Algebra and Graphs Practice Questions

IGCSE (Cambridge) · IGCSE Mathematics · 131 free MCQs with instant results and detailed explanations.

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Sample Questions from Algebra and Graphs

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Easy

Which of the following represents the equation of a line with a slope of 2 and a y-intercept of 3?

A. y = 2x + 3

B. y = 3x + 2

C. y = 2x - 3

D. y = -2x + 3

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Correct Answer: A

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Here, m = 2 and b = 3.

Easy

Which of the following expressions is equivalent to 2(a + 3)?

A. 2a + 6

B. a + 6

C. 2a + 3

D. 2a + 9

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Correct Answer: A

Using the distributive property, we multiply 2 with both terms in the parentheses: 2 * a + 2 * 3 gives 2a + 6.

Easy

If the coordinates of point A are (3, 4), what is the x-coordinate of point A?

A. 3

B. 4

C. 7

D. 0

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Correct Answer: A

In a coordinate pair (x, y), the first number represents the x-coordinate. Therefore, for point A (3, 4), the x-coordinate is 3.

Medium

If the equation of a line is given by y = 3x + 5, what is the slope of the line?

A. 3

B. 5

C. 15

D. 0

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Correct Answer: A

The slope of the line in the equation y = mx + c is given by m, which in this case is 3.

Medium

The function f(x) = x^2 - 4x + 3 is a quadratic function. What are its roots?

A. 1 and 3

B. 2 and -1

C. 0 and 4

D. -1 and -3

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Correct Answer: A

The roots of the quadratic function can be found using the factorization method: (x - 1)(x - 3) = 0, yielding roots x = 1 and x = 3.

Medium

If the equation of a line is y = 3x + 2, what is the slope of the line?

A. 3

B. 2

C. 1/3

D. 0

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Correct Answer: A

The slope of a line in the equation y = mx + b is represented by 'm'. Here, m = 3.

Medium

What is the value of x if 5(x - 2) = 3x + 4?

A. 6

B. 7

C. 5

D. 3

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Correct Answer: B

By distributing and simplifying the equation, we find x = 7, which satisfies the equation.

Hard

A quadratic equation is given by x² - 4x + 4 = 0. What is the value of x?

A. 2

B. 4

C. -2

D. 0

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Correct Answer: A

The equation can be factored as (x - 2)² = 0, thus x = 2 is the only solution.

Hard

If the function f(x) = 3x - 2 and g(x) = x² + 1, what is the value of f(g(2))?

A. 10

B. 15

C. 7

D. 5

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Correct Answer: B

First, calculate g(2) which is 2² + 1 = 5. Then, substitute this into f: f(5) = 3(5) - 2 = 15.

Q10

Hard

If the equation of a line is given by y = 3x - 5, what is the y-coordinate of the point where the line intersects the y-axis?

A. -5

B. 0

C. 5

D. 3

Show Answer & Explanation

Correct Answer: A

The y-coordinate of the y-intercept of a line can be found by setting x = 0. Substituting 0 into the equation y = 3(0) - 5 gives y = -5, which is the y-coordinate of the intersection with the y-axis.

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Algebra and Graphs — IGCSE (Cambridge) IGCSE Mathematics Practice Questions Online

This page contains 131 practice MCQs for the chapter Algebra and Graphs in IGCSE (Cambridge) IGCSE Mathematics. The questions are organized by difficulty — 28 easy, 69 medium, 34 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.