical 7.

What is (3x)^3 in expanded form?

When expanding with exponents, you take the base and multiply it how ever many times the number of the exponent is. In this example, you would take 3x and multiply it 3 times.

Multiply: (-3)(-3)

When two negative numbers are multiplied, the product is automatically positive. Thus, you can look at is as (3)(3) which is 9.

Divide c^6/C^2

When dividing exponents that share the same base, subtract the denominator's exponent from the numerators exponent for the answer.

25 is 4 less than a number. What is the number?

If 25 is 4 less than a number, adding 25 and 4 together will create the sum of the number thus the answer is 29.

Expand: (2x-7)^2

The first term is the product of (2x)^2 which is 4x^2. The last term is (-7)^2 which is 49. The middle term comes from the product of of 2[(2x)(-7)] which is -28.

Factor: 25-x^2

The answer must have alternating signs in order for it to cancel out the middle term commonly seen. The signs must also be alternating to yield a negative x^2.

What quadrant does the point (-2,1) fall in?

On a graph, the first quadrant (I) is made up of positive x's and y's. Quadrant II is made up of negative x's and positive y's. The quadrants continue in a counterclockwise fashion.

Simplify: 3 radical 24

First radical 24 is split into two radicals (4 and 6). Since four is a perfect square, it can be solved to 2. This number is then multiplied by the three in front of the radical leaving the solution as 6 radical 6.

If x=2, what is (3x)^3

If x=2, the product inside the parentheses is 6. Then hold 6 to the third power (6x6x6) and the product is 216.

Simplify: -6+5-2+1-9

Because of the PEMDAS rule, addition and subtraction can occur at the same time. This problem can be easily solved by going in order.

What is the product of: x(x^3)(x^4)

The rule for multiplying exponents with the same base is to add the exponents. While you might be tempted to think the answer is x^7, the first term 'x' has an invisible exponent - 1. Thus the addition for the exponents is 1+3+4 which will give you the final exponent of 8.

Solve this inequality: 3-x < 4

For this equation, adding 'x' to both sides and subtracting '4' from both sides of the inequality will give you the answer that x > -1.

Multiply: x(3x-4)

When x is multiplied along the terms in the parentheses, you get the answer 3x^2 - 4x

Factor: 5x^2 - 11x + 2

In order to get the first term as 5x^2, the first two terms of the factors needs to yield a product of 5x^2 which can be achieved by multiplying x by 5x. In order to get a positive 2 as the last term, the last two terms of the factors need to both carry positive signs or both carry negative signs as in answer 3.

What is the slope of the equation: 3x + 4y = 12

In order to solve for slope, 3x would have to be subtracted from both sides of the equation. Both sides of the equation would be divided by 4 leaving us with the equation y = -3/4x + 3 where the slope is -3/4.

Write using exponents: (a)(a)(a) + (b)(b)(b)(b) - (c)(c)

(A) multiplied twice yields (a)^2. How ever many times you see the letter appear is the number of its exponent.

What is the answer to 14/0?

When a number is divided by 0, the answer is never 0. It is always undefined.

What kind of line is the equation x=2?

If the equation is x=2, no matter what the y-value is, x will always be 2. This means that the line will intersect the x-axis at x=2 and will continue to move vertically.

Combine like terms: 2x + y - 5 - 5x -2y + 1

When 2x and (-5x) are combined, the difference is -3x. When y and (-2y) are combined, the answer is -y. when 1 is added to (-5) the answer is -4. This gives us the solution -3x - y - 4

The sum of three consecutive numbers is 108. What is the middle number?

If x = the smallest number, the other two numbers are x + 1 and x + 2 because they are consecutive. You'd then set up the equation x + x + 1 + x + 2 = 108. Simplifying this equation will give you 3x + 3 = 108. Simplifying this further would create the equation 3x = 105 where x = 35. In order to find the middle/second number, you would replace x into the equation for the second number which is x + 1 giving you the answer of 36.

Solve for x: 3x^2 - 3x = 0

For this equation, you want two numbers that when replaced as x, they will yield 0. Zero is an immediate answer because the product of any number with 0 is 0. The value -1 would make the first term 3 would introducing it to the second term would not properly cancel it. The other value is 1. When added to the first term (3x^2), this will yield 3. When introduced to the second term, (-3x), it will yield -3 which will cancel the first term and make the solution 0.

What is the y-intercept of the equation 3x + 4y = 12.

In order to find the y-intercept of the equation, pretend x = 0 and solve for y. This will give you the y-intercept of (0,3).

What is the name of this: c^2 = a^2 + b^2

The Pythagorean Theorem is a common formula used in algebra when dealing with a right triangle.

In this equation, which letter represents the slope : y = mx + b.

In this equation, which is known as slope-intercept form, m is used to represent the slope while b is the y-intercept.

a(bc) = (ab)c is known as what property?

This is an example of the associative property of multiplication. It states that the numbers can be multiplied regardless of the way you group them (i.e. whether the parentheses are placed around the a and b or the b and c).

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