Secondary 1 Mathematics Algebra Functions Quiz

Secondary 1 Mathematics Quiz - Algebra Functions (Answer Key)

Total Marks: 40
Topic: Algebra Functions

Section A: Algebraic Expressions and Evaluation

1. [2 marks] Evaluate $3x - 2y$ when $x = 4$ and $y = 5$.
Answer: $2$
Working:
Substitute $x = 4$, $y = 5$:
$3(4) - 2(5) = 12 - 10 = 2$
Teaching note: Substitution means replacing the letter with its given number. Multiply before subtracting.

2. [2 marks] Simplify: $2(3a - 4) + 4a$
Answer: $10a - 8$
Working:
Expand: $2 \times 3a = 6a$, $2 \times (-4) = -8$ → $6a - 8 + 4a$
Combine like terms: $6a + 4a = 10a$ → $10a - 8$
Common mistake: Forgetting to multiply both terms inside the bracket.

3. [2 marks] "5 more than twice a number $n$"
Answer: $2n + 5$
Working: Twice $n$ is $2n$; 5 more is $+5$.
Teaching note: "More than" means add after the multiplication.

4. [2 marks] Simplify: $\dfrac{2x - (x + 2)}{3}$
Answer: $\dfrac{x - 2}{3}$
Working: Inside numerator: $2x - x - 2 = x - 2$. So $\frac{x - 2}{3}$.
Note: The minus sign before bracket changes $+2$ to $-2$.

5. [2 marks] Factor $6m + 9n$
Answer: $3(2m + 3n)$
Working: HCF of 6 and 9 is 3. $6m ÷ 3 = 2m$, $9n ÷ 3 = 3n$.
Teaching note: Extract common factor by dividing each term.

Section B: Patterns and nth Term

6. [2 marks] Sequence 3, 7, 11, 15, …
Answer: $4n - 1$
Working: Difference = 4 each time → $4n$. For $n=1$: $4(1)-1=3$. So $4n - 1$.
Teaching note: Linear pattern with constant difference $d$ has nth term $dn + c$.

7. [2 marks] $n$th term $= 4n - 1$, find 6th term
Answer: $23$
Working: $4(6) - 1 = 24 - 1 = 23$.

8. [2 marks] Taxi: \3$fixed +$$2$per km for$d$km **Answer:**$F = 2d + 3$**Working:** Per km cost =$2 \times d = 2d$; add fixed 3.

9. [2 marks] Table x=1,2,3 → y=5,8,11
Answer: $y = 3x + 2$
Working: Difference in y = 3 per x → $3x$. For x=1, y=5 → $3(1)+2=5$. So $y = 3x + 2$.

10. [2 marks] Rectangle length $(x+3)$, width $x$
Answer: $4x + 6$ cm
Working: Perimeter = $2(\text{length} + \text{width}) = 2(x+3 + x) = 2(2x+3) = 4x+6$.

Section C: Functions and Graphs

11. [2 marks] $y = 2x + 1$, $x = 3$
Answer: $y = 7$
Working: $2(3)+1 = 6+1 = 7$.

12. [2 marks] Gradient of $y = -3x + 4$
Answer: $-3$
Teaching note: In $y = ax + b$, $a$ is gradient.

13. [2 marks] Points (0,2) and (2,6)
Answer: Gradient = $2$
Working: Gradient = $\frac{6-2}{2-0} = \frac{4}{2} = 2$.
Image note: Grid must show line through given points; rise 4, run 2.

14. [2 marks] $f(x) = 5 - x$, find $f(2)$
Answer: $3$
Working: $5 - 2 = 3$.

15. [2 marks] Line through (0,-1) and (1,1)
Answer: $y = 2x - 1$
Working: Gradient = $\frac{1 - (-1)}{1-0} = 2$. y-intercept = -1. So $y = 2x - 1$.

Section D: Equations from Word Problems

16. [2 marks] "p increased by 7 is 20"
Answer: $p + 7 = 20$
Teaching note: "Increased by" → add; "is" → equals.

17. [2 marks] Solve $\frac{x}{3} + \frac{x-2}{4} = 3$
Answer: $x = 6$
Working:
LCM of 3 and 4 is 12. Multiply all terms:
$12 \cdot \frac{x}{3} + 12 \cdot \frac{x-2}{4} = 12 \cdot 3$
$4x + 3(x-2) = 36$
$4x + 3x - 6 = 36$
$7x = 42$ → $x = 6$.

18. [2 marks] $q$ pens at \2$+ book$$5$=$$17$**Answer:**$q = 6$**Equation:**$2q + 5 = 17$**Working:**$2q = 12$→$q = 6$.

19. [2 marks] Solve $\frac{3}{x-2} = 6$
Answer: $x = 2.5$
Working: Multiply both sides by $(x-2)$: $3 = 6(x-2)$
$3 = 6x - 12$ → $6x = 15$ → $x = 2.5$.

20. [2 marks] $r$ red + 4 blue = 10
Answer: $r = 6$
Equation: $r + 4 = 10$ → $r = 6$.