Free Printable Year 12 Autumn Term Revision

1.

(ab⁸c)(a^-17c¹⁰)

a)

a¹⁷b⁸c¹¹

b)

a¹⁶b⁸c¹¹

c)

(b⁸c¹¹)/(a¹⁶)

d)

a^-17b⁸c¹⁰

2.

Simplify
(7a²)(5a⁶b)²

a)

35a¹⁴b²

b)

175a¹²b²

c)

175a¹⁴b²

d)

35a¹⁴b

3.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

4.

Reduce the following radicals: $8\sqrt{84}\ -\ 5\sqrt{84}$

a)

$3\sqrt{21}$

b)

$2\sqrt{21}$

c)

$6\sqrt{21}$

d)

$5\sqrt{21}$

5.

The length of a rectangle is 4a⁴b⁵ and the width is 3a²b³, what is the expression that represents the area of the rectangle?

a)

12a⁶b⁸

b)

7a⁶b⁸

c)

12a⁸b¹⁵

d)

1a²b²

6.

Simplify the following surd

a)

A

b)

B

c)

C

d)

D

7.

Simplify:

25 x ⁶

5 x ³

a)

20x³

b)

5x⁹

c)

5x³

8.

Evaluate 27^-1/3 x 49^-1/2 x 125⁰

a)

210

b)

21

c)

1/21

d)

1

9.

If 5ⁿ= 125 find n.

a)

25

b)

1/3

c)

-3

d)

3

10.

Solve 16^{2x - 1}= 64

a)

1.5

b)

1.25

c)

4/5

d)

-1.25

11.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

12.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

13.

Simplify fully:
√32

a)

4√8

b)

16√2

c)

4√2

d)

4√4

14.

Simplify fully:
√32 + √12

a)

4√2 +2√3

b)

6√5

c)

√44

d)

2√11

15.

Write the following entirely as a surd:
2√5

a)

√20

b)

√10

c)

√50

d)

√100

16.

Simplify completely:
2√3 + 4√3

a)

6√3

b)

6√6

c)

8√3

d)

8√6

17.

Simplify:
√5 x √6

a)

2√15

b)

√11

c)

√30

d)

3√10

18.

Simplify the following surd...

a)

2√2

b)

4√2

c)

2√4

d)

3√2

19.

Simplify the following surd...

a)

5√2

b)

5√3

c)

2√5

d)

10√5

20.

Simplify the following form into positive integers indices $\frac{1}{3^{-5}}$

a)

$3^{-5}$

b)

$5^3$

c)

$3^5$

d)

$5^{-3}$

21.

Describe the meaning of 2⁵

a)

5 x 2

b)

5 x 5

c)

2 x 5

d)

2 x 2 x 2 x 2 x 2

22.

Determine (-4³)⁶

a)

-4⁹

b)

4⁹

c)

-4¹⁸

d)

4¹⁸

23.

(4 x 5)³x (4 x 5)⁵

a)

20¹⁵

b)

20⁸

c)

20²

d)

20⁰

24.

Calculate $2^{-3\ }\times3^{-2}$

a)

$\frac{1}{6}$

b)

$6^{-5}$

c)

$\frac{1}{72}$

d)

$5^{-5}$

25.

Simplify as much as possible:
3√8

a)

6√2

b)

√72

c)

12√2

d)

6√4

26.

Write the following entirely as a surd:
2√5

a)

√20

b)

√10

c)

√50

d)

√100

27.

Simplify as much as possible:
√32 ÷ √8

a)

2

b)

√24

c)

√4

d)

2√6

28.

Expand and simplify:
(2 + √5)(3 + √5)

a)

11 + 5√5

b)

6 + 6√5

c)

6 + √5

d)

11 + √5

29.

Rationalise the denominator and simplify:
3/√2

a)

(3√2)/2

b)

(√6)/2

c)

(3√2)/√2

d)

6√2

30.

What is the missing index?(2⁶)^x = 2¹⁸

a)

12

b)

3

c)

10

d)

4

31.

A researcher wants to understand the dietary habits of people in a city. They randomly select 100 households from the city's population directory and survey all the members in each selected household. What sampling technique is being used?

a)

Simple Random Sampling

b)

Systematic Sampling

c)

Convenience Sampling

d)

Stratified Random Sampling

32.

A company wants to test the effectiveness of a new advertisement. They invite customers who visit their website to voluntarily participate in an online survey about their advertising preferences. What sampling technique is being used?

a)

Quota Sampling

b)

Convenience Sampling

c)

Purposive Sampling

d)

Stratified Random Sampling

33.

A city council wants to estimate the average household income of its residents. They randomly select five neighborhoods from the city and survey all the households within each selected neighborhood. What sampling technique is being used?

a)

Simple Random Sampling

b)

Systematic Sampling

c)

Cluster Sampling

d)

Convenience Sampling

34.

A researcher wants to understand the opinions of college students about online learning. They randomly select three colleges from a list of all colleges in the region, and then randomly select 50 students from each selected college. What sampling technique is being used?

a)

Quota Sampling

b)

Simple Random Sampling

c)

Purposive Sampling

d)

Cluster Sampling

35.

A survey company wants to gather opinions on political candidates. They randomly select registered voters from a database and contact them by phone to conduct interviews. What sampling technique is being used?

a)

Stratified Random Sampling

b)

Convenience Sampling

c)

Systematic Sampling

d)

Simple Random Sampling

36.

What kind of sampling technique is the following:

List the names of all the students alphabetically and contact the parent of every 25th student.

a)

Convenience Sampling

b)

Simple Random Sampling

c)

Systematic Sampling

d)

Sample

37.

What kind of sample technique is the following:

Select at random 150 parents and send them a survey.

a)

Convenience Sampling

b)

Simple Random Sampling

c)

Systematic Sampling

d)

Sample

38.

What kind of sample technique is the following:

Selecting every 8th person in line for a water slide.

a)

Convenience Sampling

b)

Simple Random Sampling

c)

Systematic Sampling

d)

Sample

39.

What kind of sample technique is the following:

Question everyone in the cafeteria.

a)

Convenience Sampling

b)

Simple Random Sampling

c)

Systematic Sampling

d)

Sample

40.

What kind of sample technique is the following:

The teacher selecting students by pulling their name out of a hat.

a)

Convenience Sampling

b)

Simple Random Sampling

c)

Systematic Sampling

d)

Sample

41.

Classify by degree of polynomial: $-6x+3x^3$

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

42.

Classify by number of terms:
2x – 9

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

43.

Add the polynomials:
(3x³+3x²–4x+5) + (x³–2x²+x–4)

a)

4x³ + 1x² – 3x + 1

b)

2x³ + 1x² - 5x + 9

c)

6x³ + 1x - 1x² - 3

d)

3x⁵ +1x - 1x⁵ - 3x

44.

Simplify the expression.
(4n⁴-8n+4) - (8n²+4n⁴+1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

45.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

46.

A = 2x² + 3x + 5
C = 3x² - 7x + 12
If A + B = C,
what must B equal?

a)

x² - 10x + 7

b)

5x² - 4x + 17

c)

x² - 4x + 7

d)

5x² - 10x + 17

47.

A rectangle has width (2x + 3) and length (2x - 4). What is the perimeter of the rectangle?

a)

4x- 12

b)

4x- 1

c)

8x- 2

d)

4x²- 2x - 12

48.

Is (x – 2) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(2) = 0

b)

No, f(2) = 20

c)

Yes, f(2) = 20

d)

No, f(2) = 0

49.

Is (x + 3) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(-3) = 0

b)

No, f(-3) = 20

c)

Yes, f(3) = 0

d)

No, f(3) = 60

50.

Is (x - 1) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(1) = 0

b)

No, f(1) = -2

c)

Yes, f(-1) = 0

d)

No, f(-1) = -2

51.

Is (x + 1) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(-1) = 0

b)

No, f(-1) = -4

c)

Yes, f(1) = 0

d)

No, f(1) = -4

52.

Is (x - 2) a factor

$f\left(x\right)\ =\ x^4-13x^2\ +36$

a)

Yes f(2) = 0

b)

No, f(2) = 2

c)

Yes, f(-2) = 0

d)

No, f(-2) = -2

53.

Is (x + 3) a factor

$f\left(x\right)\ =\ x^4-13x^2\ +36$

a)

Yes f(3) = 0

b)

No, f(3) = 3

c)

Yes, f(-3) = 0

d)

No, f(-3) = -3

54.

Is (x - 1) a factor

$f\left(x\right)\ =\ x^4-13x^2\ +36$

a)

Yes f(1) = 0

b)

No, f(1) = 24

c)

Yes, f(-1) = 0

d)

No, f(-1) = 24

55.

Is (x + 1) a factor

$f\left(x\right)\ =\ x^4-13x^2\ +36$

a)

Yes f(1) = 0

b)

No, f(1) = 24

c)

Yes, f(-1) = 0

d)

No, f(-1) = 24

56.

Is (x - 2) a factor

$f\left(x\right)\ =\ x^3-x^2\ -9x+9$

a)

Yes f(2) = 0

b)

No, f(2) = -5

c)

Yes, f(-2) = 0

d)

No, f(-2) = -5

57.

Is (x - 3) a factor

$f\left(x\right)\ =\ x^3-x^2\ -9x+9$

a)

Yes f(3) = 0

b)

No, f(3) = -5

c)

Yes, f(-3) = 0

d)

No, f(-3) = -5

58.

$Solve\ \sin x=\frac{1}{2}\ for\ 0\le x\le360\degree$

a)

30, 330

b)

30, 150

c)

60, 120

d)

60, 300

59.

$Solve\sin x=\frac{\sqrt{3}}{2}\ for\ 0≤x≤360°$

a)

30, 150

b)

60, 300

c)

30, 330

d)

60, 120

60.

$Solve\cos⁡x=-\frac{1}{2}\ for\ 0≤x≤360°$

a)

120, 240

b)

120, 60

c)

60, 300

d)

240, 300

61.

$Solve\cos⁡x=-\frac{1}{\sqrt{2}}\ for\ 0≤x≤360°$

a)

135, 45

b)

150, 210

c)

135, 225

d)

30, 330

62.

$Solve\sin⁡x=1\ for\ 0≤x≤360°$

a)

90

b)

270

c)

0

d)

180

63.

$Solve\cos⁡x=-1\ for\ 0≤x≤360°$

a)

270

b)

0

c)

90

d)

180

64.

$Solve\sin2⁡x=\frac{\sqrt{3}}{2}\ for\ 0≤x≤360°$

a)

30, 150

b)

30, 60, 210, 240

c)

60, 120

d)

15, 75, 195, 255

65.

$Solve\sin2x=\frac{1}{2}\ for\ 0≤x≤360°$

a)

60, 120

b)

30, 150

c)

30, 60, 210, 240

d)

15, 75, 195, 255

66.

$Solve\ \sin3⁡x=-\frac{1}{\sqrt{2}}\ for\ 0≤x≤360°$

a)

225, 315

b)

75, 105, 195, 225, 315, 345

c)

45, 75, 165, 195, 285, 315

d)

135, 225

67.

$Solve\cos⁡3x=0\ for\ 0≤x≤360°$

a)

0, 60, 120, 180, 240, 300

b)

30, 90, 120, 150, 270, 330

c)

0, 30, 150, 210, 240, 330

d)

30, 90, 150, 210, 270, 330

68.

$Solve\ 2\sin x-1=0\ for\ 0≤x≤360°$

a)

30, 150

b)

60, 120

c)

45, 225

d)

90, 270

69.

$Solve\sqrt{2}\cos⁡x-1=0\ for\ 0≤x≤360°$

a)

45, 225

b)

45, 135

c)

135, 225

d)

45, 315

70.

$Solve\cos⁡2x=-\frac{\sqrt{3}}{2}\ for\ 0≤x≤360°$

a)

150, 210

b)

120, 150, 300, 330

c)

45, 315

d)

75, 105, 255, 285

71.

$Solve\ 2\cos⁡x=\sqrt{3}\ for\ 0≤x≤360°$

a)

30, 330

b)

60, 300

c)

150, 210

d)

120, 240

72.

What is the distance between the two points?

a)

√40 ≈ 6.32

b)

√32 ≈ 5.66

c)

√20 ≈ 4.47

d)

none of these

73.

Find the distance.

a)

√95

b)

√115

c)

√136

d)

√162

74.

Find the midpoint of the segment with the endpoints:
(6, 7) and (6, -5)

a)

(0, -1)

b)

(6, 1)

c)

(1, 6)

d)

(0, 1)

75.

What is the formula for midpoint?

a)

b)

c)

d)

a²+b²=c²

76.

What formula is shown?

a)

slope

b)

distance

c)

midpoint

d)

Pythagorean Theorm

77.

Find the distance between the points:
(5,3) (2,3)

a)

3

b)

7

c)

10

78.

How do we prove a triangle is a right triangle?

a)

Prove all sides are different lenghts

b)

Show that the three sides satisfy the pythagorean theorem

c)

Show that opposite angles are congruent

d)

Show that two sides are congruent

79.

a)

(x+1)² + (y +1)² = 3

b)

(x+1)² + (y -1)² = 3

c)

(x+1)² + (y +1)² = 9

d)

(x-1)² + (y -1)² = 9

80.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

81.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

82.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

83.

a)

A

b)

B

c)

C

d)

D

84.

What is the equation for this circle?

a)

(x+1)+(y+1)=9

b)

x²+y²=9

c)

x+y=9

85.

What are the coordinates of the center and the radius of the circle with an equation:
(x + 7)² + (y - 6)² = 64 ?

a)

Centre (7,-6)
Radius = 8 units

b)

Centre (-7,6)
Radius = 64 units

c)

Centre (-7,6)
Radius = 8 units

d)

Centre (7,-6)
Radius = 64 units

86.

What is the center of the circle with equation x² + y² = 1?

a)

(1, 1)

b)

(0, 0)

c)

not enough information

87.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

88.

In the equation (x-3)²+(y+4)²=121, the radius of the circle is

a)

242

b)

11

c)

121

d)

22

89.

What is the equation of a circle whose diameter is 24 and whose center is at the origin?

a)

x²+y²=125

b)

x²+y²=64

c)

x²+y²=144

d)

x²+y²=576

90.

What is the equation of the circle, with center (4,2) and radius 5 units?

a)

(x + 4)² + (y + 2)² = 25

b)

(x + 4)² + (y + 2)² = 5

c)

(x - 4)² + (y - 2)² = 5

d)

(x - 4)² + (y - 2)² = 25

91.

A cyclist travelling at a speed of 4.2 m s^-1 accelerates at 1.1 m s^-2. In a time of 7.4 s, the distance travelled is

a)

30 m

b)

35 m

c)

61 m

d)

91 m

92.

A freely falling object on Earth has a speed of 5.0 m s^-1. After falling a further 20 m, its speed it

a)

15 m s^-1

b)

20 m s^-1

c)

25 m s^-1

d)

45 m s^-1

93.

A bus is travelling at a speed of 9.0 m s^-1. It then accelerates at a rate of 0.75 m s^-2 for a time of 8.0 s. What therefore is its final speed?

a)

6.0 m s^-1

b)

15 m s^-1

c)

17 m s^-1

d)

21 m s^-1

94.

The acceleration of free fall on a certain planet is 8.0 m s^-2. An object gets dropped from a height and hits the ground after 1.5 s. From what height must the object have been dropped?

a)

6.0 m

b)

9.0 m

c)

11 m

d)

12 m

95.

A ball is dropped from rest from a building 35.0 m high. If air resistance is neglected, then the ball will hit the ground with a speed of

a)

8.4 m s^-1

b)

13.1 m s^-1

c)

18.5 m s^-1

d)

26.2 m s^-1

96.

A student is asked to solve the following problem:

An object is thrown upwards with a speed of 25 m s^-1. How high will it be when the speed is 12 m s^-1?

Which equation will allow the problem to be solved in a SINGLE calculation?

a)

$s=ut+\frac{1}{2}at^2$

b)

$s=\frac{\left(u+v\right)t}{2}$

c)

$v=u+at$

d)

$v^2=u^2+2as$

97.

A marble is dropped from the roof of a building and takes 3.2 s to reach the ground.

The approximate height of the building is

a)

16 m

b)

31 m

c)

50 m

d)

100 m

98.

A girl dropped a stone into an empty well. She heard the sound of the stone hitting the bottom of the well after 4 seconds.

The depth of the well is about

a)

20 m

b)

40 m

c)

80 m

d)

160 m

99.

THINK CAREFULLY ABOUT THIS ONE. DRAW A DIAGRAM TO HELP YOU..!

A building has 5 floors. The windows on successive floors are separated by the same vertical distance. A brick is dropped from a window on each floor at the same time. The bricks should hit the ground at

a)

decreasing time intervals

b)

equal time intervals

c)

increasing time intervals

d)

the same time

100.

The acceleration due to gravity on Mars is 3.7 m s^-2.

If an object on Mars is launched vertically upwards with an initial speed of 40 m s^-1, its speed after 3.0 s will be

a)

11 m s^-1

b)

29 m s^-1

c)

36 m s^-1

d)

51 m s^-1

101.

With reference to the previous experiment, select the equation that would, by itself, enable the student to calculate a value for g.

a)

$mgh=\frac{1}{2}mv^2$

b)

$s=ut+\frac{1}{2}at^2$

c)

$v=u+at$

d)

$v^2=u^2+2as$

102.

A lunar landing module is descending to the Moon’s surface at a steady velocity of 10.0 m s^-1. At a height of 120 m a small object falls from its landing gear. Assuming that the Moon’s gravitational acceleration is 1.60 m s^-2, at what speed, in m s^-1 does the object strike the Moon?

a)

22.0

b)

19.6

c)

16.8

d)

10.0

103.

THIS ONE TAKES MORE TIME THAN YOU MIGHT INITIALLY THINK. READ IT CAREFULLY!

An object is dropped from a cliff. How far does the object fall in the third second? Assume that g = 10 m s^-2 (HINT: Remember that the initial speed of the object is 0 m s^-1)

a)

10 m

b)

20 m

c)

25 m

d)

45 m

104.

ANOTHER ONE TO MAKE YOU THINK PRACTICALLY:

The winner of a 400 m race must have the greatest

a)

acceleration.

b)

average speed.

c)

instantaneous speed.

d)

maximum speed.

Year 12 Autumn Term Revision

Total questions: 104

Worksheet time: 7hrs 26mins

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