Robin

If I did not recognize that the numerator was the difference of cubes and that I could factor out (a-b)^2 from numerator and denominator, could this be solved using polynomial division?

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a^3 – 3a^2b + 3ab^2 – b^3
________________________
(a – b )(a – b)

If I did not recognize that the numerator was the difference of cubes and that I could factor out (a-b)^2 from numerator and denominator, could this be solved using polynomial division?

Robin

Here’s a question from the May 2023 (US) SAT, non-calculator section

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Here’s a question from the May 2023 (US) SAT, non-calculator section:

Alice took 60 minutes to complete a task on her first trial. The time it took Alice to complete the task decreased by 10% of the previous time for each additional trial. Approximately how many minutes will it take Alice to complete the task on her fifth trial?

A) 50
B) 42
C) 39
D) 35

I know we can solve this by subtracting 10% of the current value 5 times, but is there a more direct way to solve, maybe as a function?

Becky

Hi Mike, Can you explain this Q #29 from Calculator section of Oct 2022 PSAT?

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Hi Mike,
Can you explain this Q #29 from Calculator section of Oct 2022 PSAT:

A quadratic function can be used to model the height, in feet, of an object above the ground in terms of time, in seconds, after the object was launched. According to the model, an object was launched into the air from a height of 0 feet and reached its maximum height of 3136 feet 14 seconds after it was launched. Based on the model, what was the height, in feet, of the object 1 second after it was launched?

User

A chemist dissolves sodium acetate in boiling water. As the temperature cools down, the crystals start to grow with increasing mass…

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m(t₂)−m(t₁)=15(t₂ − t₁ )
A chemist dissolves sodium acetate in boiling water. As the temperature cools down, the crystals start to grow with increasing mass m(t), in grams (g) t seconds (s) after crystallization. The equation above shows this relationship where t₁ < t₂. Which of the following correctly explains the growth of the crystal mass?

The crystal mass grows linearly by 15g per s
The crystal mass grows exponentially by 1g every 15s
The crystal mass grows linearly by a factor 15 every s

User

In tennis, a player must win at least 6 games to win a set. If g is the number of games the player won and s is the number of sets the player won, which of the following inequalities must be true?

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In tennis, a player must win at least 6 games to win a set. If g is the number of games the player won and s is the number of sets the player won, which of the following inequalities must be true?

A. s ≤ 6g
B. s ≥ 6g
C. 6s ≤ g
D. 6s ≥ g

I thought the answer C and D would cancel out since g is games and number of games is 6. So then I chose A but that answer was wrong. Could you explain the reason for that?

Mike McClenathan

At a school fair, students can win colored tokens that are worth a different number of points depending on the color…

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5G + 45R = 380

At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won G green tokens and R red tokens worth a total of 380 points. The given equation represents this situation. How many more points is a red token worth than a green token?

Mike McClenathan

Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint…

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Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at Store A or $66.00 at Store B. How many pints of blackberries are in this purchase?

A. 4
B. 5
C. 8
D. 12