Algebra Questions for Grade 10 with Solutions on Videos
Grade 10 algebra questions with answers presented at the bottom of the page and several questions has detailed solutions on videos..
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Which real numbers are equal to their cubes?
Solution on Video
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Write \( 4 \times 10^{-2} \) as a decimal.
Solution on Video
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Write \( 0.12 \times 10^{-3} \) as a decimal.
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Write \( 2 \log_3 x + \log_3 5 \) as a single logarithmic expression.
Solution on Video
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Factor the algebraic expression \( 6x^2 - 21xy + 8xz - 28yz \).
Solution on Video
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Factor the algebraic expression \( (x - 1)^2 - (y - 2)^2 \).
Solution on Video
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Factor the algebraic expression \( x^2 - z^4\).
Solution on Video
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Evaluate the algebraic expression \( |-2 x - y + 3| \) for \( x = 3 \) and \( y = 5 \).
Solution on Video
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Simplify the algebraic expression \( -2(x - 3) + 4(-2 x + 8) \).
Solution on Video
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Expand and simplify the algebraic expression \( (x + 3)(x - 3) - (-x - 9)\).
Solution on Video
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Which property is used to write \( a(x + y) = a x + a y \)
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Simplify \( \frac{8x^3}{2x^{-3}} \)
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Simplify \( (-a^2b^3)^2(c^2)^0 \)
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For what value of \( k \) is the point \( (-2, k) \) on the line with equation \( -3 x + 3 y = 4\) ?
Solution on Video
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For what value of \( a \) will the system given below have no solutions ?
\begin{cases}
2x + 6y = -2 \\
-3x + ay = 4
\end{cases}
Solution on Video
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Which equation best describes the relationship between \( x \) and \( y \) in this table?
\[
\begin{array}{|c|c|}
\hline
\textbf{x} & \textbf{y} \\
\hline
0 & -4 \\
\hline
4 & -20 \\
\hline
-4 & 12 \\
\hline
8 & -36 \\
\hline
\end{array}
\]
A) \( y = -\dfrac{x}{4} - 4 \)
B) \( y = -\dfrac{x}{4} + 4 \)
C) \( y = - 4 x - 4 \)
D) \( y = - 4 x + 4 \)
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Which formula best represents the area of the rectangle below?
.
A) area = \( 2(x+1) + 2(x-1) \)
B) area = \( 4(x+1)(x-1) \)
C) area = \( 2 x^2 \)
D) area = \( x^2 - 1 \)
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Which line given by its equation below contains the points \( (1, -1) \) and \( (3, 5) \) ?
A) \( -2y -6x = 0 \)
B) \( 2y = 6x - 8 \)
C) \( y = 3x + 4 \)
D) \( y = -3x + 4 \)
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Solve the equation \( 2|3x - 2| - 3 = 7. \)
Solution on Video
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Solve for \( x \) the equation \( (1/2) x^2 + mx - 2 = 0 \).
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For what values of \( k \) the equation \( -x^2 + 2 k x - 4 = 0 \) has one real solution?
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For what values of \( b \) the equation \( x^2 - 4x + 4 b = 0 \) has two real solutions?
Solution on Video
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Function \( f \) is described by the equation \( f (x) = -x^2 + 7 \) . What is the set of values of \( f(x) \) corresponding to the set for the independent variable \( x \) given by \( {1, 5, 7, 12} \)?
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Find the length and width of a rectangle whose perimeter is equal to \( 160 \) cm and its length is equal to the triple its width.
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Simplify: \( |- x| + |3 x| - |- 2 x| + 3|x| \)
Solution on Video
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If \( (x2 - y2) = 10 \) and \( (x + y) = 2 \), find \( x \) and \( y \).
Solution on Video
Answers to the Above Questions
- \(0, 1, -1\) are all equal to their respective cubes.
- \(0.04\)
- \(0.00012\)
- \(\log_3 x^2 + \log_3 5 = \log_3(5x^2)\)
- \(3x(2x - 7y) + 4z(2x - 7y) = (2x - 7y)(3x + 4z)\)
- \([(x - 1) - (y - 2)][(x - 1) + (y - 2)] = (x - y + 1)(x + y - 3)\)
- \((x + z^2)(x - z^2)\)
- \(|-2(3) - (5) + 3| = |-8| = 8\)
- \(-2x + 6 - 8x + 32 = -10x + 38\)
- \(x^2 - 9 + x + 9 = x^2 + x\)
- distributivity
- \(4x^6\)
- \(a^4b^6\)
- \(k = -\frac{2}{3}\)
- \(a = -9\)
- C. \(y = -4x - 4\)
- D. \(\text{area} = (x + 1)(x - 1) = x^2 - 1\)
- B. \(2y = 6x - 8\)
- solution set: \(\left\{ \frac{7}{3}, -1 \right\}\)
- solution set: \(\left\{ -m + \sqrt{m^2 + 4}, -m - \sqrt{m^2 + 4} \right\}\)
- \(k = 2\), \(k = -2\)
- all values of b less than 1
- \(\{6, -18, -42, -137\}\)
- \(\text{width} = 20\ \text{cm},\ \text{length} = 60\ \text{cm}\)
- \(|-x| + |3x| - |-2x| + 3|x| = 5|x|\)
- \(x = \frac{7}{2},\ y = -\frac{3}{2}\)
References and Links