Free Printable End of year 8

1.

Find the nth term of...
3,5,7,9...

a)

2n+1

b)

2n-1

c)

2n+2

d)

2n-2

2.

Find the nth term of...
1,3,5,7...

a)

2n+1

b)

2n-1

c)

2n+2

d)

2n-2

3.

Find the nth term of...
8,11,14,17...

a)

5n+3

b)

5n-2

c)

3n+5

d)

-2n+5

4.

Find the nth term of...
3,1,-1,-3...

a)

5n+3

b)

5n-2

c)

3n+5

d)

-2n+5

5.

Find the 4th term in the sequence f(n)=n²+3n+2

a)

30

b)

22

c)

25

d)

32

6.

What is the 6th term in the sequence:
f(x)= -(2)^n-2

a)

16

b)

-16

c)

8

d)

-8

7.

What is the nth term rule for the following sequence: 4, 9, 16, 25

a)

f(n)=n²

b)

f(n)=n² +1

c)

f(n)=(n+1)²

d)

f(n)=4ⁿ

8.

Is the following sequence linear or quadratic?
42, 56, 72, 90, 110

a)

Linear

b)

Quadratic

9.

Write the nth term rule for the sequence?
42, 56, 72, 90, 110

a)

n²+41

b)

2n+30

c)

2n²+30

d)

n²+11n+30

10.

Find the 18 term in the sequence: 4, 9, 16, 25

a)

324

b)

361

c)

289

d)

400

11.

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

Which of the following coordinates lies on the line y=2x-1?

a)

(-3,-7)

b)

(-6,11)

c)

(5,24)

d)

(13,6)

14.

a)

A

b)

B

c)

C

d)

D

15.

a)

A

b)

B

c)

C

d)

D

16.

a)

A

b)

B

c)

C

d)

D

17.

y = 2/3x + 9
What slope is Parallel to the equation given above?

a)

2/3

b)

-2/3

c)

-3/2

d)

3/2

18.

Which of the following coordinates lies on the line y=2x-1?

a)

(-3,-7)

b)

(-6,11)

c)

(5,24)

d)

(13,6)

19.

y = -3x +8
What slope is Parallel to the equation given above?

a)

3

b)

-3

c)

1/3

d)

-1/3

20.

Given the graph below, what are the x and y intercepts?

a)

x = -2 and y = 1

b)

x = 1 and y = -2

21.

When y = 0 what is the X intercept for the following equation:
8x - 2y = 24

a)

x = 12

b)

x = -12

c)

x = -3

d)

x = 3

22.

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

23.

Factorise 4x + 14

a)

2(2x+7)

b)

4(x+10)

c)

4(x+3)

d)

2(x+12)

24.

Factorise 8x + 12

a)

4(x+2)

b)

8(x+4)

c)

4(x+3)

d)

4(2x+3)

25.

Factorsie fully: 20x + 30

a)

10(2x+3)

b)

10(x+3)

c)

5(4x+6)

d)

2(10x+15)

26.

Factorise fully: 27x + 45

a)

27(x+18)

b)

3(9x+15)

c)

9(3x+5)

d)

9(3x+36)

27.

Factorise fully: ab + 4b

a)

a(b+4)

b)

b(a+4)

c)

ab(1+4)

d)

b(a+4b)

28.

Factorise 6b + 8

a)

4(2b+2)

b)

2(3b+4)

c)

2(b+4)

d)

4(3b+2)

29.

Factorise: 3x + 12

a)

3(x+4)

b)

3(x+5)

c)

3(3x + 9)

d)

3(x+9)

30.

Factorise: 4x² + 8x

a)

4x(x+2)

b)

4(x²+2x)

c)

2x(2x+4)

d)

2(2x²+4)

31.

Factorise: 12x² + 15x

a)

6x(2x+3)

b)

3(x²+5x)

c)

4x(3x+5)

d)

3x(4x+5)

32.

Factorise fully: 18 - 6x

a)

3(2x - 3)

b)

3(6 - 2x)

c)

6(3 - x)

d)

6(x - 3)

33.

(x +2)(x + 3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 5x + 5

d)

x² + 6x + 6

34.

(x + 5)(x + 4)

a)

x² + x + 20

b)

x² + 20x + 9

c)

x² + 9x + 20

d)

x² - 9x + 54

35.

What does FOIL stand for?

a)

Flogging Outlawed in London

b)

Fans On in Landing

c)

First Outside Inside Last

d)

Fishing Only in Lakes

36.

(x + 7)(x + 9)

a)

x² + 63x + 16

b)

x² + 16x + 63

c)

x² + 79

d)

x² + 16x + 2

37.

(x + 5)²
Hint: try (x + 5)(x + 5)

a)

x² + 25

b)

x² + 10x + 25

c)

x² + 10 x + 10

d)

x² + 10

38.

Multiply:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

39.

Find the product:
(x + 12)(x - 12)

a)

x² - 144

b)

x² + 144

c)

x² + 12x - 144

d)

x² - 12x + 144

40.

Find the product:
(3x + 2)(2x + 4)

a)

6x² + 16x + 8

b)

5x² +11x + 6

c)

5x² + 16x + 6

d)

6x² + 11x + 8

41.

Simplify:
(x - 9)(x - 7)

a)

x² - 2x - 63

b)

x² - 16x - 63

c)

x² - 2x + 63

d)

x² - 16x + 63

42.

Find the product:
(3x – 1)(x + 5)

a)

3x² + 4x + 5

b)

3x² + 4x - 5

c)

3x² + 14x + 5

d)

3x² + 14x - 5

43.

Find the product:
(n - 5)(n - 1)

a)

n² - 5n + 5

b)

n² - 6n + 5

c)

n²+ 5

d)

n² + 6n + 5

44.

Multiply:
(r + 7)(r − 7)

a)

r ²− 49

b)

r ²+ 14

c)

r ² − 7r + 49

45.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

46.

Factor: x² + 2x – 3

a)

(x - 2)(x + 1)

b)

(x + 1)(x - 3)

c)

(x + 2)(x - 1)

d)

(x - 1)(x + 3)

47.

Find two numbers that :
- Multiply to make 6
- Add to make 5

a)

2 and 3

b)

2 and -3

c)

6 and -1

d)

-6 and -1

48.

Find two numbers that :
- Multiply to make -24
- Add to make 2

a)

6 and -4

b)

-4 and -6

c)

3 and -8

d)

12 and -2

49.

Find two numbers that :
- Multiply to make 12
- Add to make -7

a)

3 and 4

b)

2 and 6

c)

-3 and -4

d)

-3 and 4

50.

Find two numbers whose:
- Product is 20
- Sum is -9

a)

3 and -3

b)

5 and -4

c)

-5 and -4

d)

5 and 4

51.

Find two numbers whose:
- Product is -10
- Sum is 3

a)

5 and -2

b)

2 and -5

c)

10 and 1

d)

10 and -1

52.

Which of the following is a correct factorisation of:
y² - 6y - 27

a)

(y - 9)(y + 3)

b)

(y + 9)(y - 3)

c)

Hint:
Product = 27
Sum = -6

53.

Which of the following is a correct factorisation of:
p² + 5p - 36

a)

(p + 12)(p - 3)

b)

(p + 9)(p - 4)

c)

(p + 2)(p - 18)

d)

(p + 6)²

54.

Factorsie x² +4x -32

a)

(x - 8)(x + 4)

b)

(x + 8)(x - 4)

c)

(x + 8)( x + 4)

d)

(x - 8)(x - 4)

55.

Find the probability of rolling greater than a 1 on a single die.

a)

6/6

b)

5/6

c)

4/6

d)

1/6

56.

Find the probability of drawing a 10 from a standard deck of 52 cards.

a)

1 out of 52

b)

13 out of 52

c)

26 out of 52

d)

4 out of 52

57.

Probability can be written as ...

a)

a fraction

b)

a decimal

c)

a percent

d)

all of the above

58.

The probability of it raining today is 30%. What is the probability that it will NOT rain?

a)

30%

b)

70%

c)

100%

d)

0%

59.

a)

blue then blue

b)

blue then red

c)

red then blue

d)

red then red

60.

a)

blue then blue

b)

blue then red

c)

red then blue

d)

red then red

61.

a)

10%

b)

30%

c)

20%

d)

60%

62.

a)

10%

b)

30%

c)

60%

d)

50%

63.

a)

It is more likely to pick the same colored marbles

b)

It is more likely to pick different colored marbles

64.

Convert 4.3 x 10⁴to an ordinary number

a)

0.00043

b)

4300

c)

43000

d)

0.0043

65.

Convert 7.03 x 10³to an ordinary number

a)

7030

b)

703

c)

70300

d)

0.000703

66.

Convert 6.79 x 10⁶to an ordinary number

a)

679000

b)

67900

c)

67900000

d)

6790000

67.

Convert 1.01 x 10^-4to an ordinary number

a)

10100

b)

0.000101

c)

0.00101

d)

101000

68.

Convert 9.2 x 10^-2 to an ordinary number

a)

0.92

b)

0.092

c)

920

d)

92

69.

Convert 4 x 10^-5to an ordinary number

a)

40000

b)

0.0004

c)

0.00004

d)

4000

70.

Change 520000 into standard form

a)

52 x 10⁴

b)

5.2 x 10⁴

c)

5.2 x 10⁵

d)

52 x 10⁵

71.

Change 0.00076 to standard form

a)

7.6 x 10⁴

b)

7.6 x 10⁵

c)

7.6 x 10^-4

d)

7.6 x 10^-5

72.

Calculate 3000 x 5000 and give your answer in standard form

a)

1.5 x 10⁷

b)

1.5 x 10⁶

c)

15000000

d)

15 x 10⁶

73.

Calculate 5 x 4 x 10³and give your answer in standard form

a)

20 x 10³

b)

2 x 10³

c)

20000

d)

2 x 10⁴

74.

Round to the nearest ten:
37

a)

10

b)

20

c)

30

d)

40

75.

Round to the nearest ten:
752

a)

700

b)

800

c)

750

d)

760

76.

Round to the nearest hundred:
149

a)

100

b)

200

c)

150

d)

140

77.

There are 293 steps to the top of the Leaning Tower of Pisa in Italy. To the nearest hundred, about how many steps are there?

a)

200

b)

300

c)

290

d)

250

78.

Tyler says 753 rounds to 800. Alexis says 753 rounds to 750. Who is correct?

a)

Tyler

b)

Alexis

c)

Both of them are right, it depends on whether you are rounding to the nearest ten or hundred

d)

Niether of them are right

79.

Which of the following numbers will NOT round to 400 when rounding to the nearest hundred?

a)

409

b)

445

c)

345

d)

398

80.

Round 1009 to three sig figs

a)

100

b)

101

c)

1010

d)

1000

81.

Round 0.010229 to four sig figs

a)

1022

b)

1023

c)

0.01023

d)

0.01022

82.

Calculate 5.50 cm + 5.50 cm and give your answer with the appropriate number of significant figures.

a)

11 cm

b)

11.0 cm

c)

11.00 cm

d)

11.000 cm

83.

Round 0.010229 to four sig figs

a)

1022

b)

1023

c)

0.01023

d)

0.01022

84.

What is 78.5 rounded to one significant figure?

a)

79

b)

78.5

c)

70

d)

80

85.

What is 0.658 rounded to 1 significant figure?

a)

0

b)

0.66

c)

0.6

d)

0.658

86.

What is 98.907 rounded to 1 significant figure?

a)

98.9

b)

90

c)

100

d)

98.91

87.

Round 0.010229 to four sig figs

a)

1022

b)

1023

c)

0.01023

d)

0.01022

88.

Estimate 27 + 36

a)

65

b)

70

c)

50

d)

60

89.

Estimate 31 + 42

a)

73

b)

80

c)

70

d)

90

90.

Estimate 79 + 11

a)

59

b)

80

c)

60

d)

90

91.

Estimate 327 + 503

a)

800

b)

1000

c)

900

d)

204

92.

Estimate 60 - 22

a)

80

b)

40

c)

30

d)

38

93.

Estimate the sum of 59 and 39.

a)

90

b)

95

c)

100

d)

110

94.

Estimate the difference of 31 and 11.

a)

10

b)

20

c)

30

d)

40

95.

Estimate the sum of 613 and 192.

a)

900

b)

700

c)

800

d)

600

96.

Estimate the SUM:
9.1 + 7.9

a)

15

b)

17

c)

18

d)

2

97.

Estimate the DIFFERENCE:
20.2 - 10.3

a)

10

b)

19

c)

22

d)

18

98.

Estimate the PRODUCT:
2.5 x 3

a)

9

b)

12

c)

6

d)

99

99.

Estimate the QUOTIENT:
24.7 ÷ 4.68

a)

7

b)

4

c)

5

d)

3

100.

ESTIMATE the PRODUCT
99 X 7=

a)

70

b)

700

c)

7,000

d)

7

101.

ESTIMATE the PRODUCT
78 X 6=

a)

4,200

b)

420

c)

480

d)

4,800

102.

Does the table represent a proportional relationship?

a)

Yes.

b)

No.

103.

In the equation y = 14x, what is the constant of proportionality?

a)

y

b)

x

c)

14

104.

Is this graph proportional?

a)

Yes

b)

No

105.

Is this graph proportional?

a)

Yes

b)

No

106.

m is directly proportional to b

m=24 when b=6

Find the equation for m and b

a)

m = 4b

b)

m = 0.25b

c)

b = 4m

d)

6m = 24b

107.

g is directly proportional to b

g=20 when b=4

Find g when b=7

a)

35

b)

5

c)

15

d)

23

108.

p is directly proportional to m

p=22 when m=2

Find the equation for p and m

a)

p = 11m

b)

p = 20m

c)

p = m + 20

d)

m = 11p

109.

t is directly proportional to n²

t=144 when n=6

Find the equation for t and n

a)

t = 4n²

b)

t = 4n

c)

t = 24n

d)

t = 6n²

110.

t is directly proportional to n²

t=144 when n=6

Find n when t=36

a)

3

b)

1.5

c)

24

d)

6

111.

t is inversely proportional to v

t=2 when v=6

Find the equation for t and v

a)

t = ¹²/_v

b)

t = ¹/₃v

c)

t = ³/_v

d)

t = 12v

112.

d is inversely proportional to j

d=6 when j=5

Find d when j=3

a)

10

b)

90

c)

3.6

d)

36

113.

The time taken, t seconds, that it takes a water heater to boil water is inversely proportional to the power, p watts, of the water heater.

When P = 2000W, T = 252 seconds.

Find the time it takes to boil water when P = 800W

a)

504000

b)

630

c)

320

d)

504

114.

Direct proportion, inverse proportion or neither?

I have 3 cats who eat a bag of cat food every 4 days. If I get another cat, how long will each bag last?

a)

Direct

b)

Inverse

c)

Neither

115.

Solve for x:
8x - 10 = -34

a)

4

b)

3

c)

-3

d)

-24

116.

Solve for w:
-6w + 1 = -11

a)

2

b)

1.2

c)

12

d)

-2

117.

Solve for b:
.5b + 4 = 20

a)

8

b)

48

c)

24

d)

32

118.

Translate:
Twelve less than a number

a)

12 - x

b)

x - 12

c)

12x

d)

x + 12

119.

Translate:
Four times a number plus six IS 30.

a)

4 + 6 = 30

b)

4x + 6 = 30

c)

x + 4 times 6 = 30

d)

30 = 4x

120.

Solve for f:
f - 4 = 6f + 26

a)

f = -5

b)

f = 5

c)

f = 6

d)

f = -6

121.

Solve for x:
5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

122.

Solve for x:
4(1-x)+3x=-2(x+1)

a)

x = -6

b)

x = 6

c)

x = 3

123.

Solve:
2(4x-3) - 8 = 4 + 2x

a)

x = 5/3

b)

x = 3

c)

x = 1

d)

x = 2

124.

Solve for x:
5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

125.

Solve the equation:
7x - 4 = 3 + 8x

a)

x = 7

b)

x = -7

c)

x = 2/7

d)

x = 11

126.

Solve the equation
12x - 15 = 3(2x+3)

a)

x = 4

b)

x = -4

c)

x = 2

d)

x = -2

127.

Solve the equation
4x - 5x + 9 =5x - 9

a)

x = -3

b)

x = 9

c)

x = 3

d)

x = -9

128.

Solve:
3c + 5 = 23

a)

c = 3

b)

c = 6

c)

c = 7

d)

c = 18

129.

Solve:
3(x-4) = -3

a)

3

b)

-3

c)

5

d)

-5

130.

Solve the equation

a)

14

b)

-14

c)

4

d)

-2

131.

Combine like terms
3x + 2x + 3y - 7y

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

132.

Solve for n

a)

n = 9

b)

n = 3

c)

n = 27

d)

n = 15

133.

x + 2 = x + 4

a)

all real numbers

b)

no solution

c)

x = 0

134.

Solve the Simultaneous Equations: 2a+b=11; a+b=8

a)

a=-3, b=5

b)

a=3, b=-5

c)

a=3, b=5

d)

a=-3, b=-5

135.

Where do these two lines intersect?

a)

No solution

b)

(-2, 3)

c)

(3, -2)

d)

(2, 3)

136.

What is the solution?

a)

(6, 3)

b)

(3, 6)

c)

(-6, 3)

d)

No solution

137.

The solution to the system is

a)

(-2, -8)

b)

(-8, -2)

c)

(2, -8)

d)

No solution

138.

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

139.

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

140.

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

141.

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

142.

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

143.

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

144.

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

145.

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

146.

Solve the following simultaneous equations:

2x + 3y = 17

4x + y = 9

a)

x = 1

y = 5

b)

x = -1

y = 5

c)

x = 1

y = -5

d)

x = -1

y = -5

147.

Solve the following simultaneous equations:

3x + 2y = 20

2x + y = 1

a)

x = 2

y = 7

b)

x = -2

y = 7

c)

x = 2

y = -7

d)

x = -2

y = -7

148.

Solve the following simultaneous equations:

5x + y = 22

3x + 3y = 18

a)

x = 4

y = 2

b)

x = -4

y = 2

c)

x = 4

y = -2

d)

x = -4

y = -2

149.

Solve the following simultaneous equations:

3x + 2y = 12

5x + 3y = 19

a)

x = 2

y = 3

b)

x = -2

y = 3

c)

x = 2

y = -3

d)

x = -2

y = -3

150.

Solve the following simultaneous equations:

7x - 4y = 20

3x + 3y = 18

a)

x = 4

y = 2

b)

x = -4

y = 2

c)

x = 4

y = -2

d)

x = -4

y = -2

151.

Solve the following simultaneous equations:

8x - 5y = 1

3x + 4y = 18

a)

x = 2

y = 3

b)

x = -2

y = 3

c)

x = 2

y = -3

d)

x = -2

y = -3

152.

Solve the following simultaneous equations:

8x - 5y = 1

3x + 4y = 18

a)

x = 2

y = 3

b)

x = -2

y = 3

c)

x = 2

y = -3

d)

x = -2

y = -3

End of year 8

Total questions: 152

Worksheet time: 4hrs 19mins

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