Maths success

Question 1

Convert the bearing 56.6° to degrees and minutes.

Answer 1

Solution:

Degrees = 56°
Decimal part = 0.6°
Convert decimal to minutes: 0.6 × 60 = 36 minutes
Answer: 56° 36’

Question 2

Express the direction of north-east as a three-figure bearing.

Answer 2

045°

Question 3

Solve for x: log₅(80/16) = x.

Answer 3

x = 1

Question 4

If f(x) = x² - 3x, find f(3).

Answer 4

f(3) = 0

Question 5

Find values of d where f(d) = d² - 3d = 10.

Answer 5

d = -2 or d = 5

Question 6

Find the next two terms in the sequence: 7, 14, 22, 31, …

Answer 6

41, 52

Question 7

Find the next two terms in the sequence: 4, 1, 1/4, 1/16, …

Answer 7

1/64, 1/256

Question 8

Convert 202₇ to base 10.

Answer 8

100₁₀

Question 9

Convert 100₁₀ to base 5.

Answer 9

400₅

Question 10

If a rectangle is enlarged by scale factor 2, what is the scale factor for its area?

Answer 10

4

Question 11

If the area of a shape is 48 cm² and a similar shape has area 12 cm², what is the linear scale factor from the larger to the smaller shape?

Answer 11

1/2

Question 12

How many lines of symmetry does a rhombus have?

Answer 12

2

Question 13

Find the length of side x in a triangle with sides 3cm and 5cm and the included angle 120°.

Answer 13

7cm

Question 14

Find the range of the data set: 17, 18, 18, 18, 20, 22, 23, 26, 28, 28.

Answer 14

11

Question 15

In a triangle, if one interior angle is 32° and another is 10°, find the exterior angle to the third angle.

Answer 15

42°

Question 16

A bag contains 3 red, 5 green, and 12 blue marbles. Find the probability of selecting a marble of the same color twice when selecting with replacement.

Answer 16

178/400 = 89/200

Question 17

An item originally costs $180. After a 20% discount, what is the new price?

Answer 17

$144

Question 18

If a = 2i + 3j and b = -i + 4j, find 2a - 3b.

Answer 18

7i - 6j

Question 19

Rotate the point (3, 2) by 90° anticlockwise around the center (2, 6).

Answer 19

(-2, 7)

Question 20

Find the length of an arc in a circle with radius 3.3cm and angle 2 radians.

Answer 20

6.6cm

Question 21

Construct a perpendicular from point P to line AB.

Answer 21

Draw line PE, which is perpendicular to AB.

Question 22

Find the determinant of the matrix (\begin{pmatrix} 5 & -1 \ 4 & 2 \end{pmatrix}).

Answer 22

14

Question 23

If n(A) = 31, n(B) = 27, n(A∩B) = x, n(A∪B) = 55, and n(U) = 61, find x.

Answer 23

3

Question 24

Simplify (\frac{2}{x-4} + \frac{1}{x+2}).

Answer 24

(\frac{3x}{(x-4)(x+2)})

Question 25

If T varies partially with N², and T = 27 when N = 6, and T = 39 when N = 8, find the formula for T.

Answer 25

T = \(\frac{81}{7} + \frac{3}{7}N²\)

Question 26

Factorize 3(m-n)(4m+2n) - 3(m-n)(m-n).

Answer 26

9(m-n)(m+n) or 9(m²-n²)

Question 27

42 hours is equivalent to how many days and hours?

Answer 27

1 day and 18 hours

Question 28

Which of these numbers is a square number: 4, 16, 18?

Answer 28

4 and 16 are square numbers

Question 29

Express 8125/10000 in its simplest form.

Answer 29

13/16

Question 30

Simplify (2³ × 3⁶) and express it in index form.

Answer 30

2³ × 3⁶