8th Grade Math Curriculum

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Questions and Answers

Which of the following numbers, when expressed in decimal form, would result in a non-terminating, repeating decimal?

  • $ rac{5}{8}$
  • $ rac{13}{16}$
  • $ rac{11}{60}$ (correct)
  • $ rac{16}{25}$

Solve for $x$: $3(x + 2) - 2(x - 1) = 7 + x$

  • No solution (correct)
  • $x = 15$
  • $x = 1$
  • Infinitely many solutions

The angles of a quadrilateral are in the ratio 2:4:5:7. What is the difference between the largest and smallest angle?

  • $120^{\circ}$
  • $90^{\circ}$ (correct)
  • $50^{\circ}$
  • $100^{\circ}$

A survey asks people their favorite color. The results are: Red (30%), Blue (25%), Green (20%), Yellow (15%), Other (10%). If a pie chart is created to represent this data, what would be the central angle corresponding to 'Green'?

<p>$72^{\circ}$ (C)</p> Signup and view all the answers

Evaluate: $\sqrt{169} + \sqrt[3]{216} - \sqrt{81}$

<p>10 (C)</p> Signup and view all the answers

If $x:y = 3:5$ and $y:z = 2:3$, then what is $x:z$?

<p>$2:5$ (D)</p> Signup and view all the answers

Simplify: $(2a + 3b)^2 - (2a - 3b)^2$

<p>$16ab$ (B)</p> Signup and view all the answers

A rectangular field is 30m long and 20m wide. A path of uniform width runs around the inside of the field. If the area of the path is 200 $m^2$, then what is the width of the path?

<p>2.5m (B)</p> Signup and view all the answers

What is the value of $\frac{2^{5} \times 2^{-3}}{2^{-2}}$?

<p>$16$ (A)</p> Signup and view all the answers

If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?

<p>24 (D)</p> Signup and view all the answers

Factorize: $4x^2 - 9y^2 + 2x + 3y$

<p>$(2x - 3y)(2x + 3y + 1)$ (B)</p> Signup and view all the answers

A point is plotted on a graph at (3, -2). If the graph is translated 4 units to the left and 3 units up, what are the new coordinates of the point?

<p>$(1,-5)$ (B)</p> Signup and view all the answers

What is the value of $(\sqrt{81})^3 - (\sqrt[3]{27})^4$?

<p>648 (C)</p> Signup and view all the answers

By what percentage is 25% of 80 greater than 20% of 60?

<p>66.67% (C)</p> Signup and view all the answers

Simplify: $(x + 2)(x - 2) - (x - 3)^2$

<p>$-6x+5$ (C)</p> Signup and view all the answers

A square has a side length of 10 cm. If the side length is increased by 20%, by what percentage does the area increase?

<p>44% (C)</p> Signup and view all the answers

If $2^x = 32$, what is the value of $2^{x-3}$?

<p>4 (D)</p> Signup and view all the answers

If $a$ is inversely proportional to $b$, and $a = 4$ when $b = 6$, what is the value of $a$ when $b = 8$?

<p>3 (D)</p> Signup and view all the answers

Factorize completely: $3x^3 - 12x$

<p>$3x(x - 2)(x + 2)$ (A)</p> Signup and view all the answers

The graph of the equation $y = 2x + 3$ is given. Which of the following points lies on the same line?

<p>$(4, 9)$ (D)</p> Signup and view all the answers

Flashcards

Rational Number

Numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero.

Linear Equation

An equation where the highest power of the variable is 1.

Quadrilateral

A closed, four-sided polygon.

Data Handling

The process of gathering, recording, and presenting information in a way that is helpful to others.

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Square of a Number

A number multiplied by itself.

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Square Root

A value that, when multiplied by itself, gives the original number.

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Cube of a Number

A number multiplied by itself twice.

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Cube Root

A value that, when cubed/multiplied by itself twice, gives the original number.

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Comparing Quantities

Finding the ratio or percentage increase/decrease between two quantities.

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Algebraic Expression

A combination of variables, numbers, and arithmetic operations.

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Algebraic Identities

Equations that are always true regardless of the value of the variables.

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Mensuration

The branch of mathematics that deals with the measurement of geometric shapes.

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Exponent

A quantity representing the power to which a given number or expression is to be raised.

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Direct Proportion

When one quantity increases, the other increases proportionally.

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Inverse Proportion

When one quantity increases, the other decreases proportionally.

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Factorization

Expressing a number or algebraic expression as a product of its factors.

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Introduction to Graphs

The representation of data through points, lines, and curves on a coordinate plane.

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Study Notes

  • Rational numbers are covered
  • Linear equations in one variable are covered
  • Understanding quadrilaterals is covered
  • Data handling is covered
  • Squares and square roots are covered
  • Cubes and cube roots are covered
  • Comparing quantities is covered
  • Algebraic expressions and identities are covered
  • Mensuration is covered
  • Exponents and powers are covered
  • Direct and inverse proportions are covered
  • Factorisation is covered
  • Introduction to graphs is covered

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