Summer 9

Question 1

Is √16 a surd?

Answer 1

No because √16 = 4 (a whole number).

Question 2

Simplify √12

Answer 2

√12 = √4*3 = √4 * √3

= 2√3

Question 3

5º =

Answer 3

1

Question 4

6² * 6³ =

Answer 4

² + ³ = ⁵

6⁵

Question 5

6³ / 6² =

Answer 5

³ - ² = ¹

6¹

Question 6

Write 235,000,000 in standard form.

Answer 6

2.35 * 10⁸

Question 7

Write 1.9 * 10⁹ as an ordinary number.

Answer 7

1,900,000,000

Question 8

5.2 * 10³ * 4.1 * 10⁹ =

Answer 8

5.2 * 4.1 = 21.32
³ + ⁹ = ¹² (10¹²)
21.32 * 10¹² → 2.132 * 10¹³

Question 9

6.5 * 10⁶ / 5 * 10³ =

Answer 9

6.5 / 5 = 1.3
⁶ - ³ = ³ (10³)
1.3 * 10³

Question 10

What must you remember when doing standard form?

Answer 10

A * 10ⁿ where 1 ≤ A < 10

Question 11

5¹ =

Answer 11

5

Question 12

Draw the table for angles and sine, cosine and tangent.

Answer 12

Is all the table correct?

Question 13

x½ =

Answer 13

²√x

Question 14

What does O, H and A stand for?

Answer 14

O: opposite
H: hypotenuse
A: adjacent

Question 15

What are the trigonometry triangles?

Answer 15

/ O \
/ S | H \
______

/ A \
/ C | H \
______

/ O \
/ T | A \
______

Question 16

√3 * √3 =

Answer 16

3

Question 17

(√3)² =

Answer 17

3

Question 18

4√2 + 3√2 + 2√2 = ?

Answer 18

4 + 3 + 2 = 9

4√2 + 3√2 + 2√2 = 9√2

Question 19

√48 ÷ √12 =

Answer 19

√48 / 12
= √4
= 2

Question 20

x⅓ =

Answer 20

³√x

Question 21

81^-½ =

Answer 21

1/81^½
= 1/√81
= 1/9

Question 22

a-ⁿ =

Answer 22

1/aⁿ

Question 23

(5²)³ =

Answer 23

² * ³ = ⁶

= 5⁶

Question 24

c * c * c * c * c / c * c =

Answer 24

c³

Question 25

Simplify √18

Answer 25

1) Find the largest square factor (√9) and the other factor that it needs to be multiplied by (√2):
  √9 * √2 = √18
2) Simplify the square factor: √9 = 3
3) Form:
  3√2

Question 26

Simplify √40

Answer 26

√40 = √4 * √10
√4 = 2
√40 = 2√10

Question 27

Simplify √200

Answer 27

√100 * √2 = √200
√100 = 10
√200 = 10√2

Question 28

What is √80 + √20

Answer 28

√80 = √16 * √5 = 4√5
√20 = √4 * √5 = 2√5
4√5 * 2√5 = 6√5

Question 29

Prove that:

2√3 * 4√3 ≠ 8√3

Answer 29

2 * 4 * √3 * √3 =
8 * (√3)² =
8 * 3 = 24

Question 30

Prove that:

√9 * √4 ≠ √13

Answer 30

√9 = 3
√4 = 2
3 * 2 = 6
6 ≠ √13

Question 31

A rectangle has a width of √8 and a length of √5. What is its area?

Answer 31

a = √8 * √5 = √40
√40 = √4 * √10 =
2√10

Question 32

6 * 2√5 =

Answer 32

6(2√5) =

12√5

Question 33

(3 * 10⁴) * (4 * 10⁵) =

Answer 33

12 * 10⁹ =

1.2 * 10¹º

Question 34

8²/³ =

Answer 34

8²/³ = (³√8)²
³c8 = 2 and 2² = 4
(³√8)² = 4

Question 35

16^-³/² =

Answer 35

16^-³/² = 1 / 16³/² = (²√16)³
²√16 = 4 and 4³ = 64
1 / 16³/² = 1/64

Question 36

a^-ᵐ/ⁿ =

Answer 36

1 / (ⁿ√a)ᵐ

Question 37

aᵐ/ⁿ =

Answer 37

(ⁿ√a)ᵐ