Year 7 Mathematics | Victorian Curriculum 2.0
Algebraic expressions
Topic 05 | Number & Algebra | Answer key

Tier 1: basic skills

Fluency

Fluency

    1. n+7n + 7
    2. 2m−52m - 5
    3. 4x4x
    4. y2+3\dfrac{y}{2} + 3
    5. −7-7
    6. 7x7x
    7. 4y4y
    8. 8a+b8a + b
    9. 5p+55p + 5
    10. 5x+4y+45x + 4y + 4
    11. 1414
    12. 1313
    13. 1717
    14. 2x+102x + 10
    15. 4y−124y - 12
    16. −3a−6-3a - 6
    17. 12m−612m - 6
    18. 2x+32x + 3
    19. 3x+113x + 11
    20. 2a+52a + 5

Tier 2: mixed practice

Reasoning

Mixed practice

    1. 6x+106x + 10. Method: 4x+12+2x−24x + 12 + 2x - 2.
    2. 7y−177y - 17. Method: 10y−5−3y−1210y - 5 - 3y - 12.
    3. 5m−25m - 2. Method: 7m+4−2m−67m + 4 - 2m - 6.
    4. 4141. Method: 3(16)−8+1=48−8+13(16) - 8 + 1 = 48 - 8 + 1.
    5. 44. Method: (3+(−1))2=22(3 + (-1))^2 = 2^2.
    6. −7x+6-7x + 6. Method: −6x+8−x−2-6x + 8 - x - 2.
    7. 2a−32a - 3. Method: divide each term.
    8. Perimeter =6x+2= 6x + 2. Method: 2(2x+1)+2x=4x+2+2x2(2x + 1) + 2x = 4x + 2 + 2x.
    9. 0.60n+0.40m0.60n + 0.40m (in dollars).
    10. 77. Method: 5+7=125 + 7 = 12.
    11. 12ab12ab. Method: 3×4×a×b3 \times 4 \times a \times b.
    12. 4x4x. Method: cancel the yys, then 12÷312 \div 3.

Tier 3: explain and spot the mistake

Reasoning

Explain and spot the mistake

    1. Wrong. 33 and 2x2x are not like terms - one is a constant, the other has a variable - so they cannot be combined into a single term. The simplest form is 3+2x3 + 2x (or 2x+32x + 3).
    2. They have different variable parts: xx vs x2x^2. Try x=2x = 2: 3x=63x = 6 but 3x2=123x^2 = 12. If they were like terms they would always be equal, but they aren’t.
    3. Wrong. −4(x−3)=−4x+12-4(x - 3) = -4x + 12. Leo forgot that −4×−3=+12-4 \times -3 = +12, not −12-12. Two negatives make a positive.
    4. Many possible answers, e.g. 4x4x, 2x+62x + 6, x2+3x^2 + 3, or 5x−35x - 3 (each gives 1212 when x=3x = 3).
    5. Not equal in general. 2(a+3)=2a+62(a + 3) = 2a + 6, which is not the same as 2a+32a + 3. Try a=1a = 1: left side =8= 8, right side =5= 5. The 22 must distribute to every term inside the bracket.

Using everyday formulas - answers

Fluency

Substitution into formulas

    1. Area 6060 cm^2; perimeter 3434 cm.
    2. 14×6+7=84+7=9114 \times 6 + 7 = 84 + 7 = 91 points.
    3. Collingwood 9×6+13=679 \times 6 + 13 = 67; Melbourne 11×6+5=7111 \times 6 + 5 = 71. Melbourne won by 44 points.
    4. $492. Method: 360+1.5×22×4=360+132360 + 1.5 \times 22 \times 4 = 360 + 132.
    5. D=7.875D = 7.875 g/cm^3. Method: 504÷64504 \div 64.
    6. 175175 bpm. Method: 220−45220 - 45.
    7. 200200 km. Method: 80×2.580 \times 2.5.
    8. 1515 km/h. Method: 45÷345 \div 3.
    9. 2020 degC. Method: 59(68−32)=59×36=20\tfrac{5}{9}(68 - 32) = \tfrac{5}{9} \times 36 = 20.

Tier 4: real-world problems

Problem solving

Real-world problems

    1. x+15x + 15; $27. Method: −5+20=+15-5 + 20 = +15; then 12+1512 + 15.
    2. 20+0.10t20 + 0.10t dollars; $35. Method: 20+0.10×15020 + 0.10 \times 150.
    3. Length =2w+3= 2w + 3; perimeter =6w+6= 6w + 6. Method: P=2(L+W)=2(2w+3+w)P = 2(L + W) = 2(2w + 3 + w).
    4. Cost =4.50+2k= 4.50 + 2k; $28.50. Method: 4.50+2×124.50 + 2 \times 12.
    5. 5x−425x - 42; $8. Method: 5×10=505 \times 10 = 50; 50−42=850 - 42 = 8.
    6. Time =Vr= \dfrac{V}{r} minutes; 400400 min (66 h 4040 min). Method: 60 000÷15060\,000 \div 150.
    7. 25+0.08t25 + 0.08t dollars; $39.40. Method: 25+0.08×18025 + 0.08 \times 180.
    8. 59+15w59 + 15w. Exceeds $200 when 15w>14115w > 141, so when w≥10w \geq 10 - first exceeded at the end of week 1010.
    9. $36 for a 240240 km trip. New formula: C=0.30dC = 0.30 d.
    10. HRmax⁡=208HR_{\max} = 208 bpm. 50%50\% zone ≈104\approx 104 bpm; 70%70\% zone ≈146\approx 146 bpm. Target zone: roughly 104104-146146 bpm.
Year 7 Mathematics study companion | Answer key