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Quizzes > Quizzes for Business > Education

Test Your Skills: Class 10 Mathematics Assessment Quiz

Gauge Your Understanding of Key Math Concepts

Difficulty: Moderate
Questions: 20
Learning OutcomesStudy Material
Colorful paper art promoting a Class 10 Mathematics Assessment Quiz

Ready to challenge yourself with a targeted Class 10 Mathematics Assessment Quiz? This practice quiz features carefully crafted questions on algebra, geometry, and trigonometry to help students and educators gauge proficiency and pinpoint areas for improvement. It's perfect for anyone preparing for exams or seeking extra practice. Customize every question freely in our editor to match your study goals. Explore more Class 10 Mathematics Practice Quiz or advance to other Mathematics Skills Assessment Quiz on the quizzes page.

Factor the quadratic equation x² - 5x + 6 = 0 and find its roots.
x = 3 or x = 6
x = -2 or x = -3
x = 2 or x = 3
x = 1 or x = 6
The expression factors as (x - 2)(x - 3) = 0, so the roots are x = 2 and x = 3. Each factor set to zero yields one root.
What is the value of sin 30°?
0
√3/2
1
1/2
By definition of the special angle, sin 30° equals 1/2. It is one of the standard trigonometric ratios.
Find the midpoint of the line segment joining (1, 2) and (3, 4).
(2, 4)
(2, 3)
(1, 4)
(3, 2)
The midpoint formula is ((x₝ + x₂)/2, (y₝ + y₂)/2). Averaging the coordinates gives (2, 3).
Simplify the expression (2x + 3) + (3x - 5).
x - 8
5x - 2
5x + 8
6x - 2
Combine like terms: 2x + 3x = 5x and 3 + ( - 5) = - 2, giving 5x - 2.
What is the 5th term of the arithmetic progression with first term 2 and common difference 3?
14
17
11
13
The nth term is a + (n - 1)d. Here a₅ = 2 + 4·3 = 14.
What is the discriminant of the quadratic x² - 4x + 7?
-28
-12
12
28
Discriminant Δ = b² - 4ac = (−4)² - 4·1·7 = 16 - 28 = -12, indicating complex roots.
In a right triangle with hypotenuse 10 and one acute angle 30°, what is the length of the side opposite the 30° angle?
5√3
10
√3
5
Opposite side = hypotenuse · sin(30°) = 10 · 1/2 = 5.
Calculate the distance between the points (2, -1) and (-2, 3).
8
6
√20
4√2
Distance = √[(2 - ( - 2))² + ( - 1 - 3)²] = √(4² + (−4)²) = √(16 + 16) = √32 = 4√2.
Expand (x + 2)(x² - 2x + 4).
x³ + 4x + 8
x³ - 8
x³ + 8
x³ - 2x² + 8
Multiplying gives x·(x² - 2x + 4) + 2·(x² - 2x + 4) = x³ - 2x² + 4x + 2x² - 4x + 8 = x³ + 8.
What is the sum of the first 20 terms of the AP 3, 7, 11, …?
820
600
380
440
Sₙ = n/2 [2a + (n-1)d] = 20/2 [2·3 + 19·4] = 10 [6 + 76] = 820.
Form a quadratic equation whose roots have sum 4 and product 3.
x² + 3x - 4 = 0
x² + 4x + 3 = 0
x² - 4x + 3 = 0
x² - 3x + 4 = 0
Standard form is x² - (sum)x + (product) = 0, giving x² - 4x + 3 = 0.
What is the equation of the line through (1, 2) with slope -3?
y = -3x + 1
y = 3x + 5
y = -3x + 5
y = 3x - 1
Point-slope: y - 2 = -3(x - 1) ⇒ y = -3x + 5.
In a circle, an angle in a semicircle is always _____ degrees.
90°
45°
180°
60°
By the circle theorem, an angle subtended by a diameter is a right angle (90°).
What is the slope of a line perpendicular to y = 2x + 1?
1/2
-1/2
2
-2
Perpendicular slope is the negative reciprocal of 2, which is -1/2.
Factorize the quadratic 4x² - 12x + 9.
(2x - 3)²
(2x - 3)(2x + 3)
(2x + 3)²
(4x - 3)(x - 3)
Notice 4x² - 12x + 9 is a perfect square trinomial: (2x - 3)².
Find the intersection point of the lines 2x + y = 5 and x - 2y = 4.
(14/5, -3/5)
(1, 3)
(2, -1)
(-2, 3)
Solving 2x + y = 5 and x - 2y = 4 by substitution or elimination yields x = 14/5, y = -3/5.
A person deposits $100 in month one and increases each monthly deposit by $20. What is the total deposit after 12 months?
2520
1200
1800
1440
This is an AP with a = 100, d = 20, n = 12. Sum = 12/2 [2·100 + 11·20] = 2520.
In a circle of radius 10, the central angle subtended by chord AB is 60°. What is the length of AB?
10
20
5√3
10√3
Chord length = 2r·sin(θ/2) = 2·10·sin30° = 20·0.5 = 10.
Solve sin²θ - 1/4 = 0 for 0° ≤ θ < 360°.
30°, 150°, 210°, 330°
45°, 135°, 225°, 315°
60°, 120°, 240°, 300°
0°, 90°, 180°, 270°
sin²θ = 1/4 ⇒ sinθ = ±1/2, giving θ = 30°, 150°, 210°, 330° within the specified range.
What is the vertex of the parabola y = x² - 4x + 1?
(4, -3)
(2, -3)
(-2, -3)
(2, 3)
Completing the square: y = (x - 2)² - 3, so the vertex is at (2, -3).
0
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Learning Outcomes

  1. Analyze quadratic equations and their solutions
  2. Apply trigonometric ratios to solve problems
  3. Interpret coordinate geometry graphs and equations
  4. Master operations with polynomials and factoring techniques
  5. Evaluate real-world problems using arithmetic progressions
  6. Demonstrate understanding of circle theorems and properties

Cheat Sheet

  1. Master the Quadratic Formula - The quadratic formula, x = ( - b ± √(b² - 4ac))❄(2a), is your go-to tool for solving any quadratic equation. Play with the discriminant (b² - 4ac) to predict whether you get two real roots, one real root, or even a pair of complex solutions. Pressbooks Quadratic Equations
  2. Understand Trigonometric Ratios - Sine, cosine, and tangent are the VIPs of triangle solving: sin(θ)=opp❄hyp, cos(θ)=adj❄hyp, tan(θ)=opp❄adj. Once you've got these down, any right-triangle challenge becomes a breeze. AskRose Trigonometry Study Guide
  3. Learn the Unit Circle - Picture a circle of radius 1 and watch sin and cos values pop up at key angles: sin(30°)=½, cos(30°)=√3❄2, and so on. Commit those special pairs to memory and you'll breeze through trig equations in record time. AskRose Unit Circle Overview
  4. Apply the Distance and Midpoint Formulas - In the coordinate plane, distance = √[(x₂ - x₝)² + (y₂ - y₝)²] and midpoint = ((x₝+x₂)❄2, (y₝+y₂)❄2). These formulas are your secret weapons for measuring span and bisecting segments like a geometry pro. Scribd Precalculus Study Guide
  5. Grasp Polynomial Operations - Polynomials are expressions with variables raised to powers. Practice adding, subtracting, multiplying, dividing, and factoring (GCF, grouping, special products) to simplify like a champ. College Sidekick Polynomial Guide
  6. Explore Arithmetic Progressions (AP) - An AP is a sequence where the gap between terms stays constant. The nth term is aₙ = a₝ + (n - 1)d and the sum Sₙ = n(a₝ + aₙ)/2. APs pop up in finance, computer science, and more! Khan Academy AP Lessons
  7. Understand Circle Theorems - From "angle in a semicircle is 90°" to "angles in the same segment are equal," these theorems unlock all circle-based angle and chord puzzles. Visualize them once and you'll spot patterns instantly. Math Is Fun: Circle Theorems
  8. Practice Factoring Techniques - Breaking polynomials into factors (GCF, grouping, difference of squares, perfect squares) turns tricky equations into straightforward products. The more you factor, the faster you solve! College Sidekick Factoring Tips
  9. Apply the Pythagorean Theorem - In any right triangle, a² + b² = c² (c is the hypotenuse). Whether you're finding a missing side or checking if a triangle is right-angled, this theorem is unbeatable. Pressbooks Pythagorean Theorem
  10. Understand Function Composition and Inverses - Composition (f∘g)(x) = f(g(x)) lets you build complex operations from simple ones, while inverses swap inputs and outputs to "undo" functions. Master these, and you'll crack advanced function puzzles in no time. CliffsNotes Function Composition & Inverses
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