Secondary 1 Mathematics Algebra Functions Quiz

Secondary 1 Mathematics Quiz - Algebra Functions (Answer Key)

---

Section A: Short Answer Questions [20 marks]

1. Solve the inequality $-3x > 12$ and illustrate the solution on the number line. Answer: $x < -4$ Working:

• $-3x > 12$
• Divide both sides by $-3$ (reverse inequality): $x < -4$
• Number line: Open circle at $-4$, arrow pointing left Marks: 1 mark for correct solution, 1 mark for correct number line representation

2. Factorize completely: $6xy + 9x - 4y - 6$ Answer: $(2y + 3)(3x - 2)$ Working:

• Group terms: $(6xy + 9x) + (-4y - 6)$
• Factor each group: $3x(2y + 3) - 2(2y + 3)$
• Factor out common factor: $(2y + 3)(3x - 2)$ Marks: 2 marks for correct factorization (1 mark for partial working)

3. If $f(x) = 3x - 7$, find the value of $f(-2)$. Answer: $f(-2) = -13$ Working: $f(-2) = 3(-2) - 7 = -6 - 7 = -13$ Marks: 2 marks for correct answer (1 mark for substitution)

4. Write down an algebraic expression for "5 more than twice a number $n$". Answer: $2n + 5$ Working: "Twice a number $n$" = $2n$, "5 more than" = $+ 5$ Marks: 2 marks for correct expression

5. Solve the equation $\frac{2x + 1}{3} = 5$. Answer: $x = 7$ Working:

• Multiply both sides by 3: $2x + 1 = 15$
• Subtract 1: $2x = 14$
• Divide by 2: $x = 7$ Marks: 2 marks for correct answer (1 mark for correct method)

---

Section B: Problem Solving [10 marks]

6. Given that $y = 4x - 3$, find the value of $x$ when $y = 9$. Answer: $x = 3$ Working:

• Substitute $y = 9$: $9 = 4x - 3$
• Add 3: $12 = 4x$
• Divide by 4: $x = 3$ Marks: 2 marks for correct answer (1 mark for substitution)

7. Simplify: $3(2a - 4) - 2(a + 1)$ Answer: $4a - 14$ Working:

• Expand: $6a - 12 - 2a - 2$
• Collect like terms: $4a - 14$ Marks: 2 marks for correct simplification (1 mark for expansion)

8. If $g(t) = t^2 + 2t$, calculate $g(3)$. Answer: $g(3) = 15$ Working: $g(3) = 3^2 + 2(3) = 9 + 6 = 15$ Marks: 2 marks for correct answer (1 mark for substitution)

9. Solve for $p$: $2p - 7 = 3p + 1$ Answer: $p = -8$ Working:

• Subtract $2p$: $-7 = p + 1$
• Subtract 1: $p = -8$ Marks: 2 marks for correct answer (1 mark for correct rearrangement)

10. Express $x$ in terms of $y$ from the equation $3x + 2y = 12$. Answer: $x = \frac{12 - 2y}{3}$ or $x = 4 - \frac{2y}{3}$ Working:

• Subtract $2y$: $3x = 12 - 2y$
• Divide by 3: $x = \frac{12 - 2y}{3}$ Marks: 2 marks for correct rearrangement

---

Section C: Application Problems [6 marks]

11. Car hire problem (a) Answer: $C = 30 + 0.5d$ Marks: 1 mark for correct formula

(b) Answer: C = 30 + 0.5(85) = 30 + 42.5 = \72.50$ Marks: 1 mark for correct calculation

12. Function $h(x) = 2x^2 - 5x + 1$ (a) Answer: $h(0) = 1$ Working: $h(0) = 2(0)^2 - 5(0) + 1 = 1$ Marks: 1 mark

(b) Answer: $h(4) = 13$ Working: $h(4) = 2(16) - 5(4) + 1 = 32 - 20 + 1 = 13$ Marks: 1 mark

13. Consecutive integers problem Answer: The three integers are 15, 16, and 17 Working:

• Let the integers be $n$, $n+1$, $n+2$
• Equation: $n + (n+1) + (n+2) = 48$
• Simplify: $3n + 3 = 48$
• Solve: $3n = 45$, so $n = 15$ Marks: 1 mark for equation setup, 1 mark for correct solution

14. Rectangular garden Answer: $x = 4$ Working:

• Perimeter = $2[(2x + 3) + (x - 1)] = 2(3x + 2) = 6x + 4$
• $6x + 4 = 28$, so $6x = 24$, therefore $x = 4$ Marks: 1 mark for perimeter expression, 1 mark for solving equation

15. Solve $2(x - 3) \leq 4x + 2$ Answer: $x \geq -4$ Working:

• Expand: $2x - 6 \leq 4x + 2$
• Rearrange: $-6 - 2 \leq 4x - 2x$
• Simplify: $-8 \leq 2x$
• Divide by 2: $-4 \leq x$ or $x \geq -4$
• Number line: Closed circle at $-4$, arrow pointing right Marks: 1 mark for algebra, 1 mark for number line

---

Section D: Extended Response [4 marks]

16. Mobile phone plan Answer: $C(t) = 25 + 0.15t$ Marks: 1 mark

17. Find $a$ such that $f(a) = 7$ where $f(x) = \frac{x + 4}{2}$ Answer: $a = 10$ Working:

• $\frac{a + 4}{2} = 7$
• Multiply by 2: $a + 4 = 14$
• Subtract 4: $a = 10$ Marks: 1 mark for correct solution

18. Factorize: $12ab - 8a + 15b - 10$ Answer: $(3b - 2)(4a + 5)$ Working:

• Group: $(12ab - 8a) + (15b - 10)$
• Factor: $4a(3b - 2) + 5(3b - 2)$
• Factor out: $(3b - 2)(4a + 5)$ Marks: 1 mark for correct factorization

19. Find number of text messages when total cost is \67$**Answer:**$t = 280$ text messages Working:

• $67 = 25 + 0.15t$
• $42 = 0.15t$
• $t = 280$ Marks: 1 mark for correct calculation

20. Solve $3(2y - 1) = 2(y + 5) + 1$ and verify Answer: $y = 3$ Working:

• Expand: $6y - 3 = 2y + 10 + 1$
• Simplify: $6y - 3 = 2y + 11$
• Solve: $4y = 14$, so $y = \frac{7}{2} = 3.5$
• Verification: LHS = $3(2(3.5) - 1) = 3(6) = 18$, RHS = $2(3.5 + 5) + 1 = 2(8.5) + 1 = 18$ ✓ Marks: 1 mark for solving, 1 mark for verification

---

Total: 40 marks

Marking Notes:

• Award partial marks for correct method even if final answer is incorrect
• Deduct marks for arithmetic errors but not method errors
• Accept equivalent forms of algebraic expressions
• Number line representations must show correct direction and circle type (open/closed)