Year 7 Mathematics · Unit 2

Patterns and Algebra Synthesis

Lesson 20 Worksheet
Name
Date
Class
Section 1, Skill Practice

Q1. Evaluate each expression when a = 4, b = −2, c = 3.

(a) a + b + c     (b) 2a − b     (c) a2 − c2     (d) 3b + c2     (e) (a + b)2

Q2. Solve each equation. Show all working.

(a) 3x + 7 = 22     (b) 2(x − 4) = 10     (c) 5x − 3 = 2x + 12

(d) x/4 + 2 = 7     (e) 3(2x + 1) = 4x + 9

Q3. Simplify each expression using index laws.

(a) 45 × 43     (b) x8 ÷ x5     (c) (23)4

(d) 3a2 × 4a5     (e) 10m6 ÷ 2m2

Section 2, Problem Solving

Q4. A pattern of squares is made from matchsticks. Pattern 1 uses 4 matchsticks, Pattern 2 uses 7, Pattern 3 uses 10.

(a) Draw Pattern 4 and state how many matchsticks it uses. 1 mark

(b) Write a rule for the number of matchsticks M in Pattern n. 1 mark

(c) How many matchsticks are in Pattern 20? 1 mark

(d) Which pattern uses 85 matchsticks? 1 mark

Q5. A shop sells notebooks for $3 each and pens for $2 each. Mia buys n notebooks and p pens.

(a) Write an expression for the total cost. 1 mark

(b) If Mia spends $26 and buys 4 notebooks, how many pens does she buy? 2 marks

(c) If Mia buys twice as many pens as notebooks and spends $21, how many of each does she buy? 2 marks

Section 3, Extended Response

Q6. Reflect on your learning in this unit.

(a) Describe a real-world situation where you would use algebra to solve a problem. 1 mark

(b) Explain the difference between an expression and an equation. 2 marks

(c) A student says: "If 2x = 10, then x must be greater than 10." Explain why this is incorrect. 1 mark

(d) Design your own word problem that can be solved using a two-step equation. Write the equation and the solution. 2 marks

Answer Key

Q1. (a) 5   (b) 10   (c) 7   (d) 3   (e) 4

Q2. (a) x = 5   (b) x = 9   (c) x = 5   (d) x = 20   (e) x = 3

Q3. (a) 48   (b) x3   (c) 212   (d) 12a7   (e) 5m4

Q4. (a) 13 matchsticks   (b) M = 3n + 1   (c) 3(20)+1 = 61   (d) 3n+1=85, 3n=84, n=28

Q5. (a) C = 3n + 2p   (b) 3(4)+2p=26, 12+2p=26, 2p=14, p=7 pens   (c) p=2n, 3n+2(2n)=21, 7n=21, n=3 notebooks, p=6 pens

Q6. (a) Open-ended (e.g. budgeting, calculating distances, comparing prices).   (b) Expression has no equals sign (represents a value); equation has an equals sign (states two expressions are equal, can be solved).   (c) If 2x = 10, dividing both sides by 2 gives x = 5, which is less than 10.   (d) Open-ended. Example: "A plumber charges $50 plus $30 per hour. The total bill is $140. How many hours did they work?" Equation: 50 + 30h = 140. Solution: h = 3 hours.

hscscience.com.au · Worksheet for Lesson 20 · Year 7 Unit 2: Algebra
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