Free Printable Year 10

1.

Simplify fully:
√32

a)

4√8

b)

16√2

c)

4√2

d)

4√4

2.

Simplify the following surd...

a)

3√2

b)

2√3

c)

9√2

d)

3√6

3.

Simplify the following surd...

a)

6√2

b)

2√6

c)

8√2

d)

4√6

4.

Simplify the following surd...

a)

4√2

b)

2√3

c)

6√2

d)

4√3

5.

Simplify the following surd...

a)

5√2

b)

5√3

c)

2√5

d)

10√5

6.

Simplify the following surd...

a)

2√2

b)

4√2

c)

2√4

d)

3√2

7.

Simplify the following surd...

a)

7√2

b)

3√5

c)

9√3

d)

3√3

8.

Simplify the following surd...

a)

5√5

b)

3√5

c)

15√3

d)

5√3

9.

Simplify the following surd...

a)

5√5

b)

3√5

c)

9√3

d)

5√3

10.

Simplify the following surd...

a)

7√7

b)

3√7

c)

9√7

d)

7√3

11.

Simplify the following surd...

a)

4√2

b)

8√2

c)

2√4

d)

2√8

12.

Simplify the following surd...

a)

10√2

b)

8√2

c)

2√8

d)

5√8

13.

Simplify the following surd...

a)

6√2

b)

2√18

c)

2√8

d)

3√8

14.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

15.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

16.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

17.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

18.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

19.

Simplify 4⁰

a)

1

b)

4

c)

0

20.

Simplify 4⁷ ÷ 4³

a)

4¹⁰

b)

4

c)

4²¹

d)

4⁴

21.

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

a)

4¹⁴

b)

4¹

c)

4⁸

d)

4⁶

22.

Evaluate 1² + 2² + 3²

a)

6

b)

12

c)

14

d)

11

23.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

24.

Simplify

a)

A

b)

B

c)

C

d)

D

25.

Simplify

a)

A

b)

B

c)

C

d)

D

26.

a×a×a

a)

3a

b)

3a³

c)

a³

d)

3a²

27.

a³×a⁴

a)

7a

b)

12a

c)

a¹²

d)

a⁷

28.

9a+a

a)

9a²

b)

9a

c)

10a

d)

11a

29.

a×a×a×a

a)

4a

b)

a⁴

c)

4a⁴

d)

2a²

30.

a²×a⁴

a)

6a

b)

6a²

c)

a⁶

d)

8a²

31.

5a×3a

a)

15a²

b)

30a

c)

15a

d)

a³⁰

32.

a×a⁸

a)

a⁸

b)

2a⁸

c)

a⁹

d)

2a⁹

33.

7a+3a

a)

21a²

b)

10a²

c)

21a

d)

10a

34.

What is the name of the big number?

a)

Base

b)

Index

c)

Indices

d)

Power

35.

What is the name of the little number?

a)

Base

b)

Index

c)

Power

d)

Indices

36.

The word INDEX is....

a)

Singular

b)

Plural

37.

The word INDICES is....

a)

Singular

b)

Plural

38.

Which number is the base in... $6^5$

a)

6

b)

5

39.

Which number is the index/power in... $6^5$

a)

6

b)

5

40.

What is the index/power in... $x^2$

a)

x

b)

2

41.

What is the base in... $x^2$

a)

x

b)

2

42.

Writing this expression in Index form 3x3x3x3x3 would give...

a)

$3^5$

b)

$5^3$

c)

243

d)

$x^5$

43.

Writing this expression in Index form 7x7x7 would give...

a)

$7^3$

b)

$3^7$

c)

343

d)

$7^x$

44.

Evaluate the following... $5^3$

a)

125

b)

5 x 5 x 5

c)

3 x 3 x 3 x 3 x 3

d)

15

45.

Show what $5^3$ means...

a)

125

b)

5 x 5 x 5

c)

3 x 3 x 3 x 3 x 3

d)

15

46.

Work out the following... $2^5$

a)

32

b)

2 x 2 x 2 x 2 x 2

c)

5 x 5

d)

10

47.

The words Index & Power mean the same thing

a)

True

b)

False

48.

The words Index & Indices have the same meaning, except one is Singular and the other is Plural

a)

True

b)

False

49.

The words Index & Base mean the same thing

a)

True

b)

False

50.

The words Power & Base mean the same thing

a)

True

b)

False

51.

The Plural version of the word Index is

(a)

52.

Write 25 using Index notation,

with base 5

a)

$5^2$

b)

$2^5$

c)

5 x 5

d)

2x2x2x2x2

53.

Write 128 using Index notation,
with base 2

a)

$7^2$

b)

$2^7$

c)

7 x 7

d)

2x2x2x2x2x2x2

54.

The triangles are similar by...

a)

SAS

b)

AA

c)

ASA

d)

SSS

55.

The triangles are similar by...

a)

SAS

b)

AA

c)

ASA

d)

SSS

56.

The triangles are similar by...

a)

SAS

b)

AAS

c)

ASA

d)

SSS

57.

Determine whether the triangles are similar.

a)

SSS

b)

AA

c)

SAS

d)

not similar

58.

How are these triangles similar?

a)

A

b)

B

c)

C

d)

D

59.

Find AE

a)

12.5

b)

18

c)

11.75

d)

13

60.

What is the height of the Tree?

a)

20

b)

15

c)

30

d)

10

61.

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. How tall is the tree?

a)

144 feet

b)

72 feet

c)

36 feet

62.

If the triangles are similar, state how.

a)

SSS

b)

SAS

c)

AA

d)

Not similar.

63.

Complete each proportion.
AB / AM = ? / DM

a)

BC

b)

AC

c)

MD

d)

MC

64.

The pair of figures is similar. Find the missing side.

a)

x = 9

b)

x = 28

c)

x = 63

d)

x = 7

65.

Are the triangles similar? If so, what similarity test is used?

a)

Similar. SAS

b)

Similar. AA

c)

Similar. SSS

d)

Not Similar

66.

Solve the proportion.

a)

20

b)

7

c)

22

d)

11

67.

What is the scale factor from MNOP to ABCD?

a)

2/3

b)

1/2

c)

3/2

d)

2

68.

What is the scale factor from ΔDEF to ΔABC?

a)

1/2

b)

7/3

c)

2

d)

10/3

69.

a)

7.6

b)

5.76

c)

10.944

d)

1.2

70.

a)

3.2

b)

7.5

c)

2

d)

5.3

71.

a)

2.6

b)

18.2

c)

2.7

d)

20.28

72.

a)

1.5

b)

4.95

c)

2.2

d)

5.4

73.

a)

2.4

b)

3.1

c)

17.856

d)

2.6

74.

a)

1.8

b)

4.2

c)

6.48

d)

3.78

75.

a)

1.4

b)

9.8

c)

5.6

d)

14

76.

a)

4.5

b)

9

c)

10

d)

9.5

77.

a)

1.6

b)

5.3

c)

13.568

d)

4.4

78.

a)

2.6

b)

1.6

c)

10.816

d)

5

79.

a)

3.2

b)

20.48

c)

4

d)

6

80.

a)

2.4

b)

9.6

c)

1.6

d)

10.4

81.

What is the Grinch's dog called?

a)

Spot

b)

Max

c)

Milo

d)

Bailey

82.

What is the name of Ebenezer Scrooge's business partner, from the play, A Christmas Carol?

a)

Jason Orange

b)

Jason Scrooge

c)

Jacob Marley

d)

Jacob Scrooge

83.

What is the name of the animated Christmas movie featuring the voice of Tom Hanks?

a)

Elf

b)

The Polar Express

c)

A Christmas Carol

d)

Arthur Christmas

84.

What is the plant that is sometimes known as the Christmas flower?

a)

Carnation

b)

Alstroemeria

c)

Gardenia

d)

Poinsetta

85.

According to the song 'The 12 days of Christmas', on the tenth day, what does my true love give to me?

a)

Turtle doves

b)

Partridge in a pear tree

c)

Lords a-leaping

d)

Drummers Drumming

86.

In the carol, 'Jingle Bells', what kind of sleigh is mentioned?

a)

Twelve horse open sleigh

b)

Father Christmas' Sleigh

c)

Rudolphs sleigh

d)

One horse open sleigh

87.

How many points does a snowflake traditionally have?

a)

Eight

b)

Seven

c)

Six

d)

Five

88.

What links Quentin Crips in 1993, Sharon Osbourne in 2002, Katie Piper in 2009, and whistleblower Edward Snowden in 2013?

a)

They married on Christmas day

b)

They've each read the alternative Christmas message

c)

They had Christmas dinner with the Queen

d)

None of them celebrate Christmas

89.

When making mince pies, which way should you stir your mince meat for good luck?

a)

Clockwise

b)

Anticlockwise

90.

In which country were Christmas trees first used to decorate homes?

a)

France

b)

Spain

c)

England

d)

Germany

91.

Solve the following

a)

16

b)

18

c)

20

d)

22

92.

Solve the following

a)

0

b)

13

c)

26

d)

29

93.

Santa had 9 reindeer, including Rudolph. Which reindeer does not belong below?

a)

Dancer

b)

Blunder

c)

Comet

d)

Dasher

94.

A year contains 365 days normally, so on what number day does Christmas fall on?

a)

359

b)

350

c)

355

d)

360

95.

How many ghosts are in A Christmas Carol?

a)

2

b)

3

c)

4

d)

5

96.

What is the correct name for the shape of the gift box?

a)

Cuboid

b)

Cube

c)

Square

d)

Rectangle

97.

What shape are the Christmas decorations?

a)

Pyramid

b)

Triangle

c)

Triangular pyramid

d)

Square based pyramid

98.

3 wise men visited baby Jesus. Which of these statements are false about the number 3?

a)

Odd number

b)

Multiple of 6

c)

Prime number

d)

Root of 9

99.

How many day does the month of December have?

a)

29

b)

30

c)

28

d)

31

100.

When is Christmas Day ?

a)

23rd

b)

24th

c)

25th

d)

26th

101.

If you multiply the number of Santa's reindeer's by the number of wise men your answer would be?

a)

10

b)

21

c)

27

d)

30

102.

If you subtract the number of days in December from number of days of Christmas your answer would be?

a)

19

b)

21

c)

30

d)

13

103.

The icicle on Rudolph's nose forms the ________ of a circle.

a)

Chord

b)

Diameter

c)

Segment

d)

Tangent

104.

Which is the next snowflake in the sequence?

a)

Snowflake A

b)

Snowflake B

c)

Snowflake C

d)

Snowflake D

105.

What number should be on the purple bauble on this Christmas factor tree?

a)

2

b)

18

c)

54

d)

270

106.

Which of Santa's elves has the correct answer to 2 significant figure?

a)

Andy

b)

Brandy

c)

Candy

d)

Dandy

107.

How many presents are there in Santa's red sack?

a)

21

b)

72

c)

80

d)

81

108.

What is the ratio of stars to candles in the calendar?

a)

8:5

b)

3:5

c)

5:8

d)

5:3

109.

Lapland to Midsomer Norton is 10.8 cm on Santa's map. How far is it actually in km?

a)

2 160 km

b)

216 km

c)

21 600 km

d)

215 000 000 km

110.

How long is slope AB?

a)

17 m

b)

16.3 m (3 s.f.)

c)

15.8 m (3 s.f.)

d)

12.7 m (3 s.f.)

111.

What is the range of temperatures recorded for the last week of December?

a)

3

b)

6

c)

9

d)

5

112.

What is the mean temperature of the last week in December?

a)

3 °C

b)

-2 °C

c)

-1 °C

d)

0 °C

113.

How many of these square Christmas cards will Brandy be able to pin up? (With no overlaps)

a)

72

b)

84

c)

96

d)

120

114.

What is the error interval for the weight (w) of the present?

a)

483 ⩽ W < 484

b)

482.5 ⩽ W < 483.5

c)

482.5 ⩽ W ⩽ 483.5

d)

482.5 < W ⩽ 483.4

115.

how much does the snowman's head weigh?

a)

70 kg

b)

100 kg

c)

140 kg

d)

175 kg

116.

When Was the first candy cane made?

a)

About 100 years ago

b)

About 150 years ago

c)

About 350 years ago

d)

About 500 years ago

117.

Snowflakes are made of _______ colored crystals.

a)

clear

b)

blue

c)

white

d)

not crystals at all

118.

Which reindeer grow antlers?

a)

male

b)

female

c)

both

d)

reindeer do not have antlers

119.

Historians believe the first Christmas tree was decorated in ________.

a)

France, 1810

b)

USA, 1776

c)

Germany, 1510

d)

England, 1620

120.

Mistletoe is very poisonous.

a)

True

b)

False

121.

Subtract y from x.

a)

y - x

b)

x - y

c)

x + y

d)

x/y

122.

Three angles form a straight line. What is the value of x?

a)

90

b)

180

c)

30

d)

60

123.

The perimeter of this rectangle is 44. What is the value of x?

(a)

124.

I think of a number, divide it by 3 and then subtract 4. My answer is 5. Choose the correct equation.

a)

$\frac{n}{3}-4\ =\ 5$

b)

$n-\frac{4}{3}=5$

c)

$\frac{\left(n-4\right)}{3}=\ 5$

d)

n3 - 4 = 5

125.

Matthew is t years old, Steve is 4 years older than Matthew. Altogether they are 48 years old. Write a simplified equation to show this

a)

t + 4 = 48

b)

t + t + 4 = 48

c)

2t + 4 = 48

d)

t = 22

126.

a)

Santa Claus is Coming to Town

b)

Angels We Have Heard on High

c)

O Holy Night

d)

Santa Baby

127.

a)

O Holy Night

b)

O Christmas Tree

c)

Silent Night

d)

Baby It's Cold Outside

128.

a)

Silent Night

b)

O Christmas Tree

c)

O Holy Night

d)

I Saw Three Ships

129.

a)

Up on the Housetop

b)

Walking in a Winter Wonderland

c)

Silent Night

d)

Baby it's Cold Outside

130.

a)

Silent Night

b)

O Christmas Tree

c)

Rudolph the Red-Nosed Reindeer

d)

Baby it's Cold Outside

131.

a)

Santa Baby

b)

I Saw Three Ships

c)

Jingle Bells

d)

We Three Kings

132.

1/2 x 3/4 (simplify if needed)

a)

3/8

b)

3/4

c)

4/6

d)

3/2

133.

6/11 x 5/6 (simplify if needed)

a)

15/33

b)

30/66

c)

11/17

d)

5/11

134.

18/45 simplifies to...

a)

6/15

b)

5/8

c)

2/5

d)

1/4

135.

6/7 divided by 3/7

a)

18/7 or 2 4/7

b)

2

c)

3/2 or 1 1/2

d)

1 2/7

136.

⁴/₉ ÷ ¹/₂

a)

⁸/₉

b)

⁵/₁₁

c)

⁶/₁₀

d)

⁴/₁₈

137.

Which Christmas film features a young boy who doubts the existence of Santa Claus, only to be taken on a magical journey to the North Pole?

a)

The Polar Express

b)

Elf

c)

Home Alone

d)

The Santa Clause

138.

In the Christmas film 'The Grinch', what is the name of the town that the Grinch tries to steal Christmas from?

a)

Whoville

b)

Christmas Town

c)

Snowflake City

d)

Santa's Village

139.

In the Christmas film 'Home Alone', what is the name of the two burglars who try to break into Kevin's house?

a)

Harry and Marv

b)

Joe and Pete

c)

Sam and Max

d)

Bill and Ted

140.

a)

Corpse Bride

b)

Gremlins 2

c)

Nightmare Before Christmas

141.

a)

Batman

b)

Die Hard

c)

Deadpool

142.

The corners or points on a 3D object are called...

a)

outlines

b)

cylinder

c)

lines

d)

vertices

143.

A prism gets its name from its

a)

faces

b)

bases

144.

A pyramid has _______ base(s).

a)

1

b)

2

145.

This is a net of what shape?

a)

Cube

b)

Rectangular Prism

c)

Triangular Prism

d)

Square Pyramid

146.

How many faces?

a)

2

b)

4

c)

6

d)

8

147.

When is Christmas Day ?

a)

31^st of December

b)

24^thof December

c)

3^rdof December

d)

25^thof December

148.

How many days are there in the Christmas advent calendar?

a)

31

b)

30

c)

24

149.

When is Christmas Eve?

a)

24th December

b)

26th December

c)

25th December

d)

31st December

150.

Who punishes naughty children in Salzburg?

(a)

151.

Where can you find a mango or banana tree as a Christmas tree?

a)

Portugal

b)

Spain

c)

India

d)

Japan

152.

3 out of 25 can be converted to what percentage?

a)

6%

b)

12%

c)

25%

d)

30%

153.

There are 100 apples. 35 are red apples and 65 are green apples. What percentage is green apple?

a)

100%

b)

65%

c)

35%

d)

30%

154.

A mixture contains 8 L of water and 42 L of milk. What is the percentage of water in the mixture?

a)

19.0%

b)

16%

c)

80.1%

d)

Not listed

155.

Ameer purchased a car for $10,000, which he later sold for $15,800.

What is the percentage of Ameer's profit?

a)

58%

b)

37%

c)

158%

d)

63%

156.

Compare: 0.025 ______ 2.5%

a)

>

b)

<

c)

=

157.

On the first day of Christmas
My true love sent to me
A ____________________

a)

partridge in a pear tree

b)

turtle dove

c)

french hen

d)

calling bird

158.

On the fourth day of Christmas
My true love sent to me
Four ____________________

a)

partridges in a pear tree

b)

turtle doves

c)

french hens

d)

calling birds

159.

On the fifth day of Christmas
My true love sent to me
Five ____________________

a)

golden rings

b)

geese a laying

c)

swans a swimming

d)

maids a milking

160.

On the ninth day of Christmas
My true love sent to me
Nine ____________________

a)

ladies dancing

b)

lords a leaping

c)

pipers piping

d)

drummers drumming

161.

On the twelfth day of Christmas
My true love sent to me
Twelve ____________________

a)

ladies dancing

b)

lords a leaping

c)

pipers piping

d)

drummers drumming

Year 10

Total questions: 161

Worksheet time: 5hrs 18mins

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