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Number and Algebra Practice Questions

IB (International Baccalaureate) · IB Math AA HL · 145 free MCQs with instant results and detailed explanations.

145
Total
47
Easy
72
Medium
26
Hard

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Sample Questions from Number and Algebra

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Q1
Easy
If a = 2 and b = 3, what is the value of 4a + 5b?
A. 23
B. 20
C. 18
D. 21
Show Answer & Explanation
Correct Answer: A
Substituting a = 2 and b = 3 into the expression gives 4(2) + 5(3) = 8 + 15 = 23.
Q2
Easy
Which of the following is a polynomial?
A. 3x^2 + 2x - 1
B. 1/x + 2
C. √x + 3
D. log(x) + 1
Show Answer & Explanation
Correct Answer: A
A polynomial is an expression consisting of variables raised to whole number powers. 3x^2 + 2x - 1 fits this criterion.
Q3
Easy
If a = 3 and b = 5, what is the result of (a^2 + b^2) / (ab)?
A. 34/15
B. 34/8
C. 34/10
D. 34/12
Show Answer & Explanation
Correct Answer: A
Calculating a^2 gives 9, b^2 gives 25. So, (9 + 25) / (3*5) = 34 / 15.
Q4
Medium
What is the value of x in the equation 4^(x+1) = 64?
A. 1
B. 2
C. 3
D. 4
Show Answer & Explanation
Correct Answer: B
To solve the equation, rewrite 64 as 4^3. Therefore, 4^(x+1) = 4^3 leads to x+1 = 3, giving x = 2.
Q5
Medium
If a quadratic function is given by f(x) = ax^2 + bx + c, which of the following conditions indicates that the function opens upwards?
A. a > 0
B. a < 0
C. b = 0
D. c = 0
Show Answer & Explanation
Correct Answer: A
A quadratic function opens upwards if the coefficient of x^2 (a) is positive. Thus, if a > 0, the parabola opens upwards.
Q6
Medium
A sequence is defined by the recurrence relation a_n = 3a_(n-1) - 2, with a_1 = 1. What is a_4?
A. 4
B. 7
C. 10
D. 12
Show Answer & Explanation
Correct Answer: C
Calculate a_2 = 3(1) - 2 = 1; a_3 = 3(1) - 2 = 1; a_4 = 3(1) - 2 = 10. Therefore, a_4 = 10.
Q7
Medium
Which of the following sets of numbers is a solution to the system of equations: 2x + 3y = 12 and 4x - y = 2?
A. (2, 2)
B. (3, 0)
C. (0, 4)
D. (1, 3)
Show Answer & Explanation
Correct Answer: A
Substituting (2, 2) into both equations satisfies them. Therefore, (2, 2) is the solution.
Q8
Hard
If the roots of the quadratic equation ax² + bx + c = 0 are given as r₁ and r₂, which of the following expressions equals (r₁ + r₂)² - 4r₁r₂?
A. b²/a²
B. b² - 4ac
C. 4c/a
D. a² + b² - 4ac
Show Answer & Explanation
Correct Answer: B
The expression (r₁ + r₂)² - 4r₁r₂ is derived from the relationships between the roots and coefficients of the equation, which gives us the discriminant b² - 4ac. Thus, the correct answer is option B.
Q9
Hard
Consider the sequence defined by a₁ = 3 and aₙ = 2aₙ₋₁ + 1 for n > 1. What is the explicit formula for aₙ?
A. 3 * 2^(n-1) - 1
B. 2^n + 1
C. 3 * 2^n - 3
D. 2^n - 1
Show Answer & Explanation
Correct Answer: A
The recursion formula defines an exponential growth in the sequence. By solving the recursion, we find that aₙ can be expressed as 3 * 2^(n-1) - 1, making option A the correct choice.
Q10
Hard
If the quadratic equation ax^2 + bx + c = 0 has roots that are both real and equal, which of the following must be true?
A. b^2 - 4ac = 0
B. b^2 - 4ac > 0
C. a > 0
D. c > 0
Show Answer & Explanation
Correct Answer: A
For a quadratic equation to have real and equal roots, the discriminant (b^2 - 4ac) must be equal to zero. This indicates that there is exactly one solution for the equation.

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Number and Algebra — IB (International Baccalaureate) IB Math AA HL Practice Questions Online

This page contains 145 practice MCQs for the chapter Number and Algebra in IB (International Baccalaureate) IB Math AA HL. The questions are organized by difficulty — 47 easy, 72 medium, 26 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.