12th grade calculus

Question 1

Find dy/dx when y = (x − 2)(x + 2).

Answer 

Question 2

Differentiate y = 2x^(3/2).

Answer 

Question 3

V(t) is the number of users of an app after t days. V′(3) = 26. What does this mean?

• A. The average rate over the whole period
• B. There are 26 users on day 3
• C. The total change since the start
• D. On day 3, users are increasing at about 26 per day

Question 4

Find the area between y = x² + 7, the x-axis, x = 0 and x = 3.

Answer 

Question 5

Find the limit as x → ∞ of (x² + x + 3)/(3x² + 7x − 1). Give a fraction if needed.

Answer (as a fraction)

Question 6

Where is f(x) = x³ − 6x² − 15x + 1 decreasing?

• A. x > 5
• B. x < −1 or x > 5
• C. −1 < x < 5
• D. −5 < x < 1

Question 7

Find the equation of the tangent to y = 2x² − 4x + 6 at x = 3. Type the right-hand side of y = … .

Answer 

Question 8

Differentiate y = −8x⁸.

Answer 

Question 9

For y = x³, find the gradient of the chord from x = 4 to x = 4.5. Give 2 decimal places.

Answer 

Question 10

An open box is made from a 42 cm square of card by cutting a square of side x cm from each corner and folding up. V = x(42 − 2x)². Find the maximum volume in cm³.

Answer 

Question 11

Find lim(x→6) (x² − x − 30)/(x − 6).

Answer 

Question 12

f(x) = (x² − 9)/(x − 3). It has no value at x = 3 itself. x: 2.9 | 2.99 | 2.999 | 3.001 | 3.01 | 3.1 f(x): 5.9 | 5.99 | 5.999 | 6.001 | 6.01 | 6.1 Estimate lim(x→3) f(x).

Answer 

Question 13

At what x is the gradient of y = x² + 4x − 9 equal to 8?

x = 

Question 14

Differentiate y = −2/x².

Answer 

Question 15

Tariq needs ∫ 4/x² dx. Which answer is correct?

• A. 4·ln x + C
• B. 4/x + C
• C. −4/x + C
• D. −8/x³ + C

Question 16

Find ∫ 2x dx. Leave out the + C.

Answer