Common Core HSF.IF.B.6 worksheet

Question 1

Evaluate ∫ from 2 to 5 of (3x² + 4) dx.

Answer 

Question 2

For y = x³, find the gradient of the chord from x = 4 to x = 4.2. Give 2 decimal places.

Answer 

Question 3

Evaluate ∫ from 1 to 3 of (x² + x) dx. Give an exact answer (a fraction is fine).

Answer (as a fraction)

Question 4

s = t³ − 9t² + 24t. At what times is the particle at rest? Separate them with a comma.

t = 

Question 5

The cost (in dollars) of making x phone cases is C(x) = 4x² + 51x + 200. Use C′(31) to estimate the extra cost of making one more case after 31.

Answer 

Question 6

Find the gradient of y = x² + 4/x at x = −2.

Answer 

Question 7

At what x is the gradient of y = x² + 5x + 9 equal to 9?

x = 

Question 8

The curve y = −(x)(x − 4) is above the x-axis between its roots. Find the area of that region. Give an exact answer.

Answer (as a fraction)

Question 9

A ball is thrown upwards. Its height in metres after t seconds is h(t) = 15t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 1 to t = 2. A negative answer means it is coming down.

Answer 

Question 10

For f(x) = x² + 4x, simplify (f(x + h) − f(x))/h.

• A. 2xh + h²
• B. 2x + h + 4
• C. x² + h + 4
• D. 2x + h² + 4

Question 11

Differentiate y = 3x³/3 + 8x²/2 + 0x.

Answer 

Question 12

s = t³ + 6t² + 2t (metres, seconds). Find the acceleration at t = 0.

Answer 

Question 13

Mateo differentiated 3x⁵ and wrote 15x⁶. What is the correct derivative?

• A. 12x⁴
• B. 15x⁴
• C. 15x⁶
• D. 8x⁴

Question 14

Differentiate y = 9x⁵.

Answer 

Question 15

f(x) = x² − 3x − 5. Find the average rate of change of f between x = −1 and x = 3.

Answer 

Question 16

Differentiate f(x) = −4x⁴ − 4x² + x + 8.

Answer