Unit 10 · Class 7 IB MYP · MCQ Test
Patterns & Functions MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Patterns & Functions — MCQ Questions
1The sequence of numbers 4, 9, 14, 19, ... continues in the same pattern. What is the next number in the sequence?
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Answer: 24
Hint: Examine the difference between consecutive terms to identify the pattern.
Solution:
Step 1: Find the difference between consecutive terms. 9 - 4 = 5, 14 - 9 = 5, 19 - 14 = 5.
Step 2: The pattern is to add 5 to the previous term.
Step 3: Add 5 to the last given term, 19. So, 19 + 5 = 24.
2A student, Clara, claims that the rule for the sequence 2, 5, 8, 11, ... is 'multiply the term number by 3, then subtract 1'. Which statement about Clara's rule is true?
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Answer: Clara's rule is correct for all terms.
Hint: Test Clara's rule with the first few terms of the sequence to see if it holds true for each one.
Solution:
Step 1: Test the first term (n=1). Clara's rule: (1 × 3) - 1 = 3 - 1 = 2. This matches the first term of the sequence.
Step 2: Test the second term (n=2). Clara's rule: (2 × 3) - 1 = 6 - 1 = 5. This matches the second term of the sequence.
Step 3: Test the third term (n=3). Clara's rule: (3 × 3) - 1 = 9 - 1 = 8. This matches the third term of the sequence.
Step 4: Since the rule works for the first three terms, it is correct for all terms in this arithmetic sequence.
3A linear pattern starts with 6 and increases by 4 each time. What is the 5th term in this pattern?
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Answer: 22
Hint: Write out the first few terms of the sequence by repeatedly adding the common difference.
Solution:
Step 1: The first term is 6.
Step 2: The pattern increases by 4 each time. So, the terms are: Term 1 = 6
Step 3: Term 2 = 6 + 4 = 10; Term 3 = 10 + 4 = 14; Term 4 = 14 + 4 = 18.
Step 4: Term 5 = 18 + 4 = 22.
4A small café in Paris charges for coffee based on the number of sugar packets requested. The table below shows the cost (C) in Euros (€) for different numbers of sugar packets (S). If the pattern continues, what is the cost for 4 sugar packets?
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Answer: €2.80
Hint: Look for a consistent change in cost as the number of sugar packets increases. This will help you find the rule.
Solution:
Step 1: Analyze the given table values. For S=0, C=€2.00. For S=1, C=€2.20. For S=2, C=€2.40.
Step 2: Find the difference in cost for each additional sugar packet. €2.20 - €2.00 = €0.20. €2.40 - €2.20 = €0.20. The cost increases by €0.20 for each sugar packet.
Step 3: Continue the pattern for 3 and 4 sugar packets. For S=3, C = €2.40 + €0.20 = €2.60.
Step 4: For S=4, C = €2.60 + €0.20 = €2.80.
5An input-output machine follows the rule: 'Multiply the input by 4, then subtract 3'. If the input is 7, what is the output?
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Answer: 25
Hint: Follow the operations in the rule in the correct order, applying them to the given input.
Solution:
Step 1: The input is 7.
Step 2: First operation: Multiply the input by 4. So, 7 × 4 = 28.
Step 3: Second operation: Subtract 3 from the result. So, 28 - 3 = 25.
Step 4: The output is 25.
6Another input-output machine follows the rule: 'Add 5 to the input, then divide by 2'. If the output is 8, what was the original input?
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Answer: 11
Hint: To find the input, you need to work backward through the machine's rule, performing the inverse operations in reverse order.
Solution:
Step 1: The output is 8. The last operation was 'divide by 2'.
Step 2: To reverse 'divide by 2', multiply by 2. So, 8 × 2 = 16.
Step 3: The first operation was 'Add 5 to the input'. To reverse 'Add 5', subtract 5. So, 16 - 5 = 11.
Step 4: The original input was 11.
7A pattern is formed using matchsticks. Figure 1 uses 3 matchsticks, Figure 2 uses 5 matchsticks, and Figure 3 uses 7 matchsticks. If this linear pattern continues, how many matchsticks will be needed for Figure 4?
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Answer: 9
Hint: Observe how many matchsticks are added from one figure to the next to find the common difference.
Solution:
Step 1: Identify the number of matchsticks in each figure: Figure 1 = 3, Figure 2 = 5, Figure 3 = 7.
Step 2: Find the difference between consecutive figures: 5 - 3 = 2, 7 - 5 = 2. The pattern is to add 2 matchsticks for each new figure.
Step 3: To find the number of matchsticks for Figure 4, add 2 to the number of matchsticks in Figure 3. So, 7 + 2 = 9.
8Consider the table of values below. Which statement best describes the relationship between 'Input (x)' and 'Output (y)'?
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Answer: y = 3x - 1
Hint: Test each given rule with the input values to see if they produce the correct output values. Start with the simplest rule or look for the common difference.
Solution:
Step 1: Look at the change in y for a change in x. When x goes from 1 to 2 (change of 1), y goes from 2 to 5 (change of 3). This suggests a '3x' component.
Step 2: Test a rule with '3x'. If y = 3x, then for x=1, y=3(1)=3, not 2. For x=2, y=3(2)=6, not 5. This means we need to adjust '3x'.
Step 3: Since 3 is 1 more than 2 (for x=1) and 6 is 1 more than 5 (for x=2), the rule likely involves subtracting 1 from '3x'.
Step 4: Test y = 3x - 1. For x=1, y = 3(1) - 1 = 2. For x=2, y = 3(2) - 1 = 5. For x=3, y = 3(3) - 1 = 8. This matches all values in the table. Input (x): 1, 2, 3. Output (y): 2, 5, 8.
9Which of the following points is located at (3, -2) on a coordinate plane?
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Answer: Point D: 3 units right of the y-axis and 2 units down from the x-axis
Hint: Remember that the first number in a coordinate pair (x-coordinate) indicates horizontal movement (right for positive, left for negative), and the second number (y-coordinate) indicates vertical movement (up for positive, down for negative).
Solution:
Step 1: The first number in the coordinate pair (x-coordinate) is 3. A positive x-coordinate means moving to the right of the y-axis.
Step 2: The second number in the coordinate pair (y-coordinate) is -2. A negative y-coordinate means moving down from the x-axis.
Step 3: Combine these movements. (3, -2) means 3 units right of the y-axis and 2 units down from the x-axis.
10A sculptor is stacking wooden blocks to create a tower. The first layer has 12 blocks, the second layer has 15 blocks, and the third layer has 18 blocks. If this pattern continues, how many blocks will be in the 6th layer?
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Answer: 27
Hint: Identify the common difference between the number of blocks in consecutive layers to extend the sequence.
Solution:
Step 1: Identify the number of blocks in the given layers: Layer 1 = 12, Layer 2 = 15, Layer 3 = 18.
Step 2: Find the difference between consecutive layers: 15 - 12 = 3, 18 - 15 = 3. The pattern is to add 3 blocks for each new layer.
Step 3: Continue the pattern: Layer 4 = 18 + 3 = 21. Layer 5 = 21 + 3 = 24.
Step 4: Layer 6 = 24 + 3 = 27.
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Tips for Patterns & Functions MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Patterns & Functions MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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