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Quizzes > Mathematics

Algebra and Geometry Quiz: Test Secondary Math Skills

Quick, free secondary math quiz. Instant feedback and results.

Editorial: Review CompletedCreated By: Dani NelsonUpdated Aug 28, 2025
Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art depicting elements related to Secondary Mathematics Algebra and Geometry Quiz.

Use this algebra and geometry quiz to check core secondary math skills and get instant feedback as you go. It covers equations, angles, and graphs in 15 multiple-choice questions. For more review, try a free algebra quiz, build key terms with a geometry vocabulary quiz, or keep going with algebra and geometry practice.

What is the perimeter of a rectangle with length 2x and width 3x?
6x
8x
10x
5x
The perimeter of a rectangle is 2-(length + width). Here, 2-(2x + 3x) = 2-5x = 10x, so 10x is the correct perimeter.
If a line segment is divided into lengths x + 1 and 2x - 1 and the total is 9, what is x?
2
4
3
5
The sum is (x + 1) + (2x - 1) = 3x. Setting 3x = 9 gives x = 3, so that is the correct value.
Evaluate f(x) = 2x² when x = 2.
8
10
4
6
Substitute x = 2 into 2x²: 2 - (2)² = 2 - 4 = 8, making 8 the correct result.
What is the midpoint of the segment connecting (0, 0) and (4, 2)?
(0, 2)
(4, 1)
(1, 2)
(2, 1)
The midpoint formula averages coordinates: ((0+4)/2, (0+2)/2) = (2, 1), so that is correct.
Find the slope of the line through points (1, 2) and (3, 6).
1
2
4
3
Slope = (6 - 2)/(3 - 1) = 4/2 = 2, so 2 is the correct slope.
In a triangle, two angles are 2x° and 3x°, and the third is 50°. What is x?
20
30
26
25
The angles sum to 180: 2x + 3x + 50 = 180 ' 5x = 130 ' x = 26, so 26 is correct.
What is the equation of the line perpendicular to y = 2x + 3 passing through (1, 4)?
y = -2x + 6
y = 1/2 x + 4
y = 2x - 1
y = -1/2 x + 9/2
A perpendicular slope is -1/2. Using point-slope: y ' 4 = -1/2(x ' 1) ' y = -1/2 x + 9/2, which is correct.
Factor the expression x² ' 9.
(x ' 1)(x + 9)
(x ' 4.5)(x + 2)
(x ' 3)(x + 3)
(x ' 9)(x + 1)
x² ' 9 is a difference of squares: x² ' 3² = (x ' 3)(x + 3), so that is correct.
What is the area of the triangle with vertices (0,0), (4,0), and (4,3)?
12
7
6
24
The base is 4 and height is 3, so area = ½ - 4 - 3 = 6, making 6 correct.
Is the function f(x) = x² ' 4x + 4 increasing or decreasing at x = 3?
Increasing
Decreasing
Not defined
Constant
The derivative is 2x ' 4; at x = 3, f' = 2(3) ' 4 = 2 > 0, so the function is increasing there.
Calculate the distance between (1, 1) and (4, 5).
5
4
7
6
Distance = √[(4'1)² + (5'1)²] = √[9 + 16] = √25 = 5, so 5 is correct.
What type of triangle has side lengths 5, 12, and 13?
Equilateral
Right
Scalene
Isosceles
Since 5² + 12² = 25 + 144 = 169 = 13², the triangle satisfies the Pythagorean theorem and is right-angled.
In a convex pentagon, interior angles are x+20, x+40, x+60, x+80, and x+100 degrees. What is x?
40
48
60
50
Sum = (5'2)-180 = 540. Summing angles gives 5x + 300 = 540 ' 5x = 240 ' x = 48, so 48 is correct.
Find the vertex of the parabola y = x² ' 6x + 5.
(3, -4)
(3, 5)
(6, -1)
(2, -3)
The vertex is at x = 'b/(2a) = 6/2 = 3; y(3) = 9 ' 18 + 5 = '4, so (3, '4) is correct.
Are the lines y = 2x + 1 and 4x ' 2y + 3 = 0 parallel, perpendicular, or neither?
Coincident
Neither
Parallel
Perpendicular
Rewriting 4x ' 2y + 3 = 0 gives y = 2x + 1.5. Both lines have slope 2 but different intercepts, so they are parallel.
In a cyclic quadrilateral, two opposite angles measure 3x° and 5x + 30°. Find x.
15
18.75
12
20
Opposite angles in a cyclic quadrilateral sum to 180°: 3x + 5x + 30 = 180 ' 8x = 150 ' x = 18.75.
Find the equation of the circle whose center lies on the x-axis and passes through (3, 4) and ('3, 4).
x² + y² = 34
x² + y² = 25
x² + (y ' 4)² = 25
(x ' 3)² + y² = 25
Symmetry shows the center is (0,0) on the x-axis. Radius² = 3² + 4² = 25, so the circle is x² + y² = 25.
What is the equation of the parabola with vertex (2, -3) and focus (2, -1)?
(y + 3)² = 8(x ' 2)
(x ' 2)² = 8(y + 3)
(y ' 1)² = 4(x + 2)
(x + 2)² = 4(y ' 1)
Focus is 2 units above vertex, so p = 2 and 4p = 8. The axis is vertical, yielding (x'2)²=8(y+3).
Find the coordinates of the centroid of the triangle with vertices (0,0), (4,0), and (0,6).
(4, 6)
(1, 1)
(2, 3)
(4/3, 2)
The centroid is the average of the vertices: ((0+4+0)/3, (0+0+6)/3) = (4/3, 2), so that is correct.
For rectangle ABCD with A(0,0), B(6,0), C(6,4), D(0,4), what is the intersection point of its diagonals?
(2, 3)
(0, 0)
(6, 4)
(3, 2)
The diagonals meet at their midpoints: midpoint of A(0,0) and C(6,4) is ((0+6)/2, (0+4)/2) = (3,2), which is correct.
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Learning Outcomes

  1. Analyze algebraic expressions in geometric contexts
  2. Apply algebraic methods to solve geometry problems
  3. Master properties of lines, angles, and shapes
  4. Identify characteristics of functions and figures
  5. Demonstrate proficiency in coordinate geometry techniques
  6. Evaluate solutions for algebraic and geometric accuracy

Cheat Sheet

  1. Distance Formula - Want to figure out how far apart two points are without leaving your desk? Just plug the coordinates into d = √((x₂ - x₝)² + (y₂ - y₝)²) and let the formula do the heavy lifting. It's like having a virtual ruler on your coordinate plane!
  2. Midpoint Formula - Curious where the exact center of a line segment lies? Use M = ((x₝ + x₂)/2, (y₝ + y₂)/2) to split any segment right down the middle. It's the perfect trick for bisecting lines with precision and style!
  3. Slope Formula - Ready to measure the steepness of your favorite hill on the grid? Calculate m = (y₂ - y₝) / (x₂ - x₝) to discover just how sharp (or flat) your line really is. This formula turns mountains into simple ratios!
  4. Section Formula - Want to find a point that divides a segment in a custom ratio? Use x = (m·x₂ + n·x₝)/(m + n) and y = (m·y₂ + n·y₝)/(m + n) to pinpoint that exact spot. It's your go-to method for partitioning lines like a pro!
  5. Equation of a Line - Ever wondered how to describe a line with an equation? Play with forms like y = mx + b (slope-intercept) or y − y₝ = m(x − x₝) (point-slope) to capture any line's identity. It's like giving your line a secret code!
  6. Parallel & Perpendicular Slopes - How can lines be best friends or perfect opposites? Parallel lines share the same slope (m₝ = m₂), while perpendicular lines have slopes that multiply to −1. It's geometry's version of friendship and rivalry!
  7. Area of a Triangle - Need the area given three points? Use Area = ½ |x₝(y₂ − y₃) + x₂(y₃ − y₝) + x₃(y₝ − y₂)| to get the perfect triangle size. No need for base and height - just plug and play!
  8. Conic Sections - Ready to meet circles, parabolas, ellipses, and hyperbolas? Study their standard equations and eccentricities to see how each shape behaves on the plane. They're the fancy curves that make coordinate geometry a thrill!
  9. Coordinate Geometry Proofs - Want to prove shapes using algebraic flair? Show that a quadrilateral is a parallelogram by verifying equal slopes of opposite sides, or use distance checks to confirm squares. It's geometry meets detective work!
  10. Barycentric Coordinates - Curious about expressing points in relation to triangle vertices? Barycentric coordinates let you write any point as a weighted combination of the triangle's corners. It's like mixing paints to get just the right shade!
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