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### Calculus primarily connects which two major mathematical concepts?

Shapes and Sizes

Speed and Direction

Past and Future

Derivatives and Integrals

Derivatives and Integrals
Next question

Calculus is fundamentally about understanding how things change (derivatives) and adding things up (integrals). These concepts are two sides of the same coin in calculus, connecting rates of change to accumulated quantities.

### What's your chance of rolling a 5 with a regular die?

1 out of 6

1 out of 5

1 out of 4

1 out of 3

1 out of 6
Next question

A regular die has six faces, and each outcome (1 through 6) is equally likely. Thus, the chance of rolling a 5 (or any specific number) is 1 in 6.

### What happens to 1/x as x gets really, really big?

It gets bigger

It stays the same

It gets smaller

It disappears

It gets smaller
Next question

As x increases, 1/x becomes smaller because you're dividing 1 by a larger and larger number, approaching zero as x goes to infinity.

### If flipping a coin gives you heads half the time, and rolling a die gives you a 6 one-sixth of the time, what's the chance of both happening at once?

1/12

1/6

1/3

1/2

1/12
Next question

The probability of two independent events both happening is the product of their individual probabilities. So, for a coin flip (1/2) and a roll of a die (1/6), it's 1/2×1/6=1/12.

### What's the slope of y=x² when x=2?

2

4

6

8

4
Next question

The slope of a curve at any point is given by its derivative. For y=x², the derivative is 2x, which means at x=2, the slope is 2(2)=4.

### If it rains, I carry my umbrella 80% of the time. If it's cloudy, it rains 50% of the time. What's the chance I take my umbrella when it's cloudy?

40%

50%

80%

100%

40%
Next question

If it rains (50% chance), I take my umbrella 80% of the time. Thus, the probability I take my umbrella when it's cloudy is 0.5×0.8=0.4 or 40%.

### If a car's speed is given by the formula speed=2t, what's the relationship between time and its acceleration?

Directly proportional

Inversely proportional

Constant

No relationship

Constant
Next question

The acceleration of a car with speed given by 2=2t is constant because the speed increases uniformly with time. There's no change in how fast the speed itself is increasing.

### A bag contains 5 blue, 3 green, and 2 red marbles. If a marble is drawn at random, what is the probability that it is not blue?

2/5

1/2

1/5

5/10

1/2
Next question

There are a total of 10 marbles (5 blue, 3 green, and 2 red). The probability of drawing a marble that is not blue is the sum of the probabilities of drawing a green or a red marble, which are 3/10 and 2/10, respectively. Adding these probabilities gives 5/10, which simplifies to 1/2.

### A hill's slope at any point x metres from its start is given by the gradient function g(x)=2x+3. What is the slope of the hill 5 metres from the start?

5

10

13

15

13
Next question

The slope of the hill can be found by substituting x=5 into the gradient function, g(5)=2(5)+3=10+3=13. This indicates a steep incline.

### If you draw one card from a standard 52-card deck, what is the probability that the card is either a King or a Queen?

1/13

1/26

1/6

2/13

2/13
Next question

There are 4 Kings and 4 Queens in a 52-card deck. So, the total number of favorable outcomes is 8. The probability is then 8/52=2/13, meaning there's a 2 in 13 chance of drawing a King or Queen.

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