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1.

Expand the expression using the Binomial Theorem.

(2x+5)⁴

a)

2x⁴ + 40x³+ 300x² + 1000x +625

b)

16x⁴+ 160x³ +600x² +1000x + 625

c)

16x⁴ + 1000x³ + 600x²+ 160x +625

2.

Expand the expression using the Binomial Theorem.
(2x+5)⁴

a)

2x⁴ + 40x³+ 300x² + 1000x +625

b)

16x⁴+ 160x³ +600x² +1000x + 625

c)

16x⁴ + 1000x³ + 600x²+ 160x +625

3.

What is row 7 of Pascal's Triangle?

a)

1, 5, 10, 5, 1

b)

1, 5, 10, 10, 5, 1

c)

1, 7, 21, 35, 35, 21, 7, 1

d)

1, 7, 21, 35, 21, 7, 1

4.

Expand

a)

A

b)

B

c)

C

d)

D

5.

Expand: $\left(a+b\right)^2$

a)

$a^2+ab+b^2$

b)

$a^2+2ab+b^2$

c)

$a^2-ab+b^2$

d)

$a^2-2ab+b^2$

6.

Choose the right Pascal's triangle

a)

b)

c)

d)

7.

Expand: $\left(a-b\right)^5$

a)

$a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$

b)

$a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5$

c)

$a^5-5a^4b+10a^2b^3-10a^3b^2+5ab^4-b^5$

d)

$a^5-5a^4b-10a^3b^2-10a^2b^3-5ab^4-b^5$

8.

Use the binomial theorem to expand $\left(4-2z\right)^3$

a)

$64-96z+48z^2+8z^3$

b)

$64-96z+48z^2-8z^3$

c)

$64+96z+48z^2+8z^3$

d)

$64-64z+144z^2-8z^3$

9.

Find the product:
(y - 3)(y + 7)

a)

y² - 21

b)

y² + 10x - 21

c)

y² + 4y - 21

d)

2y - 10

10.

Find the product:

(3x² – 1)(3x² + 5x+4)

a)

6x² + 4x + 5

b)

9x⁴ + 15x³ - 4x

c)

6x² + 15x³ - 20x²- 5x + 4

d)

9x⁴ + 15x³ - 9x²- 5x - 4

11.

Classify

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

12.

a)

Degree 3

b)

Degree 6

c)

Degree 7

d)

Degree 5

13.

What is row 7 of Pascal's Triangle?

a)

1, 5, 10, 5, 1

b)

1, 5, 10, 10, 5, 1

c)

1, 7, 21, 35, 35, 21, 7, 1

d)

1, 7, 21, 35, 21, 7, 1

14.

Expand (x−7)²

a)

x² - 14x + 49

b)

-x² - 14x - 49

c)

x² + 14x - 49

d)

49x²

15.

Select the coefficients of the 5th Row in Pascal's Triangle

a)

1;3;3;1

b)

1;4;6;4;1

c)

1;5;10;10;5;1

d)

1;6;15;20;15;6;1

16.

Expand
(b - 2)³

a)

b³ - 2b² + 4b - 8

b)

5b³ - 20b² + 40b - 40

c)

b³ - 6b² + 12b - 8

d)

4b³ - 12b² + 16b - 8

17.

What is the Binomial expansion of (x + 1)⁵ ?

a)

x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

b)

x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

c)

x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

d)

x⁵ + 1

18.

Expand (d-5)⁵

a)

d⁵ - 25 d⁴ + 250 d³ - 1250 d² + 3125 d - 3125

b)

d⁵ + 25 d⁴ + 250 d³ + 1250 d² + 3125 d + 3125

c)

d⁴- 20d³+ 150d²- 750d + 3125

d)

d⁴+ 20d³+ 150d²+ 750d + 3125

19.

What would be the 5th term of the expansion of (n+4)⁴?

a)

257

b)

256

c)

n⁴

d)

259

20.

What would be the 2nd term of the expansion of (y+4)⁴?

a)

253y

b)

256y

c)

64y

d)

96y²

21.

a)

b)

c)

d)

22.

a)

b)

c)

d)

23.

a)

$-336x^2y^4$

b)

$3360x^6y^4$

c)

$-3360x^4y^6$

d)

$3360x^4y^6$

24.

a)

$10800$

b)

$13600$

c)

$13608$

d)

$13680$

25.

a)

$\frac{\sqrt{x}}{8}$

b)

$35x^2$

c)

$\frac{35x\sqrt{x}}{8}$

d)

$\frac{35x^2}{8}$

26.

a)

$252$

b)

$210$

c)

$45$

d)

$120$

27.

a)

$126$

b)

$-126$

c)

$-36$

d)

$36$

28.

a)

$\pm2$

b)

$\pm3$

c)

$\pm4$

d)

$\pm5$

29.

a)

$1$

b)

$2$

c)

$3$

d)

$4$

30.

a)

$-10$

b)

$-30$

c)

$10$

d)

$30$

31.

Which of the following is not the pair of angle $\theta$ and its corresponding reference angle, $\alpha$

a)

$\theta=206\degree\ ,\ \alpha=26\degree$

b)

$\theta=337\degree,\ \alpha=23\degree$

c)

$\theta=112\degree,\ \alpha=68\degree$

d)

$\theta=195\degree,\ \alpha=75\degree$

32.

The diagram below shows a unit circle. State the possible values of a and b.

a)

$a=0.9397,\ b=0.3420$

b)

$a=0.9397,\ b=-0.3420$

c)

$a=-0.9397,\ b=0.3420$

d)

$\alpha=-0.9397,\ b=-0.3420$

33.

Given $\cos\ x=\frac{3}{5}$ where $270\degree\le x\le360\degree.\$ find the values of $\tan\ x$

a)

$-\frac{4}{3}$

b)

$-\frac{3}{4}$

c)

$\frac{3}{4}$

d)

$\frac{4}{3}$

34.

Find the value of $\sin\ 30\degree-\cos\ 30\degree$

a)

$\frac{1-\sqrt{3}}{2}$

b)

$-\frac{1-\sqrt{3}}{2}$

c)

$\frac{\sqrt{3}-1}{2}$

d)

$-\frac{1+\sqrt{3}}{2}$

35.

The diagram below shows the graph of $y=\sin\ x$ and $y=\cos\ x$ . Find the value of k

a)

$45\degree$

b)

$210\degree$

c)

$225\degree$

d)

$315\degree$

36.

The diagram below shows the graph of a cosinus functions. What is the function of the graph?

a)

$y=\cos\ 2x$

b)

$y=4\cos\ \frac{1}{2}x$

c)

$y=4\ \cos\ \frac{2}{3}x$

d)

$y=4\ \cos\ 2x$

37.

Which graph represents $y=\cos\ x$ for $90\degree\le x\le270\degree$

a)

b)

c)

d)

38.

The diagram below shows a part of graph $y=\cos\ x$ . What is coordinate of R?

a)

$\left(110\degree,-0.5\right)$

b)

$\left(120\degree,-0.5\right)$

c)

$\left(150\degree,-0.5\right)$

d)

$\left(160\degree,-0.5\right)$

39.

Calculate the value of p of each of the following trigonometric function

(final answer only without unit)

(a)

40.

The diagram shows he height of an ocean tide. State the amplitud of the tide.

(a)

41.

a)

a

b)

b

c)

c

d)

d

42.

a)

a

b)

b

c)

c

d)

d

43.

a)

a

b)

b

c)

c

d)

d

44.

a)

a

b)

b

c)

c

d)

d

45.

a)

a

b)

b

c)

c

d)

d

46.

a)

a

b)

b

c)

c

d)

d

47.

a)

a

b)

b

c)

c

d)

d

48.

a)

a

b)

b

c)

c

d)

d

49.

a)

a

b)

b

c)

c

d)

d

50.

a)

a

b)

b

c)

c

d)

d

51.

Q1. The principal value of $\ Sin^{-1}\left(\frac{1}{\sqrt{2}}\right)\ is\$

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{2}$

52.

Q2. The principal value of $\ Sin^{-1}\left(\frac{1}{2}\right)\ is$

a)

$\frac{\pi}{6}$

b)

$-\frac{\pi}{4}$

c)

$-\frac{\pi}{3}$

53.

Q3. The principal value of $\ Tan^{-1}\left(-1\right)\ is$

a)

$-\frac{\pi}{4}$

b)

$-\frac{\pi}{3}$

c)

$-\frac{\pi}{6}$

54.

Q4. The principal value branch of $\ \ \left(\ Sin^{-1}y\ \right)\ is\$

a)

$0\le y\le\pi$

b)

$-\frac{\pi}{2}\le y\le\frac{\pi}{2}$

c)

$-\frac{\pi}{2}<y<\frac{\pi}{2}$

55.

Q5. The principal value of $\ Cos^{-1}\frac{1}{2}\ +\ 2Sin^{-1}\ \frac{1}{2}\ is$

a)

$\frac{2\pi}{3}$

b)

$\frac{\pi}{4}$

c)

$\frac{2\pi}{6}$

56.

Q6. The principal value of $\ \ \tan^{-1}\sqrt{3}-\ \sec^{-1}\left(-2\right)\ \ is$

a)

$\pi$

b)

$\frac{\pi}{3}$

c)

$\frac{2\pi}{3}$

57.

Q7. The principal value of $\ Co\sec^{-1}\left(-\sqrt{2}\right)\ is\$

a)

$-\frac{\pi}{6}$

b)

$-\frac{\pi}{2}$

c)

$-\frac{\pi}{4}$

58.

Q8. Which of the following is NOT TRUE about inverse functions?

a)

Inverse functions are reflections of each other over the line y = x.

b)

You find the inverse by switching x and y in the equation.

c)

The domain of a function always becomes the domain of its inverse.

d)

The domain of a function always becomes the range of its inverse.

59.

Q9. $\cos^{-1}\left(\cos\ \frac{7\pi}{6}\right)\$ is equal to

a)

$\frac{7\pi}{6}$

b)

$\frac{5\pi}{6}$

c)

$\frac{-\pi}{3}$

d)

$\frac{-\pi}{6}$

60.

Q10. Find the principal value of : $\ Cos^{-1}\left\{\tan\ \left(\frac{-\pi}{4}\right)\right\}\$

a)

0

b)

π

c)

π/4

d)

3π/4

61.

Find the value of cos x if tan x = 15/8.

a)

8/17

b)

8/15

c)

17/8

d)

15/17

62.

Given that sin x = 3/5, find the value of cos x.

a)

5/4

b)

4/5

c)

5/3

d)

3/4

63.

If csc x = 13/5, what is the value of cot x?

a)

5/12

b)

12/13

c)

13/5

d)

12/5

64.

Solve for sec x if tan x = 7/24

a)

24/7

b)

24/25

c)

7/25

d)

25/7

65.

What is the value of cot x when sin x = 6/10?

a)

8/6

b)

8/10

c)

6/8

d)

6/10

66.

If sin x = 8/17, determine the value of cos x.

a)

15/8

b)

15/17

c)

8/15

d)

17/15

67.

Given that csc x = 41/9, calculate the value of cos x.

a)

9/41

b)

40/41

c)

9/40

d)

40/9

68.

Find cos x when tan x = 24/7.

a)

24/25

b)

7/25

c)

7/24

d)

25/24

69.

If sin x = 12/15, what is the value of the cot x?

a)

9/15

b)

9/12

c)

12/9

d)

15/9

70.

Determine the value of csc x if tan x = 9/40.

a)

40/9

b)

40/41

c)

41/40

d)

41/9

71.

Which equation is y=|x| transformed left 3 and up 2?

a)

y =|x+3| +2

b)

y=|x-3| + 2

c)

y=|x - 2| +3

72.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

73.

Which equation below is a quadratic function translated up 5 units?

a)

y = x² + 5

b)

y = (x + 5)²

c)

y = 5x²

d)

y = -x² - 5

74.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

75.

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

a)

y = x² + 2

b)

y = -x² + 2

c)

y = x² - 2

d)

y = -(x + 2)²

76.

Match the equation with the graph:

a)

y = (x - 2)² + 4

b)

y = -(x - 4)² + 2

c)

y = -(x - 2)² + 4

d)

y = -(x + 2)² + 4

77.

What is the equation of this graph?

a)

f(x) = (x + 2)² - 3

b)

f(x) = (x - 2)² - 3

c)

f(x) = |x + 2| - 3

d)

f(x) = |x - 2| - 3

78.

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

a)

horizontal shift right 5 units

b)

horizontal shift left 5 units

c)

vertical shift up 5 units

d)

vertical shift down 5 units

79.

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

a)

horizontal shift left 7 units

b)

horizontal shift right 7 units

c)

vertical shift up 7 units

d)

vertical shift down 7 units

80.

Which transformation transforms the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a vertical shift 4 units up

b)

a vertical shift 4 units down

c)

a horizontal shift 4 units to the left

d)

a horizontal shift 4 units to the right

81.

Which equation describes the transformation of shifting f(x)=x³ four units down?

a)

x³+ 4

b)

x³- 4

c)

(x - 4)³

d)

(x + 4)³

82.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

83.

.
If the blue is f(x)=x^2,then the red must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

84.

f(x) = 5x² + 2

a)

Stretch of 5
Up 2

b)

Shrink of 5
Up 2

c)

Stretch of 5
Down 2

d)

Shrink of 5
Down 2

85.

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

86.

a)

g(x)=2x²

b)

g(x)=0.5x²

c)

g(x)=x²+2

d)

g(x)=(x+2)²

87.

.
If the blue is f(x)=x^2,the red must be

a)

g(x)=(x+3)²

b)

g(x)=(x-3)²

c)

g(x)=x²+3

d)

g(x)=x²-2

88.

What are the following transformations?
- f(x+2)

a)

reflection over the y axis and 2 units to the right

b)

reflection over the x axis and 2 units right

c)

reflection over the y axis and 2 units left

d)

reflection over the x axis and 2 units left

89.

What are the following transformations:
f(-x) - 4

a)

reflection over the x axis and 4 units right

b)

reflection over the x axis and 4 units down

c)

reflection over the y axis and 4 units right

d)

reflection over the y axis and 4 units down

90.

Which equation describes the transformation of shifting f(x)=x³ four units down?

a)

x³+ 4

b)

x³- 4

c)

(x - 4)³

d)

(x + 4)³

91.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

92.

a)

f(x) = −(x−2)³−1

b)

f(x) = −(x+2)³−1

c)

f(x) = −(x−2)³ + 1

d)

f(x) = −(x+2)³ + 1

93.

What is the equation of this graph?

a)

f(x) = (x + 2)² - 3

b)

f(x) = (x - 2)² - 3

c)

f(x) = |x + 2| - 3

d)

f(x) = |x - 2| - 3

94.

Which equation represents this graph.

a)

f(x)=(x - 4)² - 3

b)

f(x)=-(x - 4)² + 3

c)

f(x)=(x - 4)² + 3

d)

f(x)=-(x + 4)² + 3

95.

The original function has equation f(x). State the transformations given the new function f(x) = ⅔(x - 7)²

a)

Vertical Shrink of ⅔
Right 7

b)

Horizontal Shrink of ⅔
Left 7

c)

Left ⅔
Vertical stretch of 7

d)

Right ⅔
Horizontal stretch of 7

96.

Which is an example of a reflection across the x-axis/ flip of the graph?

a)

$f\left(x\right)=\sqrt{x-2}$

b)

$f\left(x\right)\ =\ -\sqrt{x-2}$

c)

$f\left(x\right)=\sqrt{x}-2$

d)

None of the above

97.

Which is an example of a function shifting downward 2 units and to the right 3 units

a)

$f\left(x\right)\ =\left(x-2\right)^2-3$

b)

$f\left(x\right)\ =\left(x-3\right)^2-2$

c)

$f\left(x\right)\ =\left(x-3\right)^2-2$

d)

$f\left(x\right)=\ -2\ x^2+3$

98.

Match the equation with the graph:

a)

y = (x - 2)² + 4

b)

y = -(x - 4)² + 2

c)

y = -(x - 2)² + 4

d)

y = -(x + 2)² + 4

99.

What is the equation of the graph below?

a)

f(x ) = I x + 4 I + 2

b)

f(x ) = -I x - 4 I + 2

c)

f(x ) = I x - 4 I + 2

d)

f(x ) = -I x + 4 I + 2

100.

What is the equation of the graph below?

a)

f(x) = I x I -1

b)

f(x) = I x I +1

c)

f(x) = - I x I -1

d)

f(x) = -I x I +1

101.

What is the equation of the graph below? You can click the picture to zoom in!

a)

y = - | x + 2| + 4

b)

y = - | x - 2| + 4

c)

y = | x - 2 | + 4

d)

y = | x - 2| - 4

102.

a)

y = - √(x + 1)

b)

y = √(x + 1)

c)

y = - √(x) - 1

d)

y = - √(x) + 1

103.

Evaluate the geometric series below:
-2 - 10 - 50 - 250..., S6

a)

-7812

b)

-9678

c)

-8686

d)

-9932

104.

Evaluate the geometric series below:
4 - 8 - 16 - 32..., S₇

a)

195

b)

172

c)

202

d)

145

105.

Evaluate the geometric series below:
-1 -3 -9 - 27..., S8

a)

-3280

b)

-3135

c)

-3323

d)

-3343

106.

A bouncing ball reaches heights of 16 cm, 12.8 cm, and 10.24 cm on three consecutive bounces. If the ball was originally dropped from 25 cm (a₁ = 25), how much total distance in the downward direction has the ball traveled after five bounces?

a)

25 cm

b)

84.04 cm

c)

53.7956 cm

d)

59.04 cm

107.

What is the sum of the first ten terms of the sequence 4, -12, 36, -144 . . . ?

a)

59,050

b)

-59,048

c)

-78,732

d)

118,096

108.

Find the indicated sum for the geometric series.
S₆ for (-4/5) + 8 + (-80) + 800 + ....

a)

_S6 = 21,845

b)

_S6 = 72,000

c)

_S6 = 72,727.2

d)

_S6 = -128,840.8

109.

Evaluate the geometric series described.
$3+15+75+375...,\ \ \ \ n=6$

a)

11,718

b)

10,603

c)

9,769

d)

$-\frac{3}{4}$

110.

$a_1=3,\ \ \ r=5,\ \ \ n=7$ Evaluate

a)

$58,593$

b)

$52,120$

c)

$41,923$

d)

$54,646$

111.

$-3,\ \ 6,\ -12,\ \ 24,\ ....$ Find the common ratio

a)

3

b)

-2

c)

2

d)

$\frac{1}{2}$

112.

$4,\ 24,\ 144,\ 864,\ ...$ Find the next 3 terms

a)

$1024,\ \ 4096,\ \ 16384$

b)

$256,\ 1024,\ 4096$

c)

$256,\ -1024,\ 4096$

d)

$5184,\ 31104,\ 196624$

113.

Find the common ratio: -3, -9, -27, -81, ...

a)

r = 6

b)

r = -6

c)

r = 3

d)

r = -3

114.

What is the sum of the first ten terms of the sequence 4, -12, 36, -144 . . . ?

a)

59,050

b)

-59,048

c)

-78,732

d)

118,096

Charl

Total questions: 114

Worksheet time: 8hrs 25mins

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