ISEE Lower Level Quantitative Reasoning Flashcards: Data Based Predictions

What this deck covers

This deck focuses on Data Based Predictions, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Lower Level Quantitative Reasoning.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the next term in the sequence $20, 17, 13, 8, \dots$?

Answer: $2$. The differences decrease by 1 each time, becoming more negative, so subtract 6 from the last term.

Flashcard 2: What is the next term in the sequence $1, 1, 2, 3, 5, 8, \dots$?

Answer: $13$. This is the Fibonacci sequence, where each term is the sum of the two preceding ones.

Flashcard 3: What is the next term in the sequence $2, 6, 18, 54, \dots$?

Answer: $162$. This geometric sequence has a common ratio of 3, so multiply the last term by 3.

Flashcard 4: What is the predicted value after $4$ hours if a tank fills at $5$ L per hour starting from $10$ L?

Answer: $30$ L. The tank fills linearly at 5 L per hour, so add $5 \times 4$ to the initial 10 L.

Flashcard 5: What is the predicted total after $5$ days if a plant grows $3$ cm per day starting at $2$ cm?

Answer: $17$ cm. The plant grows linearly at 3 cm per day, so add $3 \times 5$ to the initial 2 cm.

Flashcard 6: What is the predicted value of $y$ when $x=4$ if the pattern is $(1,2),(2,4),(3,8)$?

Answer: $16$. The pattern shows $y = 2^x$, so substitute $x=4$ into the equation.

Flashcard 7: What is the predicted value of $y$ when $x=5$ if the pattern is $(1,3),(2,5),(3,7),(4,9)$?

Answer: $11$. The linear pattern follows $y = 2x + 1$, so substitute $x=5$ into the equation.

Flashcard 8: What is the predicted value of $y$ when $x=6$ if $y=2x$ and the pattern continues?

Answer: $12$. The linear pattern is $y = 2x$, so substitute $x=6$ into the equation.

Flashcard 9: What is the next term in the sequence $4, 12, 36, 108, \dots$?

Answer: $324$. This geometric sequence has a common ratio of 3, so multiply the last term by 3.

Flashcard 10: What is the next term in the sequence $2, 3, 5, 8, 12, \dots$?

Answer: $17$. The differences increase by 1 each time, so add 5 to the last term.

Flashcard 11: What is the next term in the sequence $10, 9, 7, 4, 0, \dots$?

Answer: $-5$. The differences decrease by 1 each time, becoming more negative, so subtract 5 from the last term.

Flashcard 12: What is the next term in the sequence $3, 8, 15, 24, \dots$?

Answer: $35$. The differences increase by 2 each time, so add 11 to the last term.

Flashcard 13: What is the next term in the sequence $1, 2, 4, 7, 11, \dots$?

Answer: $16$. The differences increase by 1 each time, so add 5 to the last term.

Flashcard 14: What is the next term in the sequence $5, 9, 17, 33, \dots$?

Answer: $65$. Each term is obtained by multiplying the previous by 2 and subtracting 1.

Flashcard 15: What is the next term in the sequence $1, 3, 6, 10, 15, \dots$?

Answer: $21$. These are triangular numbers, formed by adding the next integer to the previous term.

Flashcard 16: What is the next term in the sequence $100, 50, 25, 12.5, \dots$?

Answer: $6.25$. Each term is half of the previous in this geometric sequence with ratio $\frac{1}{2}$.

Flashcard 17: What is the next term in the sequence $2, 4, 7, 11, 16, \dots$?

Answer: $22$. The differences increase by 1 each time, so add 6 to the last term.

Flashcard 18: What is the next term in the sequence $2, 5, 10, 17, \dots$?

Answer: $26$. The differences between terms increase by 2 each time, so add 9 to the last term.

Flashcard 19: What is the next term in the sequence $1, 4, 9, 16, \dots$?

Answer: $25$. The sequence consists of perfect squares, so the next term is $5^2$.

Flashcard 20: What is the next term in the geometric sequence $3, 6, 12, 24, \dots$?

Answer: $48$. Multiply the last term by the common ratio of 2 to obtain the next term in the geometric sequence.

Flashcard 21: What is the common ratio in the geometric sequence $3, 6, 12, 24, \dots$?

Answer: $2$. The common ratio is determined by dividing consecutive terms in the geometric sequence, resulting in 2 each time.

Flashcard 22: What is the next term in the arithmetic sequence $4, 7, 10, 13, \dots$?

Answer: $16$. Add the common difference of 3 to the last term to find the next in the arithmetic sequence.

Flashcard 23: What is the common difference in the arithmetic sequence $4, 7, 10, 13, \dots$?

Answer: $3$. The common difference is found by subtracting consecutive terms in the arithmetic sequence, consistently yielding 3.