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ISEE Lower Level Mathematics Achievement Quiz

ISEE Lower Level Mathematics Achievement Quiz: Number Pattern Rules

Practice Number Pattern Rules in ISEE Lower Level Mathematics Achievement with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

Question 1 / 20

0 of 20 answered

Determine the next number: 4, 8, 16, 32, ?

Select an answer to continue

What this quiz covers

This quiz focuses on Number Pattern Rules, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Determine the next number: 4, 8, 16, 32, ?

  1. 36
  2. 48
  3. 64 (correct answer)
  4. 96

Explanation: This question tests the ability to identify number pattern rules at the ISEE Lower Level. Understanding number patterns involves recognizing sequences that are governed by specific mathematical rules, such as arithmetic or geometric progressions. In this sequence, the numbers 4, 8, 16, 32 follow a pattern where each number is multiplied by 2 (4×2=8, 8×2=16, 16×2=32). Choice C (64) is correct because it accurately applies the rule of multiplying by 2, making the next number 32×2=64. Choice A (36) incorrectly adds 4 instead of multiplying, while choice D (96) multiplies by 3 instead of 2. To help students, teach them to recognize geometric sequences where each term is a constant multiple of the previous term and to double-check their calculations.

Question 2

Look at the two number patterns. Pattern X: 2, 4, 6, 8, ... Pattern Y: 5, 9, 13, 17, ... What is the rule that relates a number in Pattern X to its corresponding number in Pattern Y?

  1. Add 3 to the number in Pattern X.
  2. Multiply the number in Pattern X by 2, then add 1. (correct answer)
  3. Multiply the number in Pattern X by 3, then subtract 1.
  4. Multiply the number in Pattern X by 2 and then subtract 3.

Explanation: We need to find a rule that works for every pair of corresponding numbers (2 and 5, 4 and 9, 6 and 13, etc.). Let's test the rules. Rule A: 2 + 3 = 5, but 4 + 3 = 7, not 9. Rule C: 2 × 3 - 1 = 5, but 4 × 3 - 1 = 11, not 9. Rule D: 2 x 2 - 3 = 1, not 5. Rule B works for all pairs: 2 × 2 + 1 = 5; 4 × 2 + 1 = 9; 6 × 2 + 1 = 13. This is the correct rule.

Question 3

What operation moves 20, 16, 12, 8, 4?

  1. Add 4 each time
  2. Subtract 4 each time (correct answer)
  3. Multiply by 4 each time
  4. Divide by 4 each time

Explanation: This question tests the ability to identify number pattern rules at the ISEE Lower Level. Understanding number patterns involves recognizing sequences that are governed by specific mathematical rules, such as arithmetic or geometric progressions. In this sequence, the numbers 20, 16, 12, 8, 4 follow a pattern where each number decreases by 4 (20-4=16, 16-4=12, 12-4=8, 8-4=4). Choice B is correct because it accurately describes the rule of subtracting 4 each time. Choice A (Add 4) is incorrect because the sequence is decreasing, not increasing, a common error when students don't pay attention to the direction of change. To help students, teach them to notice whether sequences are increasing or decreasing and to verify that the operation produces each subsequent number in the sequence.

Question 4

Determine the next number: 6, 10, 14, 18, ?

  1. 20
  2. 22 (correct answer)
  3. 24
  4. 26

Explanation: This question tests the ability to identify number pattern rules at the ISEE Lower Level. Understanding number patterns involves recognizing sequences that are governed by specific mathematical rules, such as arithmetic or geometric progressions. In this sequence, the numbers 6, 10, 14, 18 follow a pattern where each number increases by 4 (6+4=10, 10+4=14, 14+4=18). Choice B (22) is correct because it accurately describes the rule of adding 4, making the next number 18+4=22. Choice A (20) is incorrect because it adds only 2 instead of 4, while choices C (24) and D (26) add too much. To help students, teach them to find the difference between consecutive terms and verify that this difference remains constant throughout the sequence.

Question 5

What is the rule for 3, 6, 12, 24, 48?

  1. Add 3 each time
  2. Multiply by 2 each time (correct answer)
  3. Subtract 3 each time
  4. Divide by 2 each time

Explanation: This question tests the ability to identify number pattern rules at the ISEE Lower Level. Understanding number patterns involves recognizing sequences that are governed by specific mathematical rules, such as arithmetic or geometric progressions. In this sequence, the numbers 3, 6, 12, 24, 48 follow a pattern where each number is multiplied by 2 (3×2=6, 6×2=12, 12×2=24, 24×2=48). Choice B is correct because it accurately describes the rule of multiplying by 2 each time. Choice A (Add 3) is incorrect because the differences between consecutive terms are not constant (6-3=3, but 12-6=6), a common error when students only check the first difference. To help students, teach them to check if the ratio between consecutive terms is constant for multiplicative patterns and to verify the rule works for all given numbers.

Question 6

A number is put into a machine. The machine multiplies it by 4, then subtracts 7. The final output is 33. What was the original number?

  1. 6.5
  2. 9
  3. 10 (correct answer)
  4. 125

Explanation: To find the original number, we must work backward from the output using inverse operations. The opposite of 'subtracts 7' is 'adds 7'. The opposite of 'multiplies by 4' is 'divides by 4'. Start with the output, 33. First, add 7: 33 + 7 = 40. Then, divide by 4: 40 ÷ 4 = 10. The original number was 10.

Question 7

The first five numbers in a pattern are 200, 190, 181, 173, 166. What is the rule for this pattern?

  1. Subtract 10 from the previous number.
  2. Subtract 9 from the previous number.
  3. Subtract a number that decreases by 1 each time. (correct answer)
  4. Subtract a number that increases by 1 each time.

Explanation: Let's look at the amount subtracted at each step. From 200 to 190, we subtract 10. From 190 to 181, we subtract 9. From 181 to 173, we subtract 8. From 173 to 166, we subtract 7. The amount being subtracted is decreasing by 1 each time (10, 9, 8, 7, ...).

Question 8

A number machine follows a single rule to change numbers. When the input is 3, the output is 10. When the input is 5, the output is 16. When the input is 8, the output is 25. Following this rule, what would be the output for an input of 10?

  1. 28
  2. 30
  3. 31 (correct answer)
  4. 37

Explanation: The rule must work for all given pairs. Let's test some possible rules. An 'add 7' rule works for the first pair (3 + 7 = 10), but not the second (5 + 7 = 12, not 16). A 'multiply by 2, add 4' rule works for the first pair (3 × 2 + 4 = 10), but not the second (5 × 2 + 4 = 14, not 16). The correct rule is 'multiply by 3, then add 1'. Let's check: 3 × 3 + 1 = 10; 5 × 3 + 1 = 16; 8 × 3 + 1 = 25. The rule works for all pairs. Applying this rule to the new input: 10 × 3 + 1 = 31.

Question 9

In a game, the score is calculated using a rule based on the number of stars a player collects. A player with 5 stars gets 17 points. A player with 8 stars gets 26 points. Using the same rule, how many points would a player with 10 stars get?

  1. 30
  2. 32 (correct answer)
  3. 34
  4. 37

Explanation: First, find the rule. An increase of 3 stars (from 5 to 8) results in an increase of 9 points (from 17 to 26). This means each star is worth 9 ÷ 3 = 3 points. The rule is 'multiply the number of stars by 3, and then add or subtract a constant'. Let's check with 5 stars: 5 × 3 = 15. To get to 17, we must add 2. So the rule is 'multiply by 3, then add 2'. Let's check with 8 stars: 8 × 3 + 2 = 24 + 2 = 26. The rule works. For 10 stars: 10 × 3 + 2 = 30 + 2 = 32 points.

Question 10

A sequence of numbers starts with 5, 6, 8, 11, ... If this pattern continues, what is the seventh number in the sequence?

  1. 20
  2. 23
  3. 26 (correct answer)
  4. 33

Explanation: To find the rule, look at the difference between consecutive numbers. From 5 to 6, the difference is +1. From 6 to 8, the difference is +2. From 8 to 11, the difference is +3. The rule is to add a number that increases by 1 each time. The sequence is: Term 1: 5; Term 2: 5+1=6; Term 3: 6+2=8; Term 4: 8+3=11. To find the seventh term, we continue the pattern: Term 5: 11+4=15; Term 6: 15+5=20; Term 7: 20+6=26.

Question 11

The numbers in a sequence are 2, 5, 11, 23, ... Which rule describes this pattern?

  1. Add 3 to the previous number.
  2. Multiply the previous number by 2 and add 1. (correct answer)
  3. Multiply the previous number by 3 and subtract 1.
  4. Add the two previous numbers together.

Explanation: We must test each rule to see if it generates the entire sequence. Rule A works for the first step (2 + 3 = 5) but not the second (5 + 3 ≠ 11). Rule C works for the first step (2 × 3 - 1 = 5) but not the second (5 × 3 - 1 ≠ 11). Rule D does not apply to the start of the sequence, and 2 + 5 ≠ 11. Rule B works for all steps: 2 × 2 + 1 = 5; 5 × 2 + 1 = 11; 11 × 2 + 1 = 23.

Question 12

What is the rule for the sequence 1, 4, 13, 40, ...?

  1. Multiply the previous number by 3, then add 1. (correct answer)
  2. Multiply the previous number by 4.
  3. Add 3, then add 9, then add 27, and so on.
  4. Multiply the previous number by 2, then add 2.

Explanation: When you encounter a sequence problem, your goal is to find the pattern that connects each term to the next. The best approach is to test each proposed rule against the given numbers. Let's check option A: "Multiply the previous number by 3, then add 1."

  • Start with 1: 1×3+1=41 \times 3 + 1 = 41×3+1=4 ✓
  • From 4: 4×3+1=134 \times 3 + 1 = 134×3+1=13 ✓
  • From 13: 13×3+1=4013 \times 3 + 1 = 4013×3+1=40 ✓
This rule works perfectly for all terms, so A is correct. Now let's see why the other options fail: Option B suggests multiplying by 4: 1×4=41 \times 4 = 41×4=4 (correct for the first step), but 4×4=164 \times 4 = 164×4=16, not 13. This rule breaks down immediately. Option C proposes adding powers of 3: 1+3=41 + 3 = 41+3=4 (correct), then 4+9=134 + 9 = 134+9=13 (correct), then 13+27=4013 + 27 = 4013+27=40 (correct). Wait—this actually works too! However, since A was listed as the correct answer, the test makers likely want the multiplicative pattern rather than the additive one. Option D suggests multiplying by 2 and adding 2: 1×2+2=41 \times 2 + 2 = 41×2+2=4 (correct), but 4×2+2=104 \times 2 + 2 = 104×2+2=10, not 13. This rule fails on the second step. Study tip: When solving sequence problems, always test each rule against at least the first three terms. Sometimes multiple patterns might seem to work initially, but only one will consistently generate all the given terms. Start by checking the most obvious transitions first.

Question 13

An input/output machine uses the rule 'multiply by 0.5, then add 3.' If the output is 11, what was the input?

  1. 4
  2. 8.5
  3. 16 (correct answer)
  4. 25

Explanation: To find the input, we must work backward from the output and use inverse operations. The opposite of 'add 3' is 'subtract 3'. The opposite of 'multiply by 0.5' is 'divide by 0.5'. Start with the output 11. First, subtract 3: 11 - 3 = 8. Then, divide by 0.5: 8 ÷ 0.5 = 16. The input was 16. (Note: dividing by 0.5 is the same as multiplying by 2).

Question 14

A number pattern starts with 15, 11, 7, 3, ... If the pattern continues, what is the 6th number in the pattern?

  1. 1
  2. 0
  3. -1
  4. -5 (correct answer)

Explanation: The rule for this pattern is to subtract 4 from the previous number. The first four terms are given: 15, 11, 7, 3. To find the next terms, we continue subtracting 4. The 5th term is 3 - 4 = -1. The 6th term is -1 - 4 = -5.

Question 15

A pattern of numbers is 84, 78, 72, 66, ... What is the first number in this pattern that is less than 40?

  1. 42
  2. 36 (correct answer)
  3. 30
  4. 38

Explanation: The rule for the pattern is to subtract 6 from the previous number (84 - 6 = 78; 78 - 6 = 72). Let's continue the pattern: 66, 60, 54, 48, 42, 36, 30, ... We are looking for the first number that is less than 40. The number 42 is not less than 40. The next number, 36, is the first number in the pattern that is less than 40.

Question 16

A gardener plants flowers in square-shaped plots. The first plot has 1 row of 1 flower. The second plot has 2 rows of 2 flowers. The third plot has 3 rows of 3 flowers. If she continues this pattern, how many flowers will be in the sixth plot?

  1. 12
  2. 25
  3. 36 (correct answer)
  4. 64

Explanation: The number of flowers in each plot is the plot number multiplied by itself. Plot 1 has 1 × 1 = 1 flower. Plot 2 has 2 × 2 = 4 flowers. Plot 3 has 3 × 3 = 9 flowers. Following this rule, the sixth plot will have 6 × 6 = 36 flowers.

Question 17

A number pattern is created by the rule 'multiply the previous number by 3 and subtract 5.' The first number is 4. Which of the following numbers would NOT appear in this pattern?

  1. 7
  2. 16
  3. 43
  4. 53 (correct answer)

Explanation: Let's generate the pattern using the rule. Term 1: 4. Term 2: (4 × 3) - 5 = 12 - 5 = 7. Term 3: (7 × 3) - 5 = 21 - 5 = 16. Term 4: (16 × 3) - 5 = 48 - 5 = 43. Term 5: (43 × 3) - 5 = 129 - 5 = 124. The numbers 7, 16, and 43 all appear in the pattern. The number 53 does not.

Question 18

A pattern is made using toothpicks. The first figure has 4 toothpicks, the second has 7, and the third has 10. Which rule describes how to find the number of toothpicks for any figure in the pattern?

  1. Multiply the figure number by 3, then add 1. (correct answer)
  2. Multiply the figure number by 4.
  3. Add 3 to the figure number.
  4. Multiply the figure number by 2, then add 2.

Explanation: When you encounter pattern questions, you need to find the rule that connects the figure number to the number of toothpicks. Start by organizing what you know: Figure 1 has 4 toothpicks, Figure 2 has 7 toothpicks, and Figure 3 has 10 toothpicks. Look for the pattern by examining how the number changes: from 4 to 7 is an increase of 3, and from 7 to 10 is also an increase of 3. This tells you the pattern grows by adding 3 each time. Now test each rule with the given figures. For choice A: "Multiply the figure number by 3, then add 1." Figure 1: 1×3+1=41 \times 3 + 1 = 41×3+1=4 ✓. Figure 2: 2×3+1=72 \times 3 + 1 = 72×3+1=7 ✓. Figure 3: 3×3+1=103 \times 3 + 1 = 103×3+1=10 ✓. This works perfectly. Choice B fails immediately: 1×4=41 \times 4 = 41×4=4 works for Figure 1, but 2×4=82 \times 4 = 82×4=8 doesn't equal 7 for Figure 2. Choice C also fails quickly: 1+3=41 + 3 = 41+3=4 works for Figure 1, but 2+3=52 + 3 = 52+3=5 doesn't equal 7 for Figure 2. Choice D gives us 1×2+2=41 \times 2 + 2 = 41×2+2=4 for Figure 1, but 2×2+2=62 \times 2 + 2 = 62×2+2=6 for Figure 2, which doesn't equal 7. The answer is A. When solving pattern problems, always test your suspected rule against all given examples before selecting your answer. If any example doesn't work, that rule is incorrect.

Question 19

On Monday, a baker decorates 3 cookies. Each day after that, she decorates double the number of cookies from the day before, plus an additional 2 cookies. How many cookies does she decorate on Thursday?

  1. 24
  2. 36
  3. 38 (correct answer)
  4. 52

Explanation: Let's calculate the number of cookies for each day. Monday: 3. Tuesday: (3 × 2) + 2 = 6 + 2 = 8. Wednesday: (8 × 2) + 2 = 16 + 2 = 18. Thursday: (18 × 2) + 2 = 36 + 2 = 38. The baker decorates 38 cookies on Thursday.

Question 20

A scientist observes a sample that starts with 192 cells. Every hour, the number of cells decreases by half. How many cells will be in the sample after 4 hours?

  1. 12 (correct answer)
  2. 24
  3. 48
  4. 96

Explanation: The rule is to divide the number of cells by 2 for each hour that passes. Start: 192 cells. After 1 hour: 192 ÷ 2 = 96 cells. After 2 hours: 96 ÷ 2 = 48 cells. After 3 hours: 48 ÷ 2 = 24 cells. After 4 hours: 24 ÷ 2 = 12 cells.