Free Year 7 One-variable linear equations Practice | Skillo

Question 1 — Easy

Priya is arranging tables for a school event. She notices a growing pattern: 1 table seats 6 people, 2 tables joined end-to-end seat 10 people, and 3 tables joined end-to-end seat 14 people. She records this as a table of values and plots the relationship on a Cartesian plane with the number of tables (n) on the horizontal axis and the number of people seated (p) on the vertical axis. Which algebraic rule correctly describes this linear relationship?

Answer: Each time a table is added, 4 extra people can be seated (the difference between consecutive values is 4), so the coefficient of n is 4. When n = 1, p = 6, so 4(1) + b = 6 gives b = 2, confirming the rule p = 4n + 2. Option A (p = 6n) incorrectly multiplies the first value by n. Option C (p = n + 4) gives only p = 5 when n = 1, which is wrong. Option D (p = 5n + 1) gives p = 6 for n = 1 but p = 11 for n = 2, not 10.

Question 2 — Medium

Kofi is arranging chairs for a school assembly. He places the same number of chairs in each row. After setting up 6 rows, he notices that if he adds 4 more chairs to his total, he will have exactly 52 chairs. The equation representing this situation is 6c + 4 = 52, where c is the number of chairs in each row. Find the value of c.

Answer: Subtracting 4 from both sides gives 6c = 48, then dividing both sides by 6 gives c = 8. Verifying: 6(8) + 4 = 48 + 4 = 52, which is correct. Option A gives 6(9) + 4 = 58, not 52; Option C gives 6(7) + 4 = 46, not 52; Option D results from dividing 48 by 1 or confusing 6c = 48 with c = 48.

Question 3 — Hard

Tom scored the following marks on five science tests: 72, 85, 68, 91, and 74. His teacher says he needs a mean of at least 78 to receive a commendation. What is the minimum mark Tom needs on a sixth test to achieve this mean?

Answer: Required total for 6 tests = 78 × 6 = 468. Current total = 72 + 85 + 68 + 91 + 74 = 390. Minimum sixth mark = 468 − 390 = 78.