Unit 5 Advanced Worksheet

Algebra Basics & Patterns - Challenge Level - 20 Questions

Unit 5 Advanced Worksheet

Algebra Basics & Patterns

Challenge yourself with advanced algebra and pattern problems.

Question 1: If x = 8 and y = 5, what is 2x + y?

Answer: 0

2x + y = 2(8) + 5 = 16 + 5 = 21. Work with two variables and follow order of operations.

Question 2: If c = 7, what is 5c - 10? ___

Answer: 25

5c - 10 = 5(7) - 10 = 35 - 10 = 25. Multiply first, then subtract.

Question 3: A rectangle has length L and width 6. If the perimeter is 2L + 12, what does this represent?

Answer: 0

Perimeter = 2L + 2(6) = 2L + 12. This shows 2 times length plus 2 times width!

Question 4: Solve: 3m + 5 = 20. m = ___

Answer: 5

First subtract 5: 3m = 15. Then divide by 3: m = 5. Check: 3(5) + 5 = 20 ✓

Question 5: If n = 9, then 2n + n equals 3n.

Answer: True

True! 2n + n = 3n (combining like terms). When n = 9: 2(9) + 9 = 27 = 3(9) ✓

Question 6: Solve: 2x - 7 = 11. What is x?

Answer: 0

Add 7: 2x = 18. Divide by 2: x = 9. Check: 2(9) - 7 = 18 - 7 = 11 ✓

Question 7: A sequence follows the rule '3n + 2'. What is the 5th term? ___

Answer: 17

For position 5: 3(5) + 2 = 15 + 2 = 17. The 5th term is 17.

Question 8: Sam has three times as many marbles as Tom. If Tom has t marbles, write an expression for Sam's marbles.

Answer: 3t

'Three times as many' means multiply by 3: 3t marbles for Sam.

Question 9: What's the 10th term in the sequence: 4, 9, 14, 19...? (Rule: 5n - 1)

Answer: 0

Using rule 5n - 1: 5(10) - 1 = 50 - 1 = 49. The 10th term is 49.

Question 10: If 4y + 3 = 23, what is y? ___

Answer: 5

Subtract 3: 4y = 20. Divide by 4: y = 5. Check: 4(5) + 3 = 23 ✓

Question 11: A pattern grows: 1st term = 5, 2nd = 8, 3rd = 11. Write the rule as an expression using n for position.

Answer: 3n + 2

Pattern increases by 3, starts at 5. Rule: 3n + 2. Check: 3(1)+2=5, 3(2)+2=8, 3(3)+2=11 ✓

Question 12: Solve: x/2 + 6 = 10. What is x?

Answer: 0

Subtract 6: x/2 = 4. Multiply by 2: x = 8. Check: 8/2 + 6 = 4 + 6 = 10 ✓

Question 13: If the pattern doubles each time starting at 3, what's the 6th term? 3, 6, 12, 24, 48, ___

Answer: 96

Pattern: multiply by 2. After 48: 48 × 2 = 96. The 6th term is 96.

Question 14: The expressions 2x + 3x and 5x are equivalent for any value of x.

Answer: True

True! 2x + 3x = 5x (combining like terms). Try x = 4: 2(4)+3(4)=8+12=20, 5(4)=20 ✓

Question 15: A store sells shirts for $s each. You buy 4 shirts and pay $5 tax. Write expression for total cost.

Answer: 4s + 5

4 shirts at $s each: 4s. Plus $5 tax: 4s + 5 dollars total.

Question 16: In the table: 1→7, 2→11, 3→15, 4→19. What's the rule?

Answer: 0

Output increases by 4 each time, starting at 7. Rule: 4n + 3. Check: 4(1)+3=7, 4(2)+3=11 ✓

Question 17: Solve: 5p - 8 = 27. p = ___

Answer: 7

Add 8: 5p = 35. Divide by 5: p = 7. Check: 5(7) - 8 = 35 - 8 = 27 ✓

Question 18: Tom runs m miles Monday and twice as many Tuesday. Write expression for total miles for both days.

Answer: 3m

Monday: m miles. Tuesday: 2m miles. Total: m + 2m = 3m miles.

Question 19: Which number does NOT fit the pattern: 2, 5, 8, 11, 15, 17?

Answer: 0

Pattern adds 3: 2, 5, 8, 11, 14, 17. The number 15 doesn't fit; it should be 14!

Question 20: If a = 12 and b = 4, what is (a - b) ÷ 2? ___

Answer: 4

(a - b) ÷ 2 = (12 - 4) ÷ 2 = 8 ÷ 2 = 4. Work inside parentheses first!

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