Free Printable Mock Quiz (Pythagoras, Sequences and Simultaneous Equations)

1.

Calculate

a)

5

b)

4.5

c)

8

d)

10

2.

Calculate

a)

8

b)

3.5

c)

6.7

d)

7

3.

Calculate

a)

4

b)

8

c)

7.6

d)

8.6

4.

Calculate

a)

8.6

b)

8.9

c)

9

d)

12

5.

Calculate

a)

13.5

b)

12

c)

14.3

d)

11

6.

Calculate

a)

8.3

b)

4

c)

3

d)

3.2

7.

Calculate

a)

10

b)

10.6

c)

10.4

d)

9.3

8.

a)

11

b)

12

c)

9.8

d)

11.5

9.

a)

36.1

b)

36

c)

38.5

d)

32.1

10.

Calculate

a)

5

b)

6

c)

5.5

d)

8

11.

Calculate

a)

6.5

b)

8

c)

3

d)

4

12.

Calculate

a)

6

b)

6.3

c)

7.8

d)

9

13.

Calculate

a)

8.7

b)

12.3

c)

8.2

d)

9

14.

Calculate

a)

9

b)

7.8

c)

6

d)

6.7

15.

Calculate

a)

9.8

b)

5.4

c)

7.8

d)

10.4

16.

Calculate

a)

2

b)

4

c)

2.6

d)

6.7

17.

Calculate

a)

4.5

b)

6

c)

9.8

d)

4.9

18.

Calculate

a)

18.7

b)

18

c)

22

d)

17.6

19.

Calculate

a)

29.2

b)

14.2

c)

30

d)

32.2

20.

Choose the correct value for the hypotenuse

a)

6cm

b)

4.47cm

c)

5.43cm

d)

4.99cm

21.

Choose the correct value for the hypotenuse

a)

8.43cm

b)

9.16cm

c)

7.39cm

d)

6.33cm

22.

Choose the correct value for the hypotenuse

a)

7.55cm

b)

9.12cm

c)

8.34cm

d)

7.15cm

23.

Choose the correct value for the missing side

a)

5.0cm

b)

3.85cm

c)

6.56cm

d)

4.45cm

24.

Choose the correct value for the missing side

a)

7.33cm

b)

3.01cm

c)

2.55cm

d)

4.1cm

25.

Choose the correct value for the missing side

a)

4.36cm

b)

3.5cm

c)

6.16cm

d)

5.55cm

26.

Use special triangles to find the missing side of this triangle

a)

28cm

b)

20cm

c)

18cm

d)

4cm

27.

Use special triangles to find the missing side of this triangle

a)

20cm

b)

180cm

c)

60cm

d)

40cm

28.

Use special triangles to find the missing side of this triangle

a)

45cm

b)

26cm

c)

50cm

d)

39cm

29.

Is this triangle right angled?

a)

Yes

b)

No

30.

Is this triangle right angled?

a)

Yes

b)

No

31.

A ship moves 10km due North and then 15km due East. How far is it from its starting point?

4 lines

32.

A ladder 4m long, is leaning against a building. The foot of the ladder is 1.5m away from the building. How far up the building does the ladder reach?

4 lines

33.

What kind of triangles does the Pythagorean Theorem work with?

a)

Right

b)

Left

c)

Isosceles

d)

Equilateral

34.

What is the formula used to solve for the hypotenuse?

a)

a²+b²=c²

b)

a+b=c

c)

a²-b²=c²

d)

c-a=c

35.

Identify the hypotenuse.

a)

x

b)

z

c)

w

36.

What is the length of x?

a)

5.7

b)

10.6

c)

20

d)

400

37.

solve for c

a)

7

b)

9

c)

4

d)

13

38.

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

39.

Find the length of b in this triangle.

a)

31

b)

36

c)

60

d)

62

40.

Find x.

a)

35

b)

20

c)

8

d)

12

41.

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

a)

4.1cm

b)

2.4cm

c)

2.5cm

d)

4.2cm

42.

The hypotenuse is always.............

a)

The right angle side

b)

The shortest side

c)

The longest side

d)

On the outside

43.

What is the relation between the three sides of the right-angled triangle in the figure?

a)

$x^2+y^2=z^2$

b)

$x^2+z^2=y^2$

c)

$y^2+z^2=x^2$

d)

$x+z=y$

44.

a)

11

b)

12

c)

9.8

d)

11.5

45.

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

46.

If a man goes 15 m due north and then 8 m due east, then his distance from the starting point is :

a)

7 m

b)

17 m

c)

23 m

d)

120 m

47.

a)

I only

b)

II only

c)

III only

d)

None of the above

48.

Which sequence is NOT an arithmetic sequence?

a)

-7, -13, -19, -25,...

b)

-10, -6, -2, 2,..

c)

6, 8, 10, 12,...

d)

3, 15, 75, 375,...

49.

Which sequence is NOT an arithmetic sequence?

a)

12, 18, 24, 30,...

b)

10, 3, -4, -11,...

c)

2, 4, 8, 16,...

d)

16, 20, 24, 28,...

50.

We will start with the explicit formula. Given the following sequence, state the first term and common difference.

Example 1: 4, 7, 10, 13, 16, …

a)

$a_1\ =\ 3,\ \ \ d\ =\ 4$

b)

$a_1\ =\ 16,\ \ \ d\ =\ 3$

c)

$a_1\ =\ 4,\ \ \ d\ =\ 3$

d)

$a_1\ =\ 16,\ \ \ d\ =\ 13$

51.

Now, find the term BEFORE term 1 (term 0).

Example 1: 4, 7, 10, 13, 16, …

a)

1

b)

4

c)

7

d)

0

52.

Now, write the explicit formula for the given sequence.

Example 1: 4, 7, 10, 13, 16, …

a)

$a_n\ =\ 1+3n$

b)

$a_n\ =\ 0+4n$

c)

$a_n\ =\ 3\ +\ 3n$

d)

$a_n\ =\ 16\ +\ 4n\$

53.

State the common difference:

Example 2: 21, 19, 17, 15, …

(a)

54.

Write an explicit rule to model the following sequence:

Example 2: 21, 19, 17, 15, …

a)

$a_n=21-2n$

b)

$a_n=21+2n$

c)

$a_n=23+2n$

d)

$a_n=23-2n$

55.

Write and explicit rule to model the following sequence:

Example 3: -12, -7, -2, …

a)

$a_n\ =\ 5\ -12n\$

b)

$a_n\ =\ -17\ +\ 5n$

c)

$a_n\ =\ -5\ +\ 12n$

d)

$a_n\ =\ -17-5n$

56.

Find the 26th term in the arithmetic sequence: 20, 26, 32, 38, ...

a)

182

b)

176

c)

170

d)

-118

57.

***What do the three dots (ellipsis) mean at the end of a sequence?***

a)

The sequence starts going in reverse order

b)

The sequence ends

c)

The sequence goes on forever

d)

The sequence increases by one from here on

58.

Now, let's go backwards!!! Given the explicit formula, what is the first term?

$a_n\ =\ 1+2n$

(a)

59.

Now, let's go backwards!!! Given the explicit formula, list the first five terms in order. (You can ignore term 0)

$a_n\ =\ 1+2n$

a)

2, 5, 8, 11, 14, ...

b)

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

c)

3, 6, 9, 12, 15, ...

d)

3, 5, 7, 9, 11, ...

60.

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

(Hint: Use the common difference AND the zero term!.)

a)

a_n= 6n + 2

b)

a_n= 6n - 6

c)

a_n= 6n - 4

d)

a_n = -6n + 4

61.

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

a)

18

b)

17

c)

15

d)

14

62.

TRUE or FALSE?

An arithmetic sequence is an example of a linear function.

a)

True, because having a common difference also means it has a constant rate of change

b)

False, because it's not shown on a graph

63.

What is the lesson about?

a)

Arithmetic Sequences

b)

Geometric Sequences

c)

No idea

d)

Some math stuff

64.

What is each number in a sequence called?

a)

common difference

b)

term

c)

sequence

d)

arithmetic

65.

What is the difference between two numbers in an arithmetic sequence called?

a)

common difference

b)

term

c)

sequence

d)

number

66.

Identify the common difference.

10, 20, 30, 40, ...

a)

5

b)

10

c)

15

d)

20

67.

The next two terms of the sequence 12,17,22,27 are

a)

28 and 33

b)

29 and 34

c)

32 and 37

d)

30 and 35

68.

The next two terms of the sequence 4,7,10,13 are

a)

16 and 19

b)

15 and 19

c)

16 and 18

d)

15 and 18

69.

Find the common difference: 29, 21, 13, 5, ...

Remember, the common difference is the difference between the numbers.

a)

d = -10

b)

d = -9

c)

d = -8

d)

d = -7

70.

Is the sequence arithmetic: 37, 31, 25, 19, ...

a)

Yes

b)

No

71.

Which sequences are arithmetic?

(hint: select 2)

a)

2, 4, 6, 8, 10 ...

b)

5, 10, 20, 40, 80, 100 ...

c)

1, 3, 7, 9, 15, 20 ...

d)

4, 8, 12, 16, 20, 24 ...

72.

Fill in the blank: What is the next number in the arithmetic sequence?

2, 8, 14, 20, (a)

73.

If the first term of an arithmetic sequence is 5 and the common difference is 6, what are the first five terms?

a)

5, 11, 17, 23, 29

b)

6, 11, 16, 21, 26

c)

5, 10, 15, 20, 25

d)

5, 11, 15, 20, 26

74.

Which sequence has a common difference of 4?

a)

4, 6, 8, 10, 12...

b)

1, 5, 9, 13, 17....

c)

4, 4, 4, 4, 4...

d)

4, 14, 24, 34, 44...

75.

Is the sequence Arithmetic?

10, 18, 26, 34, 40

a)

Yes

b)

No

76.

Fill in the blank: What is the next number in the arithmetic sequence.

2, 8, 14, 20, (a)

77.

Do you understand what an arithmetic sequence is?

a)

Yes

b)

A little bit

c)

No

d)

Mayber

78.

Is the sequence arithmetic: 37, 31, 25, 19, ...

a)

Yes

b)

No

79.

Is the sequence arithmetic: 17, 9, 1, -7, ...

a)

Yes

b)

No

80.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

81.

Find the common difference: 29, 21, 13, 5, ...

a)

d = -10

b)

d = -9

c)

d = -8

d)

d = -7

82.

Find the common difference: -18, -23, -28, -33, ...

a)

d = -5

b)

d = 5

c)

d = -3

d)

d = 3

83.

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

a)

-1, 7, 15

b)

-5, 2, 9

c)

3, 12, 21

d)

-65, -73, -81

84.

Find the next three terms in the arithmetic sequence: -3, -8, -13, -18, ...

a)

-20, -24, -28

b)

-21, -25, -29

c)

-23, -28, -33

d)

-24, -29, -32

85.

Find the next three terms in the arithmetic sequence: 9, 19, 29, 39, ...

a)

45, 54, 63

b)

49, 59, 69

c)

39, 49, 59

d)

59, 69, 79

86.

Find the next three terms in the arithmetic sequence: 25, 34, 43, 52, ...

a)

63, 72, 81

b)

79, 88, 97

c)

70, 79, 88

d)

61, 70, 79

87.

Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...

a)

-216

b)

-148

c)

-146

d)

-150

88.

Find a₂₆ in the arithmetic sequence: -15, -35, -55, -75, ...

a)

-515

b)

-490

c)

-535

d)

460

89.

Find the 26th term in the arithmetic sequence: 20, 26, 32, 38, ...

a)

182

b)

176

c)

170

d)

-118

90.

Find a₂₀ in the arithmetic sequence: 5, 12, 19, 26...

a)

145

b)

144

c)

142

d)

138

91.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

92.

Find the first term of the given sequence:
a₁₄=68
d=3

a)

14

b)

20

c)

26

d)

29

93.

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

a)

8

b)

11

c)

-11

d)

-8

94.

Identify the common difference.
3, 7, 11, 15, ...

a)

6

b)

5

c)

4

d)

2

95.

Find the 32nd term of this sequence.
34, 37, 40, 43, ...

a)

32

b)

64

c)

127

d)

356

96.

Is the following sequence arithmetic?
21, 13, 5, -3, ...

a)

YES

b)

NO

97.

Is the following sequence arithmetic?
1, 4, 9, 16, ...

a)

YES

b)

NO

98.

Solve
$3x+y=1$
$x-2y=19$

a)

$x=-4,\ y=3$

b)

$x=3,\ y=-4$

c)

$x=3,\ y=-8$

d)

$x=4,\ y=8$

99.

Solve

3x\ +\ 4y\ =\ 7

5x-2y=16

a)

$x\ =\ 3,\ y\ =\ -\frac{1}{2}$

b)

$x=-3,\ y\ =\ \frac{1}{2}$

c)

$x=\frac{1}{2},\ y=-3$

d)

$x=-\frac{1}{2},\ y=-3$

100.

Solve
$3x-4y=11$
$5x+6y=12$

a)

$x=0.5,\ y=-3$

b)

$x=3,\ y=0.5$

c)

$x=3,\ y=-0.5$

d)

$x=6,\ y=2$

101.

Solve
$2x+3y=0$
$x-3y=9$

a)

$x=2,\ y=-3$

b)

$x=3,\ y=-2$

c)

$x=-3,\ y=2$

d)

$x=-2,\ y=3$

102.

Solve
$8c+3d=-35$
$5c=-22-2d$

a)

$c=4,\ d=-1$

b)

$c=-4,\ d=-1$

c)

$c=-1,\ d=4$

d)

$c=1,\ d=-4$

103.

Solve:

3x - y = 11

x + y = 5

a)

x = 4

y = 1

b)

x = 4

y = -1

c)

x = -4

y = 1

d)

x = -4

y = -1

104.

Solve:

2x + 3y = 5

x + 3y = 7

a)

x = -2

y = 3

b)

x = -2

y = -3

c)

x = 2

y = 3

d)

x = 2

y = -3

105.

Solve:

2x + 5y = 29

x + 5y = 22

a)

x = 7

y = 3

b)

x = -7

y = -3

c)

x = 7

y = -3

d)

x = -7

y = 3

106.

Solve:

3x + 5y = 4

4x - 5y = -18

a)

x = -2

y = 2

b)

x = -2

y = -2

c)

x = 2

y = -2

d)

x = 2

y = 2

107.

Solve:

3x - 4y = 26

2x - 4y = 20

a)

x = 6

y = -2

b)

x = -6

y = -2

c)

x = -6

y = 2

d)

x = 6

y = 2

108.

Solve:

2x + y = 16

4x - y = 2

a)

x = 3

y = 10

b)

x = -3

y = -10

c)

x = -3

y = 10

d)

x = 3

y = -10

109.

Solve:

4x - y = 17

7x - y = 32

a)

x = 5

y = 3

b)

x = -5

y = 3

c)

x = 5

y = -3

d)

x = -5

y = -3

110.

Solve:

3x + 2y = 15

7x + 2y = 19

a)

x = 1

y = 6

b)

x = -1

y = 6

c)

x = 1

y = -6

d)

x = -1

y = -6

111.

Solve for (x,y)

-2x + 6y = 16

-4x - 3y = 2

a)

(2,2)

b)

(-2, -2)

c)

(-2,2)

d)

(2,1)

112.

Some horses and chickens are in a pasture. If there are a total of 28 animals and 80 legs, how many chickens and how many horses are there? (Hint: Write simultaneous equations and then solve)

a)

10 horses, 18 chickens

b)

16 horses, 12 chickens

c)

12 horses, 16 chickens

d)

18 horses, 10 chickens

113.

A man has 100 shares of stock A and 200 shares of stock B. The total value is $420. If he sells 50 shares of stock A and buys 60 shares of stock B the value is now $402. Find the price of each share.

a)

A = $2, B = $1

b)

A = $1, B = $2

c)

A = $1.20, B = $1.80

d)

A = $1.80, B = $1.20

114.

A theatre can hold 200 people. If the price of admission is $5 for an adult and $2 per child, find the number of each if the theatre is full and the profit is $577.

a)

59 adults and 141 children

b)

40 adults and 160 children

c)

60 adults and 140 children

d)

41 adults and 159 children

115.

Rectangle A is 3 times longer than rectangle B and twice as wide. If the perimeter of A is 50cm and the perimeter of B is 20cm, find the length and width of A.

a)

15 and 20

b)

5 and 15

c)

15 and 10

d)

5 and 10

116.

Solve:

3x - y = 11

x + y = 5

a)

x = 4

y = 1

b)

x = 4

y = -1

c)

x = -4

y = 1

d)

x = -4

y = -1

117.

Solve:

2x + 3y = 5

x + 3y = 7

a)

x = -2

y = 3

b)

x = -2

y = -3

c)

x = 2

y = 3

d)

x = 2

y = -3

118.

Solve:

2x + 5y = 29

x + 5y = 22

a)

x = 7

y = 3

b)

x = -7

y = -3

c)

x = 7

y = -3

d)

x = -7

y = 3

119.

Solve:

3x + 5y = 4

4x - 5y = -18

a)

x = -2

y = 2

b)

x = -2

y = -2

c)

x = 2

y = -2

d)

x = 2

y = 2

120.

Solve:

3x - 4y = 26

2x - 4y = 20

a)

x = 6

y = -2

b)

x = -6

y = -2

c)

x = -6

y = 2

d)

x = 6

y = 2

121.

Solve:

2x + y = 16

4x - y = 2

a)

x = 3

y = 10

b)

x = -3

y = -10

c)

x = -3

y = 10

d)

x = 3

y = -10

122.

Solve:

4x - y = 17

7x - y = 32

a)

x = 5

y = 3

b)

x = -5

y = 3

c)

x = 5

y = -3

d)

x = -5

y = -3

123.

Solve:

3x + 2y = 15

7x + 2y = 19

a)

x = 1

y = 6

b)

x = -1

y = 6

c)

x = 1

y = -6

d)

x = -1

y = -6

124.

Solve for (x,y)

-2x + 6y = 16

-4x - 3y = 2

a)

(2,2)

b)

(-2, -2)

c)

(-2,2)

d)

(2,1)

125.

Solve for (x,y)

5x + y = 9

10x − 7y = −18

a)

(-4,-1)

b)

(-1,-4)

c)

(4,1)

d)

(1, 4)

126.

Some horses and chickens are in a pasture. If there are a total of 28 animals and 80 legs, how many chickens and how many horses are there? (Hint: Write simultaneous equations and then solve)

a)

10 horses, 18 chickens

b)

16 horses, 12 chickens

c)

12 horses, 16 chickens

d)

18 horses, 10 chickens

127.

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of colour brochures, which cost a total of $134. After those ran out, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of colour brochures. Which simultaneous equations represent this situation?

a)

x+y=134

x+y=120

b)

3x+3y=134

4x+3y=120

c)

4x+3y=134

3x+3y=120

d)

7xy=134

6xy=120

128.

A man has 100 shares of stock A and 200 shares of stock B. The total value is $420. If he sells 50 shares of stock A and buys 60 shares of stock B the value is now $402. Find the price of each share.

a)

A = $2, B = $1

b)

A = $1, B = $2

c)

A = $1.20, B = $1.80

d)

A = $1.80, B = $1.20

129.

A theatre can hold 200 people. If the price of admission is $5 for an adult and $2 per child, find the number of each if the theatre is full and the profit is $577.

a)

59 adults and 141 children

b)

40 adults and 160 children

c)

60 adults and 140 children

d)

41 adults and 159 children

130.

Rectangle A is 3 times longer than rectangle B and twice as wide. If the perimeter of A is 50cm and the perimeter of B is 20cm, find the length and width of A.

a)

15 and 20

b)

5 and 15

c)

15 and 10

d)

5 and 10

Mock Quiz (Pythagoras, Sequences and Simultaneous Equations)

Total questions: 130

Worksheet time: 4hrs 20mins

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