Linear equations in two variables, Mensuration: Area and Perimeter
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Linear Equations and Mensuration
English 13 leveled MCQs Free
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7 marks Long answer
Write a linear equation representing a situation where a person earns $500 per week and spends $200 per week. Let x be the number of weeks and y be the amount of money left.
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The equation is $y = 500x - 200x = 300x$.
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6 marks Long answer
A rectangle has a length that is twice its width. If the perimeter is 36 cm, find the dimensions of the rectangle.
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The dimensions are length = 12 cm and width = 6 cm.
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5 marks Long answer
Solve the linear equation $2x + 3y = 12$ for $y$ in terms of $x$.
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Rearranging gives $y = \frac{12 - 2x}{3}$.
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5 marks Long answer
Find the area of a triangle with a base of 10 cm and a height of 5 cm.
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The area is $A = \frac{1}{2} \times 10 \times 5 = 25$ cm².
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4 marks Medium answer
Calculate the perimeter of a triangle with sides measuring 5 cm, 7 cm, and 9 cm.
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The perimeter is $5 + 7 + 9 = 21$ cm.
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4 marks Medium answer
If the area of a rectangle is 48 cm² and its length is 8 cm, find its width.
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The width is $\frac{48}{8} = 6$ cm.
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3 marks Medium answer
Explain how to graph a linear equation in two variables.
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To graph a linear equation, find at least two points that satisfy the equation and plot them on a coordinate plane, then draw a straight line through these points.
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3 marks Medium answer
Differentiate between area and perimeter.
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Area measures the space inside a shape, while perimeter measures the distance around the shape.
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1 marks Short answer
Define a linear equation in two variables.
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A linear equation in two variables is an equation of the form $ax + by + c = 0$, where $a$, $b$, and $c$ are constants.
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1 marks Short answer
State the formula for the perimeter of a rectangle.
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The perimeter of a rectangle is given by $P = 2(l + w)$, where $l$ is the length and $w$ is the width.
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1 marks Short answer
What is the area of a triangle?
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The area of a triangle is given by $A = \frac{1}{2} \times base \times height$.
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1 marks Short answer
Define the term 'slope' in the context of linear equations.
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The slope of a linear equation represents the rate of change of $y$ with respect to $x$.
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1 marks Short answer
State the formula for the area of a circle.
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The area of a circle is given by $A = \pi r^2$, where $r$ is the radius.
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