Tell me the grade 8 end term exam

Mathematics

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Answers

5 parts
1

7 cm7\,\text{cm}

2

60 m260\,\text{m}^2

3

10 cm10\,\text{cm}

4

1112\dfrac{11}{12}

5

282.6 cm3282.6\,\text{cm}^3

Step-by-step solution

16 steps

Grade 8 End-Term Mathematics Exam

Part 1· 2 steps

Solve for xx: 3x−7=143x - 7 = 14. Include units if xx represents length in cm.

  1. Add 7 to both sides of the equation.

    3x−7+7=14+73x - 7 + 7 = 14 + 7 3x=213x = 21

  2. Divide both sides by 3.

    3x3=213\frac{3x}{3} = \frac{21}{3} x=7x = 7

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

Part 2

60 m260\,\text{m}^2

Find the area of a rectangle with length 12 m12\,\text{m} and width 5 m5\,\text{m}.

  1. Use the formula for area of a rectangle

    area = length ×\times width.

    A=l×wA = l \times w

  2. Substitute the values.

    A=12 m×5 mA = 12\,\text{m} \times 5\,\text{m}

  3. Multiply.

    A=60 m2A = 60\,\text{m}^2

    Final answer: 60 m2\boxed{60\,\text{m}^2}

Part 3

10 cm10\,\text{cm}

A right triangle has legs of 6 cm6\,\text{cm} and 8 cm8\,\text{cm}. Find the hypotenuse.

  1. Use the Pythagorean theorem

    c=a2+b2c = \sqrt{a^2 + b^2}.

    c=62+82c = \sqrt{6^2 + 8^2}

  2. Calculate the squares.

    62=366^2 = 36 82=648^2 = 64

  3. Add the squares.

    36+64=10036 + 64 = 100

  4. Take the square root.

    c=100=10c = \sqrt{100} = 10

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

Part 4

1112\dfrac{11}{12}

Simplify 23+14\frac{2}{3} + \frac{1}{4}.

  1. Find a common denominator, which is 12.

    23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} 14=1×34×3=312\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}

  2. Add the fractions.

    812+312=1112\frac{8}{12} + \frac{3}{12} = \frac{11}{12}

    Final answer: 1112\boxed{\dfrac{11}{12}}

Part 5

282.6 cm3282.6\,\text{cm}^3

Find the volume of a cylinder with radius 3 cm3\,\text{cm} and height 10 cm10\,\text{cm}. Use π≈3.14\pi \approx 3.14.

  1. Use the formula for volume

    V=πr2hV = \pi r^2 h.

    V=πr2hV = \pi r^2 h

  2. Substitute the values.

    V=3.14×(3)2×10V = 3.14 \times (3)^2 \times 10

  3. Calculate r2r^2.

    (3)2=9(3)^2 = 9

  4. Multiply by π\pi.

    3.14×9=28.263.14 \times 9 = 28.26

  5. Multiply by height.

    28.26×10=282.628.26 \times 10 = 282.6

    Final answer: 282.6 cm3\boxed{282.6\,\text{cm}^3}

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