Free Printable Maths Y10 Xmas Revision

1.

Convert 123₄ to base 10?

a)

18

b)

123

c)

27

d)

25

2.

Convert 145 to base 4.

a)

145₄

b)

2101₄

c)

3001₄

d)

1202₄

3.

What is the value in base 10?

\left(101011\right)_2

a)

45

b)

34

c)

43

d)

86

4.

Which number is divisible by 8?

a)

3364

b)

3064

c)

3264

d)

2364

5.

What is the value of 1203₄?

a)

67

b)

48

c)

54

d)

99

6.

a)

A

b)

B

c)

C

d)

D

7.

a)

A

b)

B

c)

C

d)

D

8.

Find the sum of the following values in base 4.

2030₄ + 1033₄

(a)

9.

Find the difference between these base 8 numbers.

4726₈ - 1062₈

(a)

10.

Convert 79₁₀to base 2

(a)

11.

11 011₂=

a)

17₁₀

b)

27₁₀

c)

33₁₀

d)

37₁₀

12.

Given that x₅ = 35_10,then x =

a)

10

b)

12

c)

20

d)

120

13.

101₂+ 111₂=

a)

1000₂

b)

1001₂

c)

1011₂

d)

1100₂

14.

Which of the following is false?

a)

101₂+ 11₂ = 1000₂

b)

101₂- 11₂ = 10₂

c)

101 110₂ = 56₈

d)

234₈ = 1 011 100₂

15.

Given that 43₅< x₁₀< 34_8,which of the following is not a possible value of x?

a)

25

b)

26

c)

27

d)

28

16.

Given that 43₅< x₁₀< 34_8,which of the following is not a possible value of x?

a)

25

b)

26

c)

27

d)

28

17.

What is the value of digit 2, in base ten, in the number 4231₅?

a)

50

b)

100

c)

200

d)

250

18.

Given that X₁₀= 11₂+ 11₅+ 11_8, find the value of X.

a)

15

b)

16

c)

17

d)

18

19.

110 100₂ - 11 011₂=

a)

10 000₂

b)

10 001₂

c)

11 001₂

d)

11 011₂

20.

Given that 4x5³+ 2x5²+ 5y = 4230_5,find the value of y.

a)

0

b)

2

c)

3

d)

6

21.

Given that 43₅< x₁₀< 34_8,which of the following is not a possible value of x?

a)

25

b)

26

c)

27

d)

28

22.

11 011₂=

a)

17₁₀

b)

27₁₀

c)

33₁₀

d)

37₁₀

23.

Change 351₁₀ to a number in base eight.
Tukar 351₁₀ kepada nombor dalam asas lapan.

a)

637₈

b)

547₈

c)

537₈

d)

532₈

24.

What is the value of digit 2, in base ten, in the number 4231₅?

a)

50

b)

100

c)

200

d)

250

25.

Given that 4x5³+ 2x5²+ 5y = 4230_5,find the value of y.

a)

0

b)

2

c)

3

d)

6

26.

Convert 123₄ to base 10?

a)

18

b)

123

c)

27

d)

25

27.

Convert 145 to base 4.

a)

145₄

b)

2101₄

c)

3001₄

d)

1202₄

28.

What is the value in base 10?

\left(101011\right)_2

a)

45

b)

34

c)

43

d)

86

29.

What is the value of 1203₄?

a)

67

b)

48

c)

54

d)

99

30.

Given that x₅ = 35_10,then x =

a)

10

b)

12

c)

20

d)

120

31.

Convert 1063₈to a number in base ten.

(a)

32.

Convert 4223₅to a number in base ten.

(a)

33.

State all digits that used in base 4.

a)

0,1,2

b)

0,1,2,3

c)

0,1,2,3,4

d)

1,2,3

34.

State the place value of the underlined digit.

341₈

a)

8¹

b)

8²

c)

8³

d)

8⁰

35.

State the value of the underlined digit.

5037₉

a)

3645

b)

45

c)

3697

d)

81

36.

Determine the value of the number 341₇

(a)

37.

Calculate the sum of the values of digit 8 and digit 3 in 1823₉.

(a)

38.

Choose any numbers which do not represent numbers in base six.

a)

245

b)

332

c)

461

d)

212

e)

371

39.

$50072_8=$

a)

$5\times8^2+7\times8+2\times8^0$

b)

$5\times8^3+7\times8^2+2\times8^1$

c)

$5\times8^4+7\times8+2\times8^0$

d)

$5\times8^5+7\times8^2+2\times8^1$

40.

The difference between the values of the digits 2 in the number $3212_5$ is

a)

8

b)

12

c)

48

d)

52

41.

It is a system for integers, where numbers "wrap around" upon reaching a certain value

a)

Remainder Theorem

b)

Congruence

c)

Modular Arithmetic

d)

Module Arithmetic

42.

Modular arithmetic studied and highlighted the concept of what theorem?

a)

Remainder Theorem

b)

Congruence

c)

Modular Arithmetic

d)

Module Arithmetic

43.

If it is already 6 o'clock, what time would it be after 17 hours?

a)

9:00

b)

10:00

c)

11:00

d)

12:00

44.

Using the assigned number of day,

(0=Sunday, 1=Monday, 2=Tuseday, 3=Wednesday, 4=Thursday, 5=Friday, 6=Saturday)

If today is Monday, what day would it be after 25 days?

a)

Thursday

b)

Friday

c)

Saturday

d)

Sunday

45.

Evaluate (35+62) mod 13

a)

(35+62) mod 13=7

b)

(35+62) mod 13=10

c)

(35+62) mod 13=13

d)

(35+62) mod 13=6

46.

Evaluate (74-25) mod 8

a)

(74-25) mod 8=1

b)

(74-25) mod 8=6

c)

(74-25) mod 8=3

d)

(74-25) mod 8=8

47.

Evaluate (14•20) mod 9

a)

(14•20) mod 9=31

b)

(14•20) mod 9=11

c)

(14•20) mod 9=3

d)

(14•20) mod 9=1

48.

Find the additive inverse of 9 in

mod 20 arithmetic

a)

29

b)

8

c)

11

d)

2

49.

In mod 11 arithmetic, find the possible multiplicative inverse of 3.

a)

4

b)

8

c)

5

d)

2

50.

Solve 7x + 3 = 3x + 6 (mod 5)

a)

3x = 6 (mod 7)

b)

7x = 3 (mod 5)

c)

10x = 9 (mod 7)

d)

4x = 3 (mod 5)

51.

For Modular Arithmetic what value is the most important?

a)

The Modulo

b)

The Given Number

c)

The Remainder

d)

The Divisor

52.

What is 7 mod 3?

a)

1 mod 3

b)

2 mod 3

c)

3 mod 3

d)

0 mod 3

53.

What is 57 mod 7?

a)

0 mod 7

b)

1 mod 7

c)

7 mod 7

d)

-1 mod 7

54.

What is 99 mod 100?

a)

99 mod 100

b)

100 mod 99

c)

1 mod 100

d)

100 mod 1

55.

What does 36 mod 13 look like using the Quotient Remainder Theorem?

a)

36 = 13 * 2 + 10

b)

36 = 10 * 3 + 6

c)

13 = 36 * 1 - 23

d)

6 = 36 - 10 * 3

56.

What does 13 mod 126 look like using the Quotient Remainder Theorem?

a)

13 = 126 * 0 + 13

b)

126 = 13 * 9 + 9

c)

13 = 126 * 0 + 13

d)

13 = 126 + 13

57.

What is 9 mod 2 - 10 mod 2 congruent to?

a)

0 mod 2

b)

1 mod 2

c)

-1 mod 2

d)

-2 mod 2

58.

What is 6 mod 9 + 11 mod 9 congruent to?

a)

8 mod 9

b)

6 mod 9

c)

7 mod 9

d)

0 mod 9

59.

what is (-5 mod 4) - (-3 mod 4) congruent to?

a)

2 mod 4

b)

1 mod 4

c)

-2 mod 4

d)

-1 mod 4

60.

What is 14 mod 8 - 15 mod 8 congruent to?

a)

7 mod 8

b)

1 mod 8

c)

0 mod 8

d)

6 mod 8

61.

Evaluate

a)

5⁴

b)

5¹⁰

c)

25¹⁰

d)

none of the above

62.

Simplify: 3⁵ x 3⁷

a)

3¹²

b)

9¹²

c)

3³⁵

d)

9³⁵

63.

Simplify: 2⁸ ÷ 2²

a)

2⁶

b)

2⁴

c)

2¹⁰

d)

1

64.

Simplify: 3x³ × 6x⁸

a)

18x¹¹

b)

18x²⁴

c)

9x¹¹

d)

9x²⁴

65.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

66.

y⁸ ÷ y

a)

y⁸

b)

y³

c)

y⁹

d)

y⁷

67.

5d⁴x3d⁸

a)

8d³²

b)

15d⁴

c)

15d¹²

d)

8d¹²

68.

a x a x a x a

a)

4a

b)

a⁴

c)

a⁶

d)

a

69.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

70.

Write (4⁷ x 4³) ∕ 4⁴ as a single power

a)

4¹⁴

b)

4¹

c)

4⁸

d)

4⁶

71.

Evaluate 2³+ 3²

a)

72

b)

36

c)

12

d)

17

72.

Write $\frac{1}{4\times4\times4\times4\times4}$ in index form

a)

$4^5$

b)

$4^{-5}$

73.

$\left(x^3\right)^4$ can be simplified into

a)

$x^{12}$

b)

$x^7$

c)

$x^{81}$

d)

$x^{-1}$

74.

Simplify 4⁰

a)

1

b)

4

c)

0

75.

Simplify: (y⁷)²

a)

y¹⁴

b)

y⁴⁹

c)

y⁵

d)

y⁹

76.

Simplify: (3h²)³

a)

27h⁶

b)

27h⁵

c)

9h⁶

d)

9h⁵

77.

Simplify

$\frac{t^3}{t}$

a)

t²

b)

t

c)

2t

d)

1

78.

What is (-2)³ equal to?

(a)

79.

Evaluate: $9^{-2}$

a)

$\frac{1}{81}$

b)

$-\frac{2}{9}$

c)

$-\frac{1}{81}$

d)

$\frac{2}{9}$

e)

$-81$

80.

Evaluate: $10^{-1}$

a)

$\frac{1}{10}$

b)

$-\frac{1}{10}$

c)

$-\frac{1}{100}$

d)

$\frac{1}{100}$

e)

$-10$

81.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

82.

Simplify: χ³ ÷ χ²

a)

χ

b)

χ⁵

c)

χ⁶

d)

χ^-1

e)

1/χ

83.

(y⁹)^-2

a)

y¹⁸

b)

y¹¹

c)

1/y¹⁸

d)

y⁹/2

84.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

85.

Simplify: 4x²y × 9xy²

a)

36x³y³

b)

36xy³

c)

13x²y²

d)

13x³y³

86.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

87.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

88.

Simplify: (4pq³)² ÷ (2p²q)³

a)

2p^-4q³

b)

8p⁴q³

c)

16p⁴q²

d)

4p^-4q²

89.

Simplify

a)

10x³

b)

x⁴ / 2

c)

x³

d)

x³ / 2

90.

a)

12

b)

8

c)

4

d)

2

91.

Simplify.

a)

A

b)

B

c)

C

d)

D

92.

Simplify

a)

A

b)

B

c)

C

d)

D

93.

$\log_216$

a)

8

b)

4

c)

6

94.

$\log_5625$

a)

5

b)

4

c)

25

95.

$\log_5\ \frac{1}{25}$

a)

$\frac{1}{2}$

b)

2

c)

-2

96.

$\log_{\frac{1}{3}}\ 9$

a)

$\frac{1}{3}$

b)

2

c)

-2

97.

$\log_{\frac{1}{3}}\ \frac{1}{9}$

a)

$\frac{1}{3}$

b)

2

c)

-2

98.

$\log_{\frac{1}{4}}\ 16$

a)

$\frac{1}{3}$

b)

2

c)

-2

99.

$\log25\ +\ \log\ 4$

a)

$\frac{1}{3}$

b)

2

c)

-2

100.

$\log_230\ -\ \log_215$

a)

$1$

b)

2

c)

-2

101.

$If\ \log_23=m,\ then\ \log_227\ =\ ...\$

a)

3m

b)

9m

c)

-3m

102.

$If\ \log_23=m,\ then\ \log_2\ \frac{1}{27}\ =\ ...\$

a)

3m

b)

9m

c)

-3m

103.

$If\ \log_23=m,\ then\ \log_3\ 2\ =\ ...\$

a)

$\frac{1}{m}$

b)

m

c)

$-m$

104.

$\frac{\log_25}{\log_23}\ is\ equal\ to\ ...\ .$

a)

$\log_35$

b)

$\log_53$

c)

$\log_215$

105.

$\log_32\times\log_25\ =\ ...\ .$

a)

$\log_35$

b)

$\log_53$

c)

$\log_215$

106.

$\log_52\times\log_23\ =\ ...\ .$

a)

$\log_35$

b)

$\log_53$

c)

$\log_215$

107.

$2^{\log_210}=...\ .$

a)

log 10

b)

log 2

c)

10

108.

Condense the Logarithm $5\log_{ }a\ -\ 25\log_{ }b$

a)

$\log\ \left(a^5+b^{25}\right)$

b)

$\log\ \left(a^5-b^{25}\right)$

c)

$\log\ \left(ab\right)^{25}$

d)

$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$

109.

Condense $3\log_{ }x+4\log_{ }y\ +\log_{ }z$

a)

$\log_{ }\ x^3y^4z$

b)

$12\log_{ }\ xyz$

c)

$\log_{ }\ 3x4yz$

d)

logx³y³z³

110.

Use the change-of-base formula to evaluate $\log_211$

a)

$3.459$

b)

$4.359$

c)

$5.123$

d)

2.345

111.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

112.

Simplify: $2\log_3\left(11x\right)$

a)

$\log_3\left(22x\right)$

b)

$\log_3\left(121x\right)$

c)

$\log_3\left(121x^2\right)$

d)

$\log_3\left(11x^2\right)$

113.

Simplify: $\frac{1}{4}\log_516+3\log_5x$

a)

$\log_5\left(4x^3\right)$

b)

$\log_5\left(2x^3\right)$

c)

$\log_5\left(6x\right)$

d)

$\log_5\left(\frac{2}{x^3}\right)$

114.

Simplify: $\frac{1}{4}\log_281+\frac{1}{2}\log_249$

a)

$\log_221$

b)

$\log_210$

c)

$\log_2\left(\frac{3}{7}\right)$

d)

$\log_244.75$

115.

Simplify: $\frac{1}{2}\log_964+\log_9x$

a)

$\log_9\left(32x\right)$

b)

$\log_9\left(8x\right)$

c)

$\log_9\left(\frac{8}{x}\right)$

d)

$\log_98x$

116.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

117.

Expand using the properties of Logaritms $\log_{ }\ \frac{x^3}{y^4z}$

a)

$\log_{ }x+4\log_{ }y\ +\log_{ }z$

b)

$3\log_{ }x-4\log_{ }y\ -\log_{ }z$

c)

$3\log_{ }x+4\log_{ }y\ +\log_{ }z$

d)

$3\log_{ }x-4\log_{ }y\ +\log_{ }z$

118.

Use these and other properties of logarithms to evaluate the expression.

$\log_232\ -\ 6^{\log_63}$

a)

$2$

b)

$-2$

c)

$8$

d)

$3$

119.

Expand the logarithm.
$\log_4\sqrt{x^3y}$

a)

$\frac{1}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

b)

$\frac{3}{2}\log_4\left(x\right)-\frac{1}{2}\log_4\left(y\right)$

c)

$\frac{1}{2}\log_4\left(x\right)-\log_4\left(y\right)$

d)

$\frac{3}{2}\log_4\left(x\right)-\log_4\left(y\right)$

120.

Use the change-of-base formula to evaluate $\log_7\ \frac{3}{16}$ rounded to two decimal places

a)

$0.82$

b)

$0.86$

c)

$0.85$

d)

$0.87$

121.

Expand the logarithm.
$\log\frac{x}{y^6}$

a)

$\log x+6\log y$

b)

$\log x-6\log y$

c)

$\log x+\log6y$

d)

$\log x-\log6y$

122.

Expand . $\log_6\left(\frac{5x^3}{y}\right)$

a)

$\log_65x^3-\log_6y$

b)

$\log_65+\log_6x^3-\log_6y$

c)

$\log_65+3\log_6x-\log_6y$

d)

$\log_65+3\log_6x+\log_6y$

123.

Evaluate $\log_52+\log_520-\log_54$ . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

a)

$1.4307$

b)

$-1.4307$

c)

$1.3470$

d)

$-1.347$

124.

Evaluate $\log_6\ \frac{1}{36}+\log_636-5^{\log_61}$ . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

a)

$1$

b)

$5$

c)

$12$

d)

$0$

125.

Evaluate $\log_6\ \frac{1}{216}+\log_24+\log_2\ \frac{1}{8}$ . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

a)

$4$

b)

$-4$

c)

$2$

d)

$5$

126.

Evaluate $\log_330-\log_4\ 4^5$ . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

a)

$1.9041$

b)

$-1.9041$

c)

$19,041$

d)

$9,041$

127.

Evaluate $1000^{\log_{10}4}-\log_464+25^{\log_510}$ . Use the table to approximate the value of the logarithmic expression or use the change-of-base formula to simplify.

a)

$161$

b)

$61$

c)

$-161$

d)

$126$

128.

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

129.

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

130.

What’s the shortest way?

a)

200 hm

b)

500 dam

c)

3 km

d)

600 hm

131.

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

132.

5.68 x 10⁸ =?

a)

568 000 000

b)

568 00000

c)

5 680 000 000

d)

0,0000568

133.

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

134.

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

135.

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

136.

0.00000005 in standar form is = ?

a)

5x10^-7 mm

b)

5x10⁸ mm

c)

5x10⁷ mm

d)

5x10^-8 mm

137.

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.

138.

Which of these numbers is the largest?

a)

$7.1\times10^{12}$

b)

$7.2\times10^{11}$

c)

$72\times10^{11}$

d)

$0.72\times10^{13}$

139.

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

Maths Y10 Xmas Revision

Total questions: 139

Worksheet time: 3hrs 1mins

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