Algebra & Equations: 14 MCQs with Explanations

2x = 12 → x = 6. Basic linear equation from PMC Algebra syllabus. Appears in PPSC PMS 2021 Math section.

x² = 9 → x = ±√9 → x = 3 or x = -3. Quadratic Equations topic in MDCAT syllabus. FPSC CSS 2021 Math paper Q9.

log₂(x) = 3 means 2³ = x, so x = 8. This tests logarithm properties and exponential form.

Sum = n(n+1)/2 = 10(11)/2 = 55. This tests arithmetic series formula.

f(-1) = (-1)² + 2(-1) + 1 = 1 - 2 + 1 = 0. This tests polynomial function evaluation.

Adding equations: 2x = 12 → x = 6. This tests solving system of linear equations.

Factor: (x²-4)/(x-2) = (x-2)(x+2)/(x-2) = x+2, so limit = 2+2 = 4. This tests limit evaluation.

log₂(x) = 3 means 2³ = x → x = 8. Logarithm properties from Algebra section. PPSC PMS 2019 Math section Q12 tested this concept.

Adding equations: 2x = 12 → x = 6. System of linear equations from Algebra. CSS 2019 General Ability Q11 tested this method.

The x-axis is a horizontal line where all points have a y-coordinate of zero. Therefore, its equation is y = 0.

Rewriting the logarithmic equation in exponential form gives x^(-3) = 1/64. This means 1/x^3 = 1/64, so x^3 = 64. Therefore, x = 4.

The discriminant (D or Δ) of a quadratic equation ax²+bx+c=0 is b² - 4ac. It determines the nature of the roots.

The integral of 1/x dx is a standard result, which is the natural logarithm of the absolute value of x plus the constant of integration: ∫(1/x) dx = ln|x| + c.

The standard form of a linear equation in one variable is ax + b = 0, where a ≠ 0. Its graph is a straight line.