Number and Algebra Practice Questions
IB (International Baccalaureate) · IB Math AI SL · 132 free MCQs with instant results and detailed explanations.
132
Total
40
Easy
67
Medium
25
Hard
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Sample Questions from Number and Algebra
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Q1
Easy
What is the value of 5x + 7 when x = 3?
A.
22
B.
15
C.
12
D.
18
Show Answer & Explanation
Correct Answer: A
Substituting x = 3 into the expression 5x + 7 gives 5(3) + 7 = 15 + 7 = 22.
Q2
Easy
What is the value of x in the equation 3x + 7 = 22?
A.
5
B.
7
C.
3
D.
9
Show Answer & Explanation
Correct Answer: A
To solve for x, subtract 7 from both sides to get 3x = 15, and then divide by 3 to find x = 5.
Q3
Easy
If a rectangular garden has a length that is twice its width, and its perimeter is 36 meters, what is the width of the garden?
A.
6 m
B.
9 m
C.
12 m
D.
3 m
Show Answer & Explanation
Correct Answer: A
Let the width be w. Then the length is 2w. The perimeter P = 2(length + width) = 2(2w + w) = 36. Simplifying gives 6w = 36, so w = 6 m.
Q4
Medium
If the sum of two numbers is 20 and their difference is 4, what are the two numbers?
A.
12 and 8
B.
10 and 10
C.
14 and 6
D.
16 and 4
Show Answer & Explanation
Correct Answer: A
Let the two numbers be x and y. From the problem, we have x + y = 20 and x - y = 4. Solving these equations simultaneously gives x = 12 and y = 8, thus A is correct.
Q5
Medium
What is the solution to the quadratic equation x² - 5x + 6 = 0?
A.
1 and 6
B.
2 and 3
C.
3 and 5
D.
0 and 6
Show Answer & Explanation
Correct Answer: B
To factor the quadratic equation x² - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 fit, so (x - 2)(x - 3) = 0 gives solutions x = 2 and x = 3. Thus, B is correct.
Q6
Medium
If a sequence is defined by the formula a_n = 3n + 2, what is the 5th term of the sequence?
A.
15
B.
17
C.
20
D.
14
Show Answer & Explanation
Correct Answer: B
To find the 5th term a_5, substitute n = 5 into the formula: a_5 = 3(5) + 2 = 15 + 2 = 17. Therefore, B is the correct answer.
Q7
Medium
If the quadratic function f(x) = ax^2 + bx + c has its vertex at the point (2, -3), what can be said about the coefficients a, b, and c?
A.
a must be positive.
B.
b must equal 0.
C.
c must equal -3.
D.
The vertex form must be used.
Show Answer & Explanation
Correct Answer: C
Since the vertex of the function is at (2, -3), this means that when x=2, f(2) = -3, indicating that c = -3 in the standard form.
Q8
Hard
A quadratic function is defined as f(x) = ax^2 + bx + c. If the vertex of this function is at the point (3, -4) and it opens upwards, what is the value of 'a' if it passes through the point (5, 0)?
A.
2
B.
1
C.
0.5
D.
1.5
Show Answer & Explanation
Correct Answer: A
To find 'a', we use the vertex form of the quadratic function, which can be expressed as f(x) = a(x - 3)^2 - 4. Plugging in the point (5, 0), we get 0 = a(5 - 3)^2 - 4. Solving for 'a' gives a = 2.
Q9
Hard
A quadratic function is given by f(x) = ax^2 + bx + c. If the vertex of the parabola represented by this function lies on the line y = 2x + 3, and the function has a minimum value of 5, what is the value of c if a = 1 and b = -4?
A.
5
B.
6
C.
7
D.
8
Show Answer & Explanation
Correct Answer: B
To find c, we need to use the vertex formula x = -b/(2a) which gives x = 2. Substituting x = 2 into the line equation y = 2(2) + 3 = 7. The minimum value of the function is 5, which means when we substitute x = 2 into f(x) = 1(2^2) - 4(2) + c = 5, we can solve for c, yielding c = 6.
Q10
Hard
If the series 2, 5, 10, 17, ... continues, which expression gives the nth term of the series?
A.
n^2 + 1
B.
n^2 + n
C.
n^2 - n + 1
D.
n^2 + 2n - 1
Show Answer & Explanation
Correct Answer: C
The differences between consecutive terms are 3, 5, 7, ..., which are successive odd numbers. This implies that the sequence can be expressed in the form of n^2 - n + 1 for n = 1, 2, 3, ... Hence, option C is the correct representation of the nth term.
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Number and Algebra — IB (International Baccalaureate) IB Math AI SL Practice Questions Online
This page contains 132 practice MCQs for the chapter Number and Algebra in IB (International Baccalaureate) IB Math AI SL. The questions are organized by difficulty — 40 easy, 67 medium, 25 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.