Free Printable NCEA 3 Calc Revision

1.

Find the derivative of:
f(x) = 7(3x+ 4)⁵

a)

35(3x + 4)⁵

b)

35(3x + 4)⁴

c)

105(3x + 4)⁵

d)

105(3x + 4)⁴

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?

a)

1/(x - 1)^-1

b)

-1/(x - 1)^-2

c)

-1/(x - 1)

d)

-1/(x - 1)²

4.

What is the derivative of y = 2π?

a)

0

b)

2

c)

-2

d)

None of the above

5.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

6.

When do you use the chain rule?

a)

anytime you want

b)

when there is a function in a function

c)

where there are multiple layers to a lasagna (yum)

d)

when there is division

7.

What rule best apply to find the derivative of y=x lnx

a)

product rule

b)

quotient rule

c)

power rule

d)

sum rule

8.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

9.

$\frac{\text{d}}{\text{d}y}\left(x^3-2xe^x\right)$

a)

$3x^2-2e^x\left(x+1\right)$

b)

$3x^2-2\left(e^x+\frac{x}{e^x}\right)$

c)

$3x^2-2xe^x\left(2x+1\right)$

d)

$3x^2-2x\left(2xe^x+\frac{1}{e^x}\right)$

10.

$\frac{\text{d}}{\text{d}y}\left(e^{\left(2x+1\right)}\right)^2$

a)

$4e^{\left(4x+2\right)}$

b)

$\frac{4}{e^{\left(4x+2\right)}}$

c)

$e^{\left(4x+2\right)}\left(8x^2+2x\right)$

d)

$\frac{\left(8x^2+2x\right)}{e^{\left(4x+2\right)}}$

11.

$\frac{\text{d}}{\text{d}y}\left(e^x+2x\right)^3$

a)

$3\left(e^x+2\right)\left(e^x+2x\right)^2$

b)

$3\left(e^x+2\right)^2$

c)

$3\left(e^x+4x^2\right)\left(e^x+2x\right)^2$

d)

$4\left(e^x+2\right)^4$

12.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

13.

The derivative of xcos(2x²)

a)

cos(2x²) - 4x²sin(2x²)

b)

sin(2x²) - 4x²cos(2x²)

c)

cos(2x²) + 4x²sin(2x²)

d)

cos(2x²) - 2x²cos(2x²)

14.

The derivative of cos(2x²)

a)

-2xcos(2x²)

b)

-4xcos(2x²)

c)

-sin(2x²)

d)

-4xsin(2x²)

15.

Find $\frac{dy}{dx}$ for $y=x^2e^x$ .

a)

$xe^x\left(x-2\right)$

b)

$xe^x\left(x+2\right)$

c)

$-xe^x\left(x+2\right)$

d)

$xe^{-x}\left(x+2\right)$

16.

$\frac{d}{dx}\left(e^{\cos x}\right)\ is$

a)

$e^{-\sin x}$

b)

$\left(-\sin x\right)\ e^{\cos x}$

c)

$\left(\cos x\right)e^{-\sin x}$

d)

$\left(\sin x\right)e^{\sin x}$

17.

Find $\frac{dy}{dx}$ for $2x-1$ .

a)

$3$

b)

$2$

c)

$2^{-1}$

d)

$2^0$

18.

Find $\frac{dy}{dx}$ for $y=x^5-\frac{3}{x^3}$ .

a)

$5x^3+\frac{9}{x^4}$

b)

$5x^3+9x^{-4}$

c)

$5x^4+\frac{9}{x^4}$

d)

$5x^4+\frac{9}{x^{-4}}$

19.

Find $\frac{dy}{dx}$ for $y=\frac{3x+2^{ }}{2x+1}$ by using quotient rule.

a)

$-\frac{1}{\left(2x+1\right)^2}$

b)

$\frac{1}{\left(2x+1\right)^2}$

c)

$\left(2x+1\right)^{-2}$

d)

$2x+1$

20.

Find $\frac{d^2y}{dx^2}$ for $y=x^3\left(x^2+5\right)$ .

a)

$5x^4+15x^2$

b)

$5x^4-15x^2$

c)

$20x^3+30x$

d)

$20x^3-30x$

21.

What is an antiderivative?

a)

The opposite of a derivative

b)

The same as a derivative

c)

A second derivative

d)

It always represents velocity.

22.

What does C represent in an antiderivative?

a)

A variable

b)

A constant

c)

None of these

d)

Unknown

23.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

24.

∫(3x⁴+2)⁴(12x³)dx

a)

½(3x⁴+2)⁴+C

b)

(3x⁴+2)⁴+C

c)

⅕(3x⁴+2)⁵+C

d)

⅓(3x⁴+2)⁶+C

25.

Integrate $\int_{ }^{ }3\ dx$

a)

= 0

b)

$=\frac{3}{x}+c$

c)

$=\ 3x\ +c$

d)

$=4+c$

26.

Integrate $\int_{ }^{ }\left(x^2+7\right)dx$

a)

$=2x+c$

b)

$=x^3+7x$

c)

$=\frac{1}{2}x^3+7x$

d)

$=\frac{1}{3}x^3+7x+c$

27.

$\int\left(\frac{4}{x}-e_{ }^x\right)dx$

a)

$\frac{4}{x^2}-xe^x+C$

b)

$4\ln\left|x\right|-e^x+C$

c)

$4\ln\left(x\right)-e^x+C$

d)

$4\ln\left|x\right|+e^x+C$

28.

$\int\cos\left(3-4x\right)dx_{ }^{ }$

a)

$\frac{1}{4}\sin\left(3-4x\right)+C$

b)

$4\sin\left(3-4x\right)+C$

c)

$-\frac{1}{4}\sin\left(3-4x\right)+C$

d)

$-4\sin\left(3-4x\right)+C$

29.

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

a)

$\frac{ax^{n+1}}{n+1}$

b)

$\frac{ax^{n-1}}{n-1}+\ c$

c)

$\frac{ax^{n+1}}{n}+\ c$

d)

$\frac{ax^{n+1}}{n+1}+\ c$

30.

$\int6x\left(x+2\right)dx$

a)

$6x^2+12x+C$

b)

$x^{2\ }-2x+C$

c)

$3x^2+6x+C$

d)

$2x^3+6x^2+C$

31.

∫ - sinx dx

a)

-cos x + C

b)

cos x + C

c)

tan x + C

d)

1/√1- x²

32.

$\int\ \frac{2}{x+3}dx^{ }=$

a)

2ln|x+3|

b)

2ln(x + 3) + c

c)

$\frac{1}{2}\ln\left|x\ +\ 3\right|\ +\ c$

d)

none of these

33.

$\int\cos(4x+5)\ dx$

a)

-¼sin(4x + 5) + C

b)

4sin(4x + 5) + C

c)

¼sin(4x + 5) + C

d)

4cos(4x + 5) + C

34.

$\int_{-2}^22-x^2\ dx$

a)

62

b)

64/11

c)

56/3

d)

50/3

35.

$\int_2^4\ \frac{2}{x^2}\ dx$

a)

3

b)

½

c)

-3/2

d)

4/11

36.

a)

A

b)

B

c)

C

d)

D

37.

Simplify $\sqrt{-4}$

a)

2x

b)

2

c)

2i

d)

-2

38.

Simplify $\sqrt{-8}$

a)

$2x\sqrt{2}$

b)

$\sqrt{2i}$

c)

$2i\sqrt{2}$

d)

$\sqrt{-4i}$

39.

Simplify $\sqrt{-18}$

a)

$3i\sqrt{2}$

b)

$9i$

c)

$2i\sqrt{3}$

d)

$3i$

40.

a)

10

b)

-10

c)

10i

d)

-10i

41.

Simplify √-28

a)

-√28

b)

-2i√7

c)

2i√7

d)

28i

42.

√-36

a)

6

b)

-6

c)

-6i

d)

6i

43.

What is the complex conjugate of 4-3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

44.

Simplify:
i⁷

a)

i

b)

-i

c)

1

d)

-1

45.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

46.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

47.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

48.

Simplify
(-6 - 2i)²

a)

32

b)

36-4i

c)

36+24i

d)

32+24i

49.

Where is point B located?

a)

2 + i

b)

-3

c)

2i

d)

-1 - i

50.

Where is point C located?

a)

2 + i

b)

-3

c)

2i

d)

-1 - i

51.

Where is point A located?

a)

2 + i

b)

-3

c)

2i

d)

-1 - i

52.

(3 + 2i) + (4 - 5i)

a)

7 + 7i

b)

1 - 3i

c)

1 - 7i

d)

7 - 3i

53.

(-7 + 9i) + (2 - 10i)

a)

-5 + i

b)

-5 - i

c)

-9 + 1

d)

9 - i

54.

(4 - 2i) - (3 + 6i)

a)

7 - 4i

b)

1 + 4i

c)

1 - 8i

d)

7 - 8i

55.

What does i² equal?

a)

-1

b)

√-1

c)

1

d)

-√1

56.

The expression (2 + 3i)² is equal to

a)

-5

b)

-5 + 12i

c)

13

d)

13 + 12i

57.

(3 + 8i)(-2 - i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

58.

Simplify

a)

(-10+6i)/17

b)

(1+50i)/61

c)

(-23+36i)/25

d)

(-21+33i)/34

59.

(-5 + 10i)(-5 - 10i) = 125

a)

True

b)

False

60.

What letter represents an imaginary number?

a)

a

b)

i

c)

j

d)

x

61.

Simplify:
(10+ 15i)-(48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

62.

Simplify
3i - (4 + 7i)

a)

-4 + 10i

b)

21 - 12i

c)

4 - 10i

d)

-4 - 4i

63.

Multiply
(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

64.

Multiply
(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

65.

(4-5i)(4+5i)

a)

41

b)

-9

c)

41+40i

d)

-9+40i

66.

2 - √-9

a)

2-3i

b)

2+3= 5

c)

2+3i

d)

2 - 3= -1

67.

What complex number is represented by the graph?

a)

-3-i

b)

-3+i

c)

1+3i

d)

1-3i

68.

How do you write a complex number?

a)

a-bi

b)

a+bi

c)

ai+b

d)

ai-b

69.

Match the expression to the graph shown in the complex plane.

a)

-2i-3i

b)

(0,-5)

c)

-6i

d)

-2(3i)

NCEA 3 Calc Revision

Total questions: 69

Worksheet time: 52mins

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