Tell me the grade 8 end term exam

Grade 8 End-Term Mathematics Exam

Question 1: Solve for $x$: $3x - 7 = 14$. Include units if $x$ represents length in cm.

Step 1: Add 7 to both sides of the equation.
$3x - 7 + 7 = 14 + 7$
$3x = 21$

Step 2: Divide both sides by 3.
$\frac{3x}{3} = \frac{21}{3}$
$x = 7$

Final answer: $\boxed{7\,cm}$

Question 2: Find the area of a rectangle with length $12\,\text{m}$ and width $5\,\text{m}$.

Step 1: Use the formula for area of a rectangle: area = length $\times$ width.
$A = l \times w$

Step 2: Substitute the values.
$A = 12\,m \times 5\,\text{m}$

Step 3: Multiply.
$A = 60\,m^2$

Final answer: $\boxed{60\,m^2}$

Question 3: A right triangle has legs of $6\,\text{cm}$ and $8\,\text{cm}$. Find the hypotenuse.

Step 1: Use the Pythagorean theorem: $c = \sqrt{a^2 + b^2}$.
$c = \sqrt{6^2 + 8^2}$

Step 2: Calculate the squares.
$6^2 = 36$
$8^2 = 64$

Step 3: Add the squares.
$36 + 64 = 100$

Step 4: Take the square root.
$c = \sqrt{100} = 10$

Final answer: $\boxed{10\,cm}$

Question 4: Simplify $\frac{2}{3} + \frac{1}{4}$.

Step 1: Find a common denominator, which is 12.
$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Step 2: Add the fractions.
$\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

Final answer: $\boxed{\dfrac{11}{12}}$

Question 5: Find the volume of a cylinder with radius $3\,\text{cm}$ and height $10\,\text{cm}$. Use $\pi \approx 3.14$.

Step 1: Use the formula for volume: $V = \pi r^2 h$.
$V = \pi r^2 h$

Step 2: Substitute the values.
$V = 3.14 \times (3)^2 \times 10$

Step 3: Calculate $r^2$.
$(3)^2 = 9$

Step 4: Multiply by $\pi$.
$3.14 \times 9 = 28.26$

Step 5: Multiply by height.
$28.26 \times 10 = 282.6$

Final answer: $\boxed{282.6\,cm^3}$