Algebra Simple Test Paper wit Solution for School Students. [New]

📝 Simple Algebra Test 🧠

A quick and fun test to check your basic algebra skills. Try your best!

Question 1: Simplifying Expressions ➕

Simplify the following expression: \( 5x + 3y - 2x + 4y \)

✅ Solution

To simplify, we combine 'like terms'. This means we group the \(x\) terms together and the \(y\) terms together.

Group the terms: \( (5x - 2x) + (3y + 4y) \)

Perform the operations:

\( 5x - 2x = 3x \)

\( 3y + 4y = 7y \)

The simplified expression is \( 3x + 7y \). 👍

Question 2: Solving an Equation ⚖️

Solve for the variable \(a\) in the equation: \( 3(a + 2) = 21 \)

✅ Solution

First, distribute the 3 on the left side of the equation:

\( 3 \times a + 3 \times 2 = 21 \)

\( 3a + 6 = 21 \)

Next, subtract 6 from both sides to isolate the term with \(a\):

\( 3a = 21 - 6 \)

\( 3a = 15 \)

Finally, divide by 3 to solve for \(a\):

\( a = \frac{15}{3} \)

\( a = 5 \)

The value of \(a\) is 5. 🎉

Question 3: Evaluating Expressions 🔢

If \( p = 4 \) and \( q = 3 \), find the value of the expression: \( 2p + q^2 \)

✅ Solution

We substitute the given values of \(p\) and \(q\) into the expression.

Given expression: \( 2p + q^2 \)

Substitute \(p=4\) and \(q=3\):

\( 2(4) + (3)^2 \)

Now, follow the order of operations (PEMDAS/BODMAS). First, calculate the exponent:

\( 2(4) + 9 \)

Next, perform the multiplication:

\( 8 + 9 \)

Finally, perform the addition:

\( 17 \)

The value of the expression is 17. ✨

Question 4: Word Problem 🗣️

If a number is doubled and then 5 is added to it, the result is 19. What is the number?

✅ Solution

Let's translate the sentence into a mathematical equation. Let the unknown number be \(n\).

"A number is doubled": \( 2n \)

"and then 5 is added": \( 2n + 5 \)

"the result is 19": \( 2n + 5 = 19 \)

Now, we solve this equation for \(n\):

Subtract 5 from both sides:

\( 2n = 19 - 5 \)

\( 2n = 14 \)

Divide by 2:

\( n = \frac{14}{2} \)

\( n = 7 \)

The number is 7. 🎯

Great work! Keep practicing and you'll become an algebra star! ⭐