Algebra Paper One Test Paper for Students Practice. [New]

🧮 ALGEBRA FUNDAMENTALS QUIZ ✏️

Let's check your understanding of the basic building blocks of algebra!

Question 1: Order of Operations 🚦

Calculate the value of the following expression: \( 20 - (4 + 2) \times 3 \)

✅ Solution

We must follow the order of operations (PEMDAS/BODMAS):

1. Parentheses / Brackets
2. Exponents / Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Step 1 (Parentheses): First, solve the part inside the parentheses.

\( 4 + 2 = 6 \)

The expression becomes: \( 20 - 6 \times 3 \)

Step 2 (Multiplication): Next, perform the multiplication.

\( 6 \times 3 = 18 \)

The expression becomes: \( 20 - 18 \)

Step 3 (Subtraction): Finally, perform the subtraction.

\( 20 - 18 = 2 \)

The final answer is 2. 👍

Question 2: Working with Integers ❄️🔥

What is the value of: \( (-8) + 5 - (-4) \)

✅ Solution

Let's solve this step-by-step from left to right.

Step 1: First, handle the double negative. Subtracting a negative number is the same as adding a positive number.

\( -(-4) \) becomes \( +4 \)

So the expression is now: \( -8 + 5 + 4 \)

Step 2: Add the first two numbers.

\( -8 + 5 = -3 \)

The expression becomes: \( -3 + 4 \)

Step 3: Perform the final addition.

\( -3 + 4 = 1 \)

The answer is 1. 🎉

Question 3: Solving for a Variable ❓

Find the value of \(y\) in the following equation: \( y - 7 = 15 \)

✅ Solution

Our goal is to get the variable \(y\) by itself on one side of the equation.

The equation is: \( y - 7 = 15 \)

To undo the subtraction of 7, we need to do the opposite operation, which is adding 7.

We must add 7 to both sides of the equation to keep it balanced.

\( y - 7 + 7 = 15 + 7 \)

On the left side, \(-7 + 7\) equals 0, leaving just \(y\).

\( y = 22 \)

The value of \(y\) is 22. You can check this by putting it back into the original equation: \(22 - 7 = 15\), which is true! ✅

Question 4: Writing an Expression 🍕

A large pizza costs $12, and each extra topping costs $2. Write an algebraic expression for the total cost of a pizza with \(t\) toppings.

✅ Solution

Let's break down the cost.

There is a fixed cost (the base price of the pizza) and a variable cost (which depends on the number of toppings).

• The fixed cost is $12.
• The cost for toppings is $2 per topping. If there are \(t\) toppings, this cost is \(2 \times t\) or simply \(2t\).

The total cost is the sum of the fixed cost and the variable cost.

Total Cost = (Fixed Cost) + (Topping Cost)

So, the expression is: \( 12 + 2t \) 💸

Fantastic job! Every problem you solve makes your brain stronger. Keep it up! ⭐