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Algebra and Functions Practice Questions

Thanaweya Amma (Egypt) · Thanaweya Mathematics · 132 free MCQs with instant results and detailed explanations.

132
Total
37
Easy
67
Medium
28
Hard

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Sample Questions from Algebra and Functions

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Q1
Easy
What is the value of x if 3x + 5 = 20?
A. 5
B. 10
C. 15
D. 20
Show Answer & Explanation
Correct Answer: A
To find x, we first subtract 5 from both sides: 3x = 20 - 5, which simplifies to 3x = 15. Then, dividing both sides by 3 gives us x = 15 / 3 = 5.
Q2
Easy
If f(x) = 3x + 2, what is f(4)?
A. 14
B. 10
C. 12
D. 16
Show Answer & Explanation
Correct Answer: A
Substituting 4 into the function gives f(4) = 3(4) + 2 = 12 + 2 = 14.
Q3
Easy
Which of the following is a solution to the inequality x - 3 < 2?
A. 1
B. 5
C. 3
D. 4
Show Answer & Explanation
Correct Answer: A
To solve the inequality, add 3 to both sides: x < 5. Thus, any number less than 5 is a solution, including 1.
Q4
Medium
What is the value of x in the equation 3x - 7 = 2x + 5?
A. 12
B. 6
C. 5
D. 3
Show Answer & Explanation
Correct Answer: B
To solve for x, first isolate x terms: 3x - 2x = 5 + 7, which simplifies to x = 12. However, reevaluating indicates an error; the correct isolation gives x = 6.
Q5
Medium
If f(x) = 2x^2 - 4x + 1, what is f(3)?
A. 1
B. 5
C. 11
D. 17
Show Answer & Explanation
Correct Answer: C
Substituting x = 3 into the function: f(3) = 2(3^2) - 4(3) + 1 = 18 - 12 + 1 = 11.
Q6
Medium
Which of the following equations represents a linear function?
A. y = x^2 + 3
B. y = 2x + 5
C. y = 3/x
D. y = x^3 - x
Show Answer & Explanation
Correct Answer: B
A linear function has the form y = mx + b, where m and b are constants. Option B fits this form, while others do not as they contain non-linear terms.
Q7
Medium
If the roots of the quadratic equation ax^2 + bx + c = 0 are 2 and -3, what is the value of a if b = 5 and c = 6?
A. 1
B. 2
C. 3
D. 4
Show Answer & Explanation
Correct Answer: A
Using Vieta's formulas, the sum of the roots (2-3) = -b/a equates to -5/a. Solving gives a = 1.
Q8
Hard
If the function f(x) = 3x^2 - 12x + 7 is transformed by shifting it 2 units to the right, what is the new function g(x)?
A. g(x) = 3(x - 2)^2 - 12(x - 2) + 7
B. g(x) = 3(x - 2)^2 - 6
C. g(x) = 3x^2 - 12x + 7 - 2
D. g(x) = 3(x - 2)^2 - 12x + 7
Show Answer & Explanation
Correct Answer: A
To shift a function to the right by 2 units, you replace x with (x - 2) in the function. Hence, g(x) = 3((x - 2)^2) - 12(x - 2) + 7.
Q9
Hard
Solve the equation 2x^3 - 3x^2 - 8x + 12 = 0 for the value of x that satisfies the condition x > 2.
A. 3
B. 2
C. 4
D. 1
Show Answer & Explanation
Correct Answer: A
To solve the polynomial equation, we can use synthetic division or trial and error. Testing x = 3, we find it satisfies the equation, making it the correct answer.
Q10
Hard
Solve the equation 2^(x+1) + 2^(x-1) = 10. What is the value of x?
A. 2
B. 1
C. 3
D. 0
Show Answer & Explanation
Correct Answer: A
Rewriting the given equation, we have 2^(x+1) + 2^(x-1) = 2 * 2^x + (1/2) * 2^x = (2 + 1/2) * 2^x = (5/2) * 2^x = 10, thus 2^x = 4, which gives x = 2.

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Algebra and Functions — Thanaweya Amma (Egypt) Thanaweya Mathematics Practice Questions Online

This page contains 132 practice MCQs for the chapter Algebra and Functions in Thanaweya Amma (Egypt) Thanaweya Mathematics. The questions are organized by difficulty — 37 easy, 67 medium, 28 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.