SECTION B: THEORY 20 MARKS (ANSWER ANY FOUR QUESTIONS) Express the following numbers in standard form. (i)…

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SECTION B: THEORY 20 MARKS (ANSWER ANY FOUR QUESTIONS) Express the following numbers in standard form. (i) 4,700,000 (ii) 2.345 (iii) 0.04723 Express each of these numbers to two significant figures. (i) 835.24 (ii) 0.01084 Copy and complete the table for y=2x−2

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Here are the answers to your questions:

Calculate the square root of $\frac{1}{16}$ .

Apply the square root to the numerator and denominator.
$$ \sqrt{\frac{1}{16}} = \frac{\sqrt{1}}{\sqrt{16}} $$
Calculate the square roots.
$$ \frac{\sqrt{1}}{\sqrt{16}} = \frac{1}{4} $$ The final answer is $\boxed{\frac{1}{4}}$.
12. Express $\frac{4}{x} + \frac{y}{3}$ as a single fraction.
Find a common denominator, which is $3x$.

Rewrite each fraction with the common denominator and add.

$$
\frac{4}{x} + \frac{y}{3} = \frac{4 \cdot 3}{x \cdot 3} + \frac{y \cdot x}{3 \cdot x} = \frac{12}{3x} + \frac{xy}{3x}
$$

Combine the fractions.

$$
\frac{12}{3x} + \frac{xy}{3x} = \frac{12 + xy}{3x}
$$
The final answer is $\boxed{\frac{12 + xy}{3x}}$.

13. Find the multiplicative inverse of $\frac{1}{7}$ .

The multiplicative inverse of a number is its reciprocal.
Find the reciprocal of $\frac{1}{7}$ .
$$ \text{Multiplicative inverse of } \frac{1}{7} = \frac{1}{\frac{1}{7}} = 7 $$ The final answer is $\boxed{7}$.
14. A bag contains 15 red, 13 green and 12 white balls. The probability of taking 1 red ball out of it is:
Calculate the total number of balls.
$$ \text{Total balls} = 15 + 13 + 12 = 40 $$
Determine the number of red balls.
$$ \text{Number of red balls} = 15 $$

Calculate the probability.

$$
P(\text{red ball}) = \frac{\text{Number of red balls}}{\text{Total balls}} = \frac{15}{40}
$$
The final answer is $\boxed{\text{d. } \frac{15}{40}}$.

15. The sides of a rectangle are 5cm and 12cm, find the length of the diagonal.

Use the Pythagorean theorem, $a^2 + b^2 = c^2$ , where $a$ and $b$ are the sides and $c$ is the diagonal.

$$
\text{Diagonal}^2 = (5 \text{ cm})^2 + (12 \text{ cm})^2
$$
$$
\text{Diagonal}^2 = 25 \text{ cm}^2 + 144 \text{ cm}^2
$$
$$
\text{Diagonal}^2 = 169 \text{ cm}^2
$$

Take the square root.
$$ \text{Diagonal} = \sqrt{169 \text{ cm}^2} = 13 \text{ cm} $$ The final answer is $\boxed{\text{b. } 13 \text{ cm}}$.
16. How many lines of symmetry has a kite? A kite has one line of symmetry, which is its main diagonal. The final answer is $\boxed{\text{b. } 1}$ .
1. Convert the bearing $269^\circ$ to a compass bearing.
A bearing of $269^\circ$ is in the third quadrant (between $180^\circ$ and $270^\circ$ ).

Calculate the angle from the South line ( $180^\circ$ ).

$$
269^\circ - 180^\circ = 89^\circ
$$
Since it's in the third quadrant, the direction is West of South.  
The final answer is $\boxed{\text{a. S } 89^\circ \text{ W}}$.

18. What is the area of a parallelogram whose length is 7cm and base 5cm?

Assume "length" is the base and "base" is the perpendicular height for area calculation.
Use the formula for the area of a parallelogram
Area = base $\times$ height. $\text{Area} = 7 \text{ cm} \times 5 \text{ cm} = 35 \text{ cm}^2$ The final answer is $\boxed{\text{b. } 35 \text{ cm}^2}$ .
1. Ibadan is on a bearing of $240^\circ$ from Yola. What is the bearing of Yola from Ibadan?
To find the back bearing, if the original bearing is greater than $180^\circ$ , subtract $180^\circ$ .
$$ \text{Back bearing} = 240^\circ - 180^\circ = 60^\circ $$ The final answer is $\boxed{\text{d. } 060^\circ}$.
20. What is the perimeter of a regular hexagon with the length of sides 1.6cm?
A regular hexagon has 6 equal sides.
Calculate the perimeter by multiplying the side length by 6.
$$ \text{Perimeter} = 6 \times 1.6 \text{ cm} = 9.6 \text{ cm} $$ The final answer is $\boxed{\text{d. } 9.6 \text{ cm}}$.
SECTION B: THEORY
1. (A) Express the following numbers in standard form.
  
  (i) 4,700,000 $\boxed{4.7 \times 10^6}$
  
  (ii) 2.345 $\boxed{2.345 \times 10^0}$
  
  (iii) 0.04723 $\boxed{4.723 \times 10^{-2}}$
2. (B) Express each of these numbers to two significant figures.
  
  (i) 835.24
Identify the first two significant figures (8 and 3).
Round up the second significant figure because the next digit (5) is 5 or greater.
$$ \boxed{840} $$ * **(ii) 0.01084**
Identify the first two significant figures (1 and 0).
Round up the second significant figure (0) because the next digit (8) is 5 or greater.
$$ \boxed{0.011} $$
3. (a) Copy and complete the table for $y = 2x - 2$ . * For $x = -4$ : $y = 2(-4) - 2 = -10$ * For $x = -3$ : $y = 2(-3) - 2 = -8$ * For $x = -2$ : $y = 2(-2) - 2 = -6$ * For $x = -1$ : $y = 2(-1) - 2 = -4$ * For $x = 0$ : $y = 2(0) - 2 = -2$ * For $x = 1$ : $y = 2(1) - 2 = 0$ * For $x = 2$ : $y = 2(2) - 2 = 2$ * For $x = 3$ : $y = 2(3) - 2 = 4$
The completed table is: $$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & -10 & -8 & -6 & -4 & -2 & 0 & 2 & 4 \\ \hline \end{array} $$
4. (b) Using the completed table of values above and the scale of 1cm to 1 unit on both the y and x axes, plot the graph for $y = 2x - 2$ .
Draw a Cartesian coordinate system with x and y axes.
Label the axes and mark units, ensuring 1 cm represents 1 unit on both axes.
Plot the points from the table
$(-4, -10)$ , $(-3, -8)$ , $(-2, -6)$ , $(-1, -4)$ , $(0, -2)$ , $(1, 0)$ , $(2, 2)$ , $(3, 4)$ .
Draw a straight line connecting these points.
This line represents the graph of $y = 2x - 2$ .
1. (a) Find the value of x in the figure below.
In a rectangle, opposite sides are equal.
Set the given side lengths equal. $13 = 2x + 5$
Solve for x.
$$ 13 - 5 = 2x $$ $$ 8 = 2x $$ $$ x = \frac{8}{2} $$ $$ \boxed{x = 4} $$
6. (b) Calculate the area of the rectangle above.
Substitute $x=4$ to find the dimensions of the rectangle.
Length = 13 cm Width = $(x+1)$ cm = $(4+1)$ cm = 5 cm

Calculate the area.

$$
\text{Area} = \text{Length} \times \text{Width} = 13 \text{ cm} \times 5 \text{ cm} = 65 \text{ cm}^2
$$
$$
\boxed{65 \text{ cm}^2}
$$

7. (a) Find the circumference of a circle whose radius is 14 cm.

Use the formula for circumference, $C = 2\pi r$ .
Use $\pi = \frac{22}{7}$ . $C = 2 \times \frac{22}{7} \times 14 \text{ cm}$
Simplify the expression.
$$ C = 2 \times 22 \times 2 \text{ cm} $$ $$ \boxed{C = 88 \text{ cm}} $$
8. (b) State three differences between an Isosceles triangle and an equilateral triangle. - An isosceles triangle has at least two sides of equal length, while an equilateral triangle has all three sides of equal length. - An isosceles triangle has at least two equal angles, while an equilateral triangle has all three angles equal to $60^\circ$ . - An isosceles triangle has one line of symmetry (unless it's also equilateral), while an equilateral triangle has three lines of symmetry.
1. (a) State three properties of a square.
  
  All four sides are of equal length.
  
  All four interior angles are right angles ( $90^\circ$ ).
  
  Opposite sides are parallel.
2. (b) The sum of the interior angles of a regular polygon is $1440^\circ$ , find the number of its sides.
Use the formula for the sum of interior angles
Sum $= (n-2) \times 180^\circ$ .
Set the sum equal to $1440^\circ$ and solve for $n$ .
$$ (n-2) \times 180^\circ = 1440^\circ $$
Divide by $180^\circ$ .
$$ n-2 = \frac{1440}{180} $$ $$ n-2 = 8 $$
Solve for $n$ .
$$ n = 8 + 2 $$ $$ \boxed{n = 10 \text{ sides}} $$
11. (a) A surveyor is interested in determining the height of a tree. The angle of elevation of the top of the tree is $42^\circ$ . The distance of the foot of the tree from the surveyor is 15 cm. How tall is the tree?
Use the tangent function
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ . $\tan(42^\circ) = \frac{\text{Height}}{15 \text{ cm}}$

Solve for Height.

$$
\text{Height} = 15 \text{ cm} \times \tan(42^\circ)
$$

Calculate the value ( $\tan(42^\circ) \approx 0.9004$ ).
$$ \text{Height} \approx 15 \text{ cm} \times 0.9004 $$ $$ \boxed{\text{Height} \approx 13.51 \text{ cm}} $$
12. (b) Mention five examples of quadrilateral. - Square - Rectangle - Rhombus - Parallelogram - Trapezium

Point	x	y
y-intercept	0	−2
x-intercept	1	0

SECTION B: THEORY 20 MARKS (ANSWER ANY FOUR QUESTIONS) Express the following numbers in standard form. (i) 4,700,000 (ii) 2.345 (iii) 0.04723 Express each of these numbers to two significant figures. (i) 835.24 (ii) 0.01084 Copy and complete the table for y=2x−2

Step-by-step solution

Apply the square root to the numerator and denominator.

Calculate the square roots.

Find a common denominator, which is $3x$.

Rewrite each fraction with the common denominator and add.

Combine the fractions.

The multiplicative inverse of a number is its reciprocal.

Find the reciprocal of 17\frac{1}{7}71​.

Calculate the total number of balls.

Determine the number of red balls.

Calculate the probability.

Use the Pythagorean theorem, a2+b2=c2a^2 + b^2 = c^2a2+b2=c2, where aaa and bbb are the sides and ccc is the diagonal.

Take the square root.

A bearing of 269∘269^\circ269∘ is in the third quadrant (between 180∘180^\circ180∘ and 270∘270^\circ270∘).

Calculate the angle from the South line (180∘180^\circ180∘).

Assume "length" is the base and "base" is the perpendicular height for area calculation.

Use the formula for the area of a parallelogram

To find the back bearing, if the original bearing is greater than 180∘180^\circ180∘, subtract 180∘180^\circ180∘.

A regular hexagon has 6 equal sides.

Calculate the perimeter by multiplying the side length by 6.

Identify the first two significant figures (8 and 3).

Round up the second significant figure because the next digit (5) is 5 or greater.

Identify the first two significant figures (1 and 0).

Round up the second significant figure (0) because the next digit (8) is 5 or greater.

Draw a Cartesian coordinate system with x and y axes.

Label the axes and mark units, ensuring 1 cm represents 1 unit on both axes.

Plot the points from the table

Draw a straight line connecting these points.

In a rectangle, opposite sides are equal.

Solve for x.

Substitute x=4x=4x=4 to find the dimensions of the rectangle.

Calculate the area.

Use the formula for circumference, C=2πrC = 2\pi rC=2πr.

Simplify the expression.

Use the formula for the sum of interior angles

Set the sum equal to 1440∘1440^\circ1440∘ and solve for nnn.

Divide by 180∘180^\circ180∘.

Solve for nnn.

Use the tangent function

Solve for Height.

Calculate the value (tan⁡(42∘)≈0.9004\tan(42^\circ) \approx 0.9004tan(42∘)≈0.9004).

Still stuck on this one?

More Mathematics Questions

Find the reciprocal of $\frac{1}{7}$ .

Use the Pythagorean theorem, $a^2 + b^2 = c^2$ , where $a$ and $b$ are the sides and $c$ is the diagonal.

A bearing of $269^\circ$ is in the third quadrant (between $180^\circ$ and $270^\circ$ ).

Calculate the angle from the South line ( $180^\circ$ ).

To find the back bearing, if the original bearing is greater than $180^\circ$ , subtract $180^\circ$ .

Substitute $x=4$ to find the dimensions of the rectangle.

Use the formula for circumference, $C = 2\pi r$ .

Set the sum equal to $1440^\circ$ and solve for $n$ .

Divide by $180^\circ$ .

Solve for $n$ .

Calculate the value ( $\tan(42^\circ) \approx 0.9004$ ).