Free Printable 6th HL Maths diff and trig

1.

What rule should be used in deriving f(x) = x⁵

a)

Constant rule

b)

Sum rule

c)

Power rule

d)

Difference rule

2.

What rule should be used in deriving h(x) = 2(x - 4)³

a)

Power rule

b)

Product rule

c)

Quotient rule

d)

Chain rule

3.

What is the derivative of f(x) = 2x³- 4x + 5?

a)

f'(x) = 6x² - 4x

b)

f'(x) = 2/3x² - 4x

c)

f'(x) = 3x² - 4

d)

f'(x) = 6x² - 4

4.

At which point(s) will the slopes of the tangent line are zero?

a)

at C only

b)

at points A, C and E only

c)

at point B and D only

d)

at points A and E only

5.

Let f(x) = (x - 1)(x + 2). Find f'(0)

a)

0

b)

1

c)

2

d)

3

6.

Given f(x) = ax² + 2bx. What are a and b if f'(x) = 8x + 6?

a)

a = 2 and b = 3

b)

a = 3 and b = 2

c)

a = 3 and b = 4

d)

a = 4 and b = 3

7.

What is the equation of the line tangent to the curve y = x² at x = 1?

a)

y = 2x + 1

b)

y = 2x - 1

c)

y = -2x + 1

d)

y = x - 1

8.

What is the derivative of f?

a)

1/(x - 1)^-1

b)

-1/(x - 1)^-2

c)

-1/(x - 1)

d)

-1/(x - 1)²

9.

What is the derivative of y = 2π?

a)

0

b)

2

c)

-2

d)

None of the above

10.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

integral

11.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

12.

Differentiate 6x^⅔.

a)

4x^-⅓

b)

4x^-^⅔

c)

6x^⅓

d)

4x^⅓

13.

$If\ y\ =\ \tan\left(x^4\right)\ then\ \frac{\text{d}y}{\text{d}x}=$

a)

$\tan\left(3x^4\right)\$

b)

$\sec\left(x^4\right)\tan\left(x^4\right)$

c)

$\sec^2\left(x^4\right)$

d)

$\sec^2\left(x^4\right).4x^3$

14.

$If\ y\ =\ \sin^5\left(x\right)\ then\ \frac{\text{d}y}{\text{d}x}\ =$

a)

$\cos^5\left(x\right)\$

b)

$5\sin x.\cos x$

c)

$5\cos x$

d)

$5\sin^4x.\ \cos x$

15.

Find the derivative of:

f(x) = (x²+1)⁶

a)

12(x² + 1)⁶

b)

12x(x² + 1)⁶

c)

12x(x² + 1)⁵

d)

12(x² + 1)⁵

16.

10. What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

17.

11. What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

18.

a)

20.35

b)

12.72

c)

14.99

d)

21.83

19.

Find the value of a.

a)

13.35

b)

12.91

c)

13.05

d)

12.83

20.

What is the measure of angle A?

a)

50 degrees

b)

60.63 degrees

c)

77.78 degrees

d)

74.5 degrees

21.

What Subject are you planning on studying the most over Easter?

a)

Maths

b)

Mathematics

c)

Some less important subject

6th HL Maths diff and trig

Total questions: 21

Worksheet time: 2hrs 41mins

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