Part 2 — Answer key

Compare your answers after you have finished Part 1.

1. In this maths quiz, suppose the quz of a number n is defined as quz(n) = n + 4. What is quz(3)?
   7
2. The function quz(n) = n + 3 is a linear function of n.
   True
3. In a set of common math problems, the function quz is defined by quz(x) = 3x − 2. If quz(x) = 10, what is the value of x?
   4
4. A quz transform is defined by y = quz(x) = 2x + 5. Which expression correctly gives x in terms of y?
   (y − 5) / 2
5. In a set of example math questions, quz(n) is defined as quz(n) = 5n + 2. If quz(n) = 27, what is n?
   5
6. If quz(x) = x², then for all real numbers a and b, quz(a + b) equals quz(a) + quz(b).
   False
7. If quz(x) = 3x − 7, then its inverse function is quz⁻¹(y) = 3y + 7.
   False
8. In a simple quz rule used for basic math questions, quz(n) = 2n + 1. Which of the following evaluations are correct? Select all that apply.
   quz(2) = 5; quz(4) = 9; quz(3) = 7
9. A data engineer uses a quz function in a pipeline: first apply quz(x) = x², then add 1 to the result. For an input of 3, what final value does the pipeline output?
   10
10. A sequence is defined using a simple quz rule: a₁ = 2 and for n > 1, aₙ = quz(aₙ₋₁) with quz(x) = x + 3. In this maths quiz example, what is a₃?
    8
11. A pricing rule uses a quz function quz(p) = 1.2p + 5 to model tax and a service fee on price p. For a base price of 50, what is the total charge?
    65
12. A quz scoring rule in a maths quiz with answers is given by quz(s) = 0.5s + 10. If a student's raw score increases from 60 to 68, by how much does their quz score increase?
    4
13. For a quz-based grading rule g(s) = 2s + 10, increasing a student's raw score by 5 points will always increase their quz grade by exactly 10 points.
    True
14. Let quz(x) = x + 2 and r(x) = 3x. You want the value of r(quz(4)) as part of a technical quz computation. Which expressions are equal to r(quz(4))? Select all that apply.
    3 · (4 + 2); r(4) + r(2)
15. A sequence is generated by repeated use of a quz function: quz(x) = x + 5, a₁ = 0, and aₙ = quz(aₙ₋₁) for n > 1. Which statements about the sequence are correct? Select all that apply.
    a₂ = 5; a₃ = 10
16. You want to simplify the expression quz(3x + 1), where quz(t) = 2t − 5, as part of a step-by-step quz math problem. Arrange these steps in the correct order to obtain the simplified expression in terms of x.
    Correct order: Substitute 3x + 1 for t in quz(t) → Multiply 3x + 1 by 2 → Distribute to get 6x + 2 → Subtract 5 to obtain 6x − 3
17. Let quz(x) = 2x − 1 and g(x) = x + 4. A program computes quz(g(3)) as part of a technical quz drill. What value does it obtain?
    13
18. A sequence in a quz-based maths quiz is defined by a₁ = 1 and aₙ = quz(aₙ₋₁) for n > 1, where quz(x) = 2x + 1. What is the value of a₄?
    15
19. A shop uses a quz rule to compute final prices: first apply quz(p) = 0.9p to give a 10% discount, then add a fixed fee of 5. For an item with original price 80, what is the final charge?
    77
20. Let quz(t) = 4t − 3. A system accepts inputs t only if 5 ≤ quz(t) ≤ 13. Which of the following t values are accepted? Select all that apply.
    4; 3; 2
21. A developer defines quz(x) = x² − 1 and then creates h(x) = quz(quz(x)) to reuse the quz function. In this advanced quz math question, what is h(3)?
    63
22. A data scientist designs a linear quz transformation q(x) = ax + b to rescale a metric. They require q(0) = 10 and q(50) = 100. In this advanced maths quiz item, which x values will produce scores between 40 and 70 inclusive? Select all that apply.
    30; 20; 25