Free Printable Complex formulae

1.

1.) Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

2.

3.) Simplify
(45x⁶y²)/(5x⁴y⁹)

a)

(9x²)/y⁷

b)

40x²y⁷

c)

9x²y⁷

d)

9x¹⁰y¹¹

3.

2.) Simplify
(3x³y⁵)⁴

a)

3x¹²y²⁰

b)

81x¹²y²⁰

c)

12x¹²y²⁰

d)

81x⁷y⁹

4.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

5.

Simplify the expression:

$\left(x^8\right)\left(x^{-5}\right)$

a)

$x^{-40}$

b)

$x^{-13}$

c)

$x^{13}$

d)

$x^3$

6.

Re-write the expression in radical form.
x^2/3

a)

∛x²

b)

√x³

c)

(1/x)

d)

∛x

7.

Without using a calculator, what is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

8.

Simplify the following expression without using a calculator:

a)

5

b)

25

c)

125

d)

625

9.

Simplify without a calculator:

a)

2

b)

8

c)

16

d)

32

10.

$i^2=$

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

11.

$i^5=$

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

12.

$i^9=$

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

13.

$\sqrt{-64}$

a)

$8i$

b)

$-8$

c)

$8$

d)

$\pm8i$

14.

Solve: $x^2+36=0$

a)

$\pm6$

b)

$-6$

c)

$6i$

d)

$\pm6i$

15.

$\left(3-i\right)-\left(2+4i\right)=$

a)

$10+10i$

b)

$1-5i$

c)

$6-4i^2$

d)

$10$

16.

$\left(3-i\right)\left(2+4i\right)=$

a)

$10+10i$

b)

$1-5i$

c)

$6-4i^2$

d)

$10$

17.

$x^2+5x\ +8\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$\frac{-5\pm\sqrt{57}}{2}$

b)

$\frac{5\pm\sqrt{57}}{2}$

c)

$\frac{-5\pm i\sqrt{7}}{2}$

d)

$\frac{5\pm i\sqrt{7}}{2}$

18.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

19.

$x^2-6x\ +12\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$3\pm i\sqrt{3}$

b)

$3\pm\ \sqrt{3}$

c)

$\frac{6\pm\sqrt{-12}}{2}$

d)

$3\pm i$

20.

$-x^2+6x\ -10\ =0$

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

a)

$\frac{-6\pm\sqrt{76}}{-2}$

b)

$3\pm i$

c)

$-3\pm i$

d)

$\frac{6\pm\sqrt{76}}{-2}$

21.

What letter represents an imaginary number?

a)

a

b)

i

c)

b

d)

x

e)

z

22.

What does i² = ?

a)

$-1$

b)

$\sqrt[]{-1}$

c)

$1$

d)

$-\sqrt[]{1}$

e)

$i$

23.

Given the following Complex Number, identify the REAL part:

$7-8i$

a)

Real Part is 7

b)

Real Part is -7

c)

Real Part is -8

d)

Real Part is 8

24.

Given the following Complex Number, identify the IMAGINARY part:

$7-8i$

a)

Imaginary Part is 7

b)

Imaginary Part is -7

c)

Imaginary Part is -8i

d)

Imaginary Part is 8i

25.

Given the following Complex Number, identify the REAL part:

$37i$

a)

Real Part is 37

b)

Real Part is -37

c)

Real Part is 0

26.

Given the following Complex Number, identify the IMAGINARY part:

$37i$

a)

Imaginary Part is 37i

b)

Imaginary Part is -37i

c)

Imaginary Part is 0

27.

$(1+3i)+(7-2i)$

a)

$8+i$

b)

$i+8$

c)

$8+5i$

d)

$8-5i$

28.

Find the sum. $(5-2i)+(-7+8i)$

a)

$-2+6i$

b)

$12+6i$

c)

$-35-16i^2$

d)

$-35-16i$

29.

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

a)

$-5+i$

b)

$-5-i$

c)

$-9+i$

d)

$9-i$

30.

$\left(7\ +\ 3i\right)\ -\ \left(1-8i\right)$

a)

$6+11i$

b)

$6-5i$

c)

$6-5i^2$

d)

$31-53i$

31.

$(10-6i)-(2+3i)$

a)

$12+3i$

b)

$8-3i$

c)

$8-9i$

d)

$-9i+8$

32.

Choose the correct answer for the operation pictured.

a)

$7-13i$

b)

$7-i$

c)

$1-13i$

d)

$1-i$

33.

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

a)

$2-19i$

b)

$23-i$

c)

$34+5i$

d)

$-6-8i$

34.

$(1-3i)(2+5i)$

a)

$22-i$

b)

$16-i$

c)

$17-i$

d)

$-2+7i$

35.

a)

b)

c)

d)

36.

What is the simplified form of the above?

a)

$\frac{7}{10}+\frac{11}{10}i$

b)

$\frac{13}{10}+\frac{1}{10}i$

c)

$\frac{5}{4}-\frac{3}{2}i$

d)

$\frac{7}{10}-\frac{11}{10}i$

37.

What is the conjugate of $7-2i$ ?

a)

$7+2i$

b)

$7-2i$

c)

$2-7i$

d)

$2+7i$

38.

Find the sum.
(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

39.

Simplify
3i - (4 + 7i)

a)

-4 + 10i

b)

21 - 12i

c)

4 - 10i

d)

-4 - 4i

40.

(10-6i) - (2+3i)

a)

12 + 3i

b)

8 - 3i

c)

8 - 9i

d)

-9i + 8

41.

Multiply
3i(-2 + 4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

42.

The product of (3 -2i) and (7+6i) is

a)

21 - 12i

b)

9 + 4i

c)

33 + 4i

d)

21 + 16i

43.

-i(4-9i)

a)

-13i

b)

13i

c)

9 - 4i

d)

-9 - 4i

44.

(7 - 5i)(7 + 5i)

a)

74

b)

24

c)

49 - 25i

d)

49 + 25i

45.

The expression (2 + 3i)² is equal to

a)

-5

b)

-5 + 12i

c)

13

d)

13 + 12i

46.

What is the conjugate of
7-2i?

a)

7+2i

b)

7-2i

c)

2-7i

d)

2+7i

47.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

48.

a)

0

b)

-i

c)

1

d)

i

49.

√-4

a)

-2

b)

-2i

c)

2

d)

2i

50.

a)

A

b)

B

c)

C

d)

D

51.

a)

10

b)

-10

c)

10i

d)

-10i

52.

What is the quadratic formula?

a)

b)

c)

d)

53.

Solve 4x² - 2x + 4 = 0 using the quadratic formula

a)

x = 2, -1

b)

x = 3, -1

c)

x = 1, -2

d)

x = 1, -3

e)

No Solution

54.

Solve x² - 2x - 8 = 0 using the quadratic formula

a)

x = 2 , -3

b)

x = 4 , -2

c)

x = 2 , -4

d)

x = 3 , -2

e)

No Solution

55.

Solve 2p² - 3a + 1 = 0 using the quadratic formula

a)

x = 5, -4

b)

x = 4, -5

c)

x = 1, 1/2

d)

x = -1/2, -1

e)

No Solution

56.

Solve a² - 4a + 4 = 0 using the quadratic formula

a)

2

b)

-2

c)

4

d)

-4

e)

No Solution

57.

What is this formula?

a)

This is the standard formula.

b)

This is the quadratic formula.

c)

This is the square root formula.

d)

This is the Pythagorean formula

58.

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

59.

a)

A

b)

B

c)

C

d)

D

60.

How many solutions does a quadratic equation have?

a)

0

b)

1

c)

2

d)

All of the above

61.

Donovan is getting a new pool. If the length (L) is twice as long as it is wide (W), which equation represents the area (A) of the pool?

a)

A = (L)(2L)

b)

A = (W)(2W)

c)

A = L + 2L

d)

A = W + 2W

62.

Donovan is getting a new pool. If the length (L) is twice as long as it is wide (W), and the area is 200 ft², how wide is the pool?

a)

W = 15 ft.

b)

W = 20 ft.

c)

W = 10 ft.

d)

W = 13 ft.

63.

Calista is painting a new picture. The following equation represents the area. 35 = (W)(2 + W). Which equation is equivilant?

a)

W²- 2W - 35 = 0

b)

W²+ 2W - 35 = 0

c)

W²+ 2W + 35 = 0

d)

W²- 2W + 35 = 0

64.

When is a number written in standard form?

a)

when a number between 1 and 9.9 is multiplied by a power of 10.

b)

when a number between 1 and 10 is multiplied by a power of 10.

c)

when it only multiplies by 10

d)

when it is only multiplied by 100

65.

How do you write this number 650,000,000 in standard form?

a)

6.5 ✕ 10⁷

b)

6.5 x 10⁹

c)

6.5 ✕ 10¹⁰

d)

6.5 ✕ 10⁸

66.

What’s the shortest way?

a)

200 hm

b)

500 dam

c)

3 km

d)

600 hm

67.

Express 0.000056 in standard form

a)

5,6 x 10^-5

b)

56 x 10^-5

c)

5,6 x 10^-4

d)

5,6 x 10⁵

68.

5.68 x 10⁸ =?

a)

568 000 000

b)

568 00000

c)

5 680 000 000

d)

0,0000568

69.

Planet Earth is 150 million kilometers from the sun. This number in standard form is ...

a)

1,5 × 10⁸ km

b)

0,15 × 10¹⁰ km

c)

1,5 × 10^-10 km

d)

0,15 × 10⁹ km

70.

The mass of an electron is approximately 0,000 000 000 000 000 000 000 000 910 938 22 kg. In standard form and rounded to three significant figures is written:

a)

9,10 × 10^-31 kg

b)

9,11 × 10³¹ kg

c)

9,11 × 10^-31 kg

d)

9,109 × 10^-31 kg

71.

The size of a red globle is about 7,5×10⁻⁷ mm. Which of the following numbers equals?

a)

0,000 000 75

b)

0,000 000 007 5

c)

75000000

d)

75000000000

72.

0.00000005 in standar form is = ?

a)

5x10^-7 mm

b)

5x10⁸ mm

c)

5x10⁷ mm

d)

5x10^-8 mm

73.

When multiplying a number by a power of 10, the decimal point moves...

a)

To the left if the exponent is positive and to the right if the exponent is negative.

b)

To the right if the exponent is positive and to the left if the exponent is negative.

74.

Which of these numbers is the largest?

a)

$7.1\times10^{12}$

b)

$7.2\times10^{11}$

c)

$72\times10^{11}$

d)

$0.72\times10^{13}$

75.

It relates each number in standard form, with its respective expression in decimal notation.

a)

$1.2\times10^{-8}$

1.

0.000000012

b)

$1.2\times10^{-7}$

2.

0.00000012

c)

$6.02\times10^9$

3.

6020000000

d)

$6.02\times10^8$

4.

602000000

76.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

77.

Which of the following equations matches vertex form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

78.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

79.

What is the axis of symmetry for the following quadratic function: f(x)=1/2(x-4)²+3

a)

x=4

b)

x=-4

c)

x=1/2

d)

x=3

80.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

81.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

82.

Which equation is graphed above?

a)

$y=-\left(x-1\right)^2+4$

b)

$y=\left(x-1\right)^2+4$

c)

$y=-\left(x-4\right)^2+1$

d)

$y=\left(x-4\right)^2+1$

83.

Which equations matches the graph above?

a)

$h\left(x\right)=\ \left(x+1\right)^2-4$

b)

$h\left(x\right)=-\left(x+1\right)^2-4$

c)

$h\left(x\right)=\left(x+4\right)^2-1$

d)

$h\left(x\right)=-\left(x+4\right)^2+1$

84.

What is the vertex of the graph?

a)

$\left(0.13\right)$

b)

$\left(3,4\right)$

85.

$f\left(x\right)=-\left(x-4\right)^2+1$

Choose the correct graph of the equation.

a)

b)

c)

d)

86.

Which way does the following equation open? $f\left(x\right)=-\frac{1}{2}\left(x-5\right)^2+6$

a)

upward

b)

downward

87.

Which of the following is the correct equation for the given graph?

a)

f(x) = (x - 2)² - 1

b)

f(x) = (x + 2)² - 1

c)

f(x) = -(x + 2)² - 1

d)

f(x) = -(x - 2)² - 1

88.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

89.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

90.

(3x²y³)²

a)

9x⁴y⁶

b)

3x⁴y⁵

c)

6x⁴y⁶

d)

9xy

91.

What is the area of a rectangle if its dimensions are listed below:
length = 10x⁷
width = 7x⁵Hint: Area = (length)(width)

a)

70x¹²

b)

70x³⁵

c)

17x¹²

d)

17x³⁵

92.

Simplify.

a)

A

b)

B

c)

C

d)

D

93.

8

a)

W

b)

O

c)

R

d)

K

94.

Simplify -9⁰

a)

1

b)

-1

c)

-9

d)

9

95.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

96.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

97.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

98.

What is the correct law for multiplication? a^m x aⁿ=

a)

a^m+n

b)

a^m + aⁿ

c)

a^mxn

d)

a^mⁿ

99.

What is the correct law for division? a^m ÷ aⁿ =

a)

a^m-n

b)

a^m - aⁿ

c)

a^m÷n

d)

a^m/n

100.

What is the correct law for powers of powers? (a^m)ⁿ =

a)

a^mxn

b)

a^m+n

c)

a^m x aⁿ

d)

a^men

101.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

102.

Simplify 4⁰

a)

1

b)

4

c)

0

103.

2m⁵n³÷ 3m²n

a)

2/3 m⁵n²

b)

2/3 m³n²

c)

6 m³n²

d)

2/3 m²n3

104.

Simplify
3s⁴x 2t²x s³

a)

5st¹⁴

b)

5s⁷t²

c)

12 s⁷t ²

d)

6 s⁷t²

105.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

36xy³

c)

13x²y²

d)

13x³y³

106.

Simplify: (3x)² × (2x³y)² ÷ 6y³

a)

6x⁸y^-1

b)

6x⁸y

c)

3x⁷y

d)

3x⁷y^-1

107.

Which expression is equivalent to the following?

a)

32x³y⁴

b)

32x⁹y¹³

c)

16x⁸y¹²

d)

16x⁶y⁷

108.

It is a small number that tells us how many times a term has been multiplied by itself.

a)

Index

b)

Expanded Form

c)

Index Notation

d)

Base

109.

we can read this $4^3$

a)

4 to the superpower of 3

b)

4 by 3

c)

4 third

d)

'4 to the power of 3'

110.

It provides us rules for simplifying calculations or expressions involving powers of the same base.

a)

Laws of the Jungle

b)

Laws of Equation

c)

Laws of Indices

d)

Laws of Arithmetic

111.

This equation shows the law in multiplying indices

a)

$a^m\times a^n=a^{m+n}$

b)

$a^m\div a^n=a^{m-n}$

c)

$\left(a^m\right)^n=\ a^{m-n}$

d)

$a^0=1$

112.

This equation shows the law in raising a power to a power indices

a)

$a^m\times a^n=a^{m+n}$

b)

$a^m\div a^n=a^{m-n}$

c)

$\left(a^m\right)^n=\ a^{m-n}$

d)

$a^0=1$

113.

This equation shows the power of 0

a)

$a^m\times a^n=a^{m+n}$

b)

$a^m\div a^n=a^{m-n}$

c)

$\left(a^m\right)^n=\ a^{m-n}$

d)

$a^0=1$

114.

This equation shows the law in dividing indices.

a)

$a^m\times a^n=a^{m+n}$

b)

$a^m\div a^n=a^{m-n}$

c)

$\left(a^m\right)^n=\ a^{m-n}$

d)

$a^0=1$

115.

This equation shows the law of negative indices.

a)

$a^m\times a^n=a^{m+n}$

b)

$a^m\div a^n=a^{m-n}$

c)

$a^{-m}=\frac{1}{a^m}$

d)

$a^0=1$

116.

It a way of representing numbers and variables that have been multiplied by themselves a number of times.

a)

Indices

b)

Index Notation

c)

base

d)

power

117.

This is the plural of Index.

a)

Indices

b)

Indexes

c)

Index

d)

Indice

118.

Indices powers or exponents can also be called as powers of exponents.

a)

true

b)

false

c)

not sure

d)

maybe

119.

Turn a negative index to a positive index when flipping the term

a)

true

b)

false

c)

not sure

d)

maybe

120.

In fraction indices, what is the meaning of the denominator?

a)

The denominator of the fraction is the root of the number or letter.

b)

The denominator of the fraction is the power to raise the answer to.

c)

The denominator of the fraction is the root of the power.

d)

The denominator of the fraction is the power of the number or letter.

121.

In fraction indices, what is the meaning of the numerator?

a)

The numerator of the fraction is the root of the number or letter.

b)

The numerator of the fraction is the power to raise the answer to.

c)

The numerator of the fraction is the root of the power.

d)

The numerator of the fraction is the power of the number or letter.

122.

THE INDICES ARE ALSOKNOWN AS POWERS OREXPONENTS.

a)

True

b)

false

c)

maybe

d)

I don't know

123.

The individual numbers in a sequences are called...

a)

Common difference

b)

Successive term

c)

Term

d)

Geometric term

124.

Which kind of sequence has a common ratio?

a)

Arithmetic

b)

Geometric

125.

Which kind of sequence has a common difference?

a)

Arithmetic

b)

Geometric

126.

Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}

a)

Arithmetic

b)

Geometric

c)

Neither

127.

Is this sequence Arithmetic, Geometric, or Neither?
{2, 9, 7, 14, 12, 19, ... }

a)

Arithmetic

b)

Geometric

c)

Neither

128.

Identify the common difference.
97, 86, 75, 64, ...

a)

8

b)

11

c)

-11

d)

-8

129.

What is the common ratio: 5, 25, 125, 625...

a)

25

b)

20

c)

5

d)

4

130.

Which sequence is an arithmetic sequence?

a)

3, 6, 2, 7, ...

b)

3, 6, 12, 24, ...

c)

3, 6, 10, 15, ...

d)

3, 7, 11, 15, ...

131.

This is an arithmetic sequence. 5, 2, –1, –4, . . .

What is a_{7 (7th term)}?

a)

-13

b)

-11

c)

-18

d)

-22

132.

Create the explicit formula for the arithmetic sequence: 2, 8, 14, ...

a)

a_n=2+6(n-1)

b)

a_n=2+6^(n-1)

c)

a_n=6(n-2)

d)

a_n=14-6(n - 1)

133.

You have $10 in you bank account. It doubles every month. How much money will you have after 5 months?

a)

$50

b)

$35

c)

$320

d)

$250

134.

What is a_{5 (5th term)} in the sequence defined as follows? a_n = 5 ⋅ 2^(n-1)

a)

a₅ = 160

b)

a₅ = 40

c)

a₅ = 10

d)

a₅ = 80

135.

What is the explicit rule for the geometric sequence: 11, 22, 44, 88...

a)

a_n = 2(11)^n-1

b)

a_n = 11(2)

c)

a_n = 11(2)^n-1

136.

What is the 38th term of this arithmetic sequence? {26, 22, 18, 14, ... }

a)

-4

b)

10

c)

-122

d)

174

137.

What is the common ratio of this sequence?
{2, 10, 50, 250, ... }

a)

1,250

b)

5

c)

10

d)

50

138.

Write the explicit formula for the sequence.

9, 5, 1, -3, ...

a)

$a_n=9+5\left(n-1\right)$

b)

$a_n=9-4\left(n-1\right)$

c)

$a_n=4+9\left(n-1\right)$

d)

$a_n=9\cdot4^{\left(n-1\right)}$

139.

Write the explicit formula for the sequence.

216, 72, 24, 8, ...

a)

$a_n=216\cdot\left(\frac{1}{3}\right)^{\left(n-1\right)}$

b)

$a_n=8\cdot3^{\left(n-1\right)}$

c)

$a_n=216-144\left(n-1\right)$

d)

$a_n=216\cdot3^{\left(n-1\right)}$

140.

What is the next term in the sequence 12, 31, 40, 49, ... ?

a)

56

b)

57

c)

58

d)

59

141.

What is the eleventh term of an arithmetic sequence in which a1 = 3 and d = 6?

a)

63

b)

39

c)

69

d)

36

142.

What is the common ratio of this sequence ? 5, 25, 125, ...

a)

4

b)

2

c)

5

d)

6

143.

What is the common ratio of the geometric sequence -1, 6, -36, 216, ...?

a)

-6

b)

6

c)

12

d)

-4

144.

Find the common ratio: 64, -16, 4, -1, ...

a)

r = -8

b)

r = -1/4

c)

r = -4

d)

r = 4

145.

Solving for the nth term of geometric sequence, given thata₁ = 1 and r= 2, what is the value of the 4th term?

a)

2

b)

8

c)

4

d)

16

146.

Write the explicit formula for the geometric sequence.

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

147.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

148.

Find the 9th term in the following geometric sequence:

4, 8, 16, 32, ...

a)

384

b)

512

c)

768

d)

1,024

149.

What is the 11th term of the geometric sequence?

a)

-5120

b)

97,656,250

c)

19,531,250

d)

-19,531,250

150.

Given the sequence:

125, 25, 5, ....

Write the rule a_n using the geometric sequence formula:

a)

a_n = (125)(1/5)^(n-1)

b)

a_n = 625(1/5)^(n-1)

c)

a_n = 625(5)^(n-1)

d)

a_n = 125 + 5n

151.

A geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)?

a)

3

b)

6

c)

18

d)

2

152.

Find X

a)

500 cm

b)

250√3 cm

c)

125

153.

Find X

a)

√87.5

b)

9

c)

√81.25

154.

a)

1:√2

b)

√2:1

c)

1:2

d)

2:1

155.

a)

15

b)

6

c)

9

156.

a)

√2837

b)

√2937

c)

45

d)

50

157.

a)

2

b)

√2.25

c)

3

d)

√3.5

158.

a)

6

b)

6√2

c)

7

d)

5

159.

a)

Longest

b)

Shortest

c)

Not defined

160.

a)

Yes

b)

No

161.

a)

12

b)

13

c)

13.5

d)

14

162.

Identify the hypotenuse.

a)

x

b)

z

c)

w

163.

What is the length of x?

a)

5

b)

7

c)

8

d)

25

164.

Find the length of b in this triangle.

a)

31

b)

36

c)

60

d)

62

165.

Find x.

a)

35

b)

20

c)

8

d)

12

166.

Find the missing side of this right angled triangle...

a)

4.1cm

b)

2.4cm

c)

2.5cm

d)

4.2cm

167.

a)

11

b)

12

c)

9.8

d)

11.5

168.

a)

36.1

b)

36

c)

38.5

d)

32.1

169.

Calculate

a)

29.2

b)

14.2

c)

30

d)

32.2

170.

Does an 8, 15, 16 triangle have a Right Angle?

a)

Yes

b)

no

171.

What is the length of the monitor diagonally in two decimal places ?

a)

32.1

b)

32.10

c)

54.75

d)

47.2

172.

Given that the height of the wall is 2m , then what is the length of the plank that leans against the wall ?

a)

6.8

b)

1.7

c)

2.5

d)

3.9

173.

Which of the following are not right angled triangled triangle?

a)

3cm , 4cm , 5cm

b)

18cm, 34cm, 30cm

c)

15cm, 8cm, 17cm

d)

37cm, 35cm, 48cm

174.

A 2.5m long ladder leans against the wall of a building. The base of the ladder is 1.5m away from the wall. What is the height of the wall?

a)

2 cm

b)

8 m

c)

2 m

d)

5 m

175.

PQ is the base of a right angled triangle... RQ is the height of the right angled triangle... Then, determine the hypotenuse of the right angled triangle.

a)

PQR

b)

RQP

c)

QP

d)

PR

176.

To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

a)

35

b)

22

c)

58

d)

75

177.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

178.

Is this triangle a right triangle?

a)

yes

b)

no

179.

If a man is 6 ft. tall and he casts a shadow that is 3 ft. long, what is the distance from the top of the man's head to the end of his shadow.?

a)

9 feet

b)

6 feet

c)

6.7 feet

d)

9.7 feet

180.

Round to the nearest hundredth.

a)

5.57

b)

10.63

c)

5.32

d)

9

181.

In a computer catalog, a computer monitor is listed as being 27 cm. This distance is the diagonal distance across the screen. If the screen measures 15 cm in height, what is the actual width of the screen to the nearest inch?

a)

22 cm

b)

23 cm

c)

24 cm

d)

25 cm

182.

An investment of 600 earns 8% interest compounded annually for 1 year.

Which of the following is the appropriate calculation.

a)

$600\left(1.08\right)^1$

b)

$600\left(1.08\right)^{12}$

c)

$1.08\left(600\right)^{12}$

d)

$600\left(1.04\right)^2$

183.

Your 3 year investment of $20,000 received 5.2% interest compounded annually. What is your total return?

a)

$23,285.05

b)

$3,285.05

c)

$2,385

d)

$32,285

184.

The cost of a burger when from £5 to £6. What is the percentage increase in the price of the burger

a)

£1

b)

20%

c)

16.3%

d)

120%

185.

Prices are reduced by 27% in a sale at SuperMart. Georgia buys a TV, saving £75.60 on the original price. Calculate the original price

a)

103.56

b)

£280

c)

£2.80

d)

None of these

186.

My dog's weight is now 125% of what she weighted one year ago. If her weight then was 30kg, what is her weight now?

a)

31.25

b)

30.125

c)

37.5

d)

37.125

187.

Jack bought a bike for $550 and then sold it for $680. What was his percentage profit?

a)

130

b)

23.6

c)

19.1

d)

25.2

188.

The number of people signed up for a bus trip increased from 32 to 45. What is the percent increase? Round to the nearest percent.

a)

52%

b)

41%

c)

42%

d)

45%

189.

A grocery store has a 20% markup on bottle of soda. The bottle of soda costs the store $1.25. Find the selling price. Round to nearest cent if necessary.

a)

$1.5

b)

$1.50

c)

$.25

d)

$1.45

190.

Find the percent change from 28 to 42.

a)

50% decrease

b)

50% increase

c)

33% decrease

d)

33% increase

191.

Find each percent decrease. Round to the nearest percent.
From $80 to $64

a)

35%

b)

10%

c)

20%

d)

25%

192.

Find the PERCENT of change.
20 dogs to 5 dogs

a)

Decrease 15%

b)

Increase 15%

c)

Increase 75%

d)

Decrease 75%

193.

75 people to 25 people

a)

Increase

b)

Decrease

194.

Tickets to Disney World are $100.The price is going to increase on January 1. What is the percent of change if the cost increases to a $120?

a)

25%

b)

18%

c)

20%

d)

50%

195.

A Chicago Cubs baseball cap costs $30. Michael has a coupon that will save him 30% of the price. How much money will Michael pay for the cap?

a)

$9.00

b)

$22.00

c)

$21.36

d)

$21.00

196.

200 children attended the school play. Of the total attendance, 40% were boys. How many girls attended the school play?

a)

800

b)

180

c)

80

d)

120

197.

The regular price of a scooter is $65.50. It is on sale for $52.40. What is the percent decrease from the regular price to the sale price of the scooter?

a)

35%

b)

25%

c)

30%

d)

20%

198.

A sweater is $43. It is on sale for 20% off. What is the final price?

a)

$47

b)

$34.40

c)

$23

d)

$8.60

199.

A shoe sales associate earned $300 in August. In September she earned 8% more than she did in August. How much did she earn in September?

a)

$308

b)

$324

c)

$200

d)

$380

200.

An Ipad that costs $500 is on sale for 15% off. Then has a 6% tax. What's the final price?

a)

$450.50

b)

$521

c)

$491

d)

$400

201.

A store pays $32.00 for each video game. The store’s percent of mark up is 75%. Which shows the retail price of the video game?

a)

$60.00

b)

$56.00

c)

$24.00

d)

$8.00

202.

A computer store is selling a new MacBook for $899, but has a special back to school 20% discount for students. Arkansas sales tax is 6.5%. Find the final price of the MacBook.

a)

$879.80

b)

$719.20

c)

$672.80

d)

$765.95

203.

While on vacation in Florida, Mrs. Allison bought 2 Gucci bags at $278 each, on sale for 25% off. Florida sales tax is 9%. What is the final price of the bags?

a)

$227.27

b)

$303.02

c)

$454.53

d)

$417.53

204.

A store pays $32.00 for each video game. The store’s percent of mark up is 75%. You buy 3 video games, get a 10% discount, and pay 7.5% sales tax. What is your total?

a)

$168.00

b)

$151.20

c)

$162.54

d)

$92.88

205.

A moving point P maintains an equal distance from two parallel lines. Which of the following does the locus of P belong to?

a)

A circle

b)

A straight line

c)

Two parallel lines

d)

Two perpendicular lines

206.

The figure shows an equilateral triangle ABC. Which of the following lines may represent the locus of a point P such that AP = PB?

a)

b)

c)

d)

None of the above

207.

In the figure, ABCD is a square and its diagonals intersect at E. P is a moving point inside or on the square such that P is equidistant from AB and AD. The locus of P is

a)

AE

b)

AC

c)

BE

d)

BD

208.

Let A and B be two points. P is a point such that PA = PB, what is the locus of P?

a)

The locus of P is a circle with diameter AB

b)

The locus of P is circle with centre A and radius AB

c)

The locus of P is the perpendicular bisector of AB

d)

The locus of P is a pair of lines parallel to AB.

209.

Which of the following describes the locus X correctly?

a)

Locus of X is the locus of a moving point which is always equidistant from point Q

b)

Locus of X is the locus of a moving point which is always equidistant from point P and point R

c)

Locus of X is the locus of a moving point which is always equidistant from lines QP and QR

d)

Locus of X is the locus of a moving point which is always equidistant from line PR

210.

a)

A

b)

B

c)

C

d)

D

211.

Lakarkan lokus bagi titik C.

Sketch the locus of point C.

a)

b)

c)

d)

212.

Given a line segment AB of length 4 cm, which of the following dotted lines may represent the locus of a point P such that the area of △PAB is always equal to 4 cm²?

a)

b)

c)

d)

213.

The diagram shows a circle with centre O and a radius of 5 cm. The circle is divided into 8 equal parts.

Which two points are intersections of two loci which are always 5 cm from point O and 5 cm from the line LOQ?

a)

L and Q

b)

N and S

c)

M and R

d)

K and P

214.

In the diagram, PQRS is a square. PTR is an arc of a circle with centre S. QUS is an arc of a circle with centre P.

X is the locus of a point which moves such that its distance from S is always constant. Y is the locus of a point which moves such that it is equidistant from the lines PQ and QR. Which of the points, A, B, C or D, is the intersection of the locus X and the locus Y?

a)

A

b)

B

c)

C

d)

D

215.

In the diagram, P is the common centre of two circles, KRUQM and LTN, while Q is the common centre of the circles KLPUS and MNT.

A point Y moves such that it is always equidistant from points R and S.

The locus of Y is

a)

the arc KM.

b)

the straight line KU.

c)

the arc LN.

d)

the straight line LM.

216.

In the diagram, FGKL and GHJK are squares each with sides of 3 cm. LGJ is a semicircle with centre K.

X is a point which moves such that its distance from K is always 3 cm.

Y is a point which moves such that its perpendicular distance from line FGH is always 3 cm.

Which of the following are the intersection points of loci of X and Y?

a)

L and G

b)

L and J

c)

G and J

d)

L, G and J

217.

The diagram shows two circles with centres O and P. Given OP = 4 cm, S is the midpoint of OP and Q is the midpoint of SP.

A point L moves such that it is always 3 cm from point O. A point M moves such that it is always 2 cm from point P.

Which of the following points are the intersection of locus L and locus M?

a)

S and T

b)

Q and R

c)

R and T

d)

P and T

218.

What is the locus of a coconut falling from a tree?

a)

A vertical line

b)

A horizontal line

c)

A parabola

d)

A circle

219.

What shape would be produced by all the points which are 20cm away from a point?

a)

Circle

b)

Discorectangle (rectangle with semicircles on the end)

c)

Straight line

d)

Arc

220.

The figure shows an equilateral triangle ABC. Which of the following lines may represent the locus of a point P such that AP = PB?

a)

b)

c)

d)

None of the above

221.

Given two parallel straight lines AB and CD which are 2 cm apart, which of the following dotted lines may represent the locus of a point P such that it is equidistant from AB and CD?

a)

b)

c)

d)

222.

In the figure, ABCD is a square and its diagonals intersect at E. P is a moving point inside or on the square such that P is equidistant from AB and AD. The locus of P is

a)

AE

b)

AC

c)

BE

d)

BD

223.

What is the definition of a locus of points?

a)

The sum of two numbers

b)

The product of two numbers

c)

A set of points that satisfy a certain condition or property

d)

The square root of a number

224.

Caroline drives her car down a straight roadway so that the car is always equidistant from the two parallel curbs on the sides of the road. Describe Caroline's driving.

a)

Caroline is driving in the right hand lane.

b)

Caroline is driving in the left hand lane.

c)

Caroline is driving in the middle of the road.

d)

Caroline is swerving from the right lane to the left lane.

225.

What shape would be produced by all the points which are 20cm away from a point?

a)

Circle

b)

Discorectangle (rectangle with semicircles on the end)

c)

Straight line

d)

Arc

Complex formulae

Total questions: 225

Worksheet time: 8hrs 20mins

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