Algebra Questions for Grade 10

26 Practice Problems with Answers and Video Solutions

The following algebra questions are designed for Grade 10 students. They cover simplifying expressions, factoring, solving linear and quadratic equations, and working with functions. Use the interactive boxes below to reveal the answers.

Questions 1 - 10

Question 1: Which real numbers are equal to their cubes?

Answer: \(0, 1, -1\)

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Question 2: Write \( 4 \times 10^{-2} \) as a decimal.

Answer: \(0.04\)

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Question 3: Write \( 0.12 \times 10^{-3} \) as a decimal.

Answer: \(0.00012\)

Question 4: Write \( 2 \log_3 x + \log_3 5 \) as a single logarithmic expression.

Answer: \( \log_3(5x^2) \)

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Question 5: Factor the algebraic expression \( 6x^2 - 21xy + 8xz - 28yz \).

Answer: \( (2x - 7y)(3x + 4z) \)

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Question 6: Factor the algebraic expression \( (x - 1)^2 - (y - 2)^2 \).

Answer: \( (x - y + 1)(x + y - 3) \)

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Question 7: Factor the algebraic expression \( x^2 - z^4 \).

Answer: \( (x + z^2)(x - z^2) \)

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Question 8: Evaluate the algebraic expression \( |-2 x - y + 3| \) for \( x = 3 \) and \( y = 5 \).

Answer: \( 8 \)

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Question 9: Simplify the algebraic expression \( -2(x - 3) + 4(-2 x + 8) \).

Answer: \( -10x + 38 \)

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Question 10: Expand and simplify \( (x + 3)(x - 3) - (-x - 9) \).

Answer: \( x^2 + x \)

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Questions 11 - 20

Question 11: Which property is used to write \( a(x + y) = a x + a y \)?

Answer: Distributive Property (Distributivity)

Question 12: Simplify \( \frac{8x^3}{2x^{-3}} \).

Answer: \( 4x^6 \)

Question 13: Simplify \( (-a^2b^3)^2(c^2)^0 \).

Answer: \( a^4b^6 \)

Question 14: For what value of \( k \) is the point \( (-2, k) \) on the line \( -3 x + 3 y = 4 \)?

Answer: \( k = -2/3 \)

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Question 15: For what value of \( a \) will the system have no solutions? \( \{2x+6y=-2; -3x+ay=4\} \)

Answer: \( a = -9 \)

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Question 16: Find the equation for the table: (0,-4), (4,-20), (-4,12), (8,-36).

Answer: C) \( y = -4x - 4 \)

Question 17: Which formula best represents the area of the rectangle shown?

Answer: D) \( \text{area} = x^2 - 1 \)

rectangle algebra diagram
Question 18: Which line contains the points \( (1, -1) \) and \( (3, 5) \)?

Answer: B) \( 2y = 6x - 8 \)

Question 19: Solve the equation \( 2|3x - 2| - 3 = 7 \).

Answer: Solution set: \( \{ 7/3, -1 \} \)

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Question 20: Solve for \( x \) the equation \( (1/2) x^2 + mx - 2 = 0 \).

Answer: \( \{ -m \pm \sqrt{m^2 + 4} \} \)

Questions 21 - 26

Question 21: Find \( k \) for \( -x^2 + 2 k x - 4 = 0 \) to have one real solution.

Answer: \( k = 2, k = -2 \)

Question 22: Find \( b \) for \( x^2 - 4x + 4 b = 0 \) to have two real solutions.

Answer: All values of \( b < 1 \)

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Question 23: Set of values of \( f(x) = -x^2 + 7 \) for \( x \in \{1, 5, 7, 12\} \)?

Answer: \( \{6, -18, -42, -137\} \)

Question 24: Rectangle dimensions: Perimeter = 160 cm, Length = 3 × Width.

Answer: Width = 20 cm, Length = 60 cm

Question 25: Simplify: \( |- x| + |3 x| - |- 2 x| + 3|x| \).

Answer: \( 5|x| \)

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Question 26: If \( (x^2 - y^2) = 10 \) and \( (x + y) = 2 \), find \( x \) and \( y \).

Answer: \( x = 3.5, y = -1.5 \)

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