Introduction to Algebra

Multiple Choice

Which of the following expressions correctly demonstrates the distributive property?

• a(b + c) = ab + ac

• a(b + c) = ab + c

• a(b + c) = a + bc

• a(b + c) = ab + a

Open Ended

Simplify the expression using the distributive law.

Open Ended

Simplify the expression using the distributive law.

Open Ended

Simplify the expression using the distributive law.

Multiple Choice

Which of the following is the correct first step when adding or subtracting like terms in an algebraic expression?

• Combine the numbers first

• Identify the like terms of the expression

• Multiply the coefficients

• Apply the distributive property

Open Ended

Simplify: 4y−7y+y

Open Ended

Simplify: 3x+5x−2x

Open Ended

Simplify: 5k−3k+7k−2k

Multiple Select

Which of the following are correct laws of exponents?

• Product Rule: a^m × a^n = a^(m+n)

• Quotient Rule: a^m ÷ a^n = a^(m-n)

• Zero Exponent Rule: a^0 = 0

• Power of a Power Rule: (a^m)^n = a^(mn)

Open Ended

Find the product of the expression.

Open Ended

Find the product of the expression.

Open Ended

Solve for the quotient of the expression.

Open Ended

Solve for the quotient of the expression.

Open Ended

Solve for the quotient of the expression.

Open Ended

What is the perimeter of a rectangle with a length of 8 cm and a width of 5 cm?

Open Ended

Calculate the perimeter of a triangle with sides measuring 6 m, 7 m, and 8 m.

Open Ended

The radius of a circle is 3 cm. What is the area of the circle? Use π≈3.14.

Open Ended

What is the area of a rectangle with a length of 10 cm and a width of 5 cm?

One Unknown Example

6x + 9 = 5 + 5x

One Unknown Example

2 (x - 13) = 12

One Unknown Example

Two Unknown Example

Complete the following table for
3x - y = 1

​x	​y
​	5​
​4	​
​	-10​

Open Ended

Solve for x if 2x+5=15

Open Ended

Solve for x if x/4 +6=10

Open Ended

Solve for x if 3x + 7 = 28

Open Ended

Determine one solution to the following linear equation: y = 7x + 6

Open Ended

Determine one solution to the following linear equation: 6t - 3u =10

Open Ended

The ratio of tomatoes to red apples is 2:5. If there are 20 tomatoes, how many red apples are there?

Open Ended

In a Math test, the ratio of Shakeel's score to Ryan's score is 3:4. If Ryan obtained 84 marks, find the score of Shakeel.

Open Ended

$3,600 is shared between two children in the ratio 4:5. Find the amount of the smaller share and the larger share.

Open Ended

A car used 1 liter of fuel to travel 18 km. How far could the car travel on 30 liters of fuel at the same rate?

Open Ended

9 cow can graze a field in 24 days. How long will 15 cows take to graze the same field?

Open Ended

The time taken, t hours, to do a paint job is inversely proportional to the number of workers N. Given that 16 workers rake 15 days to paint a factory. How long will 24 workers take to paint the same factory?