Algebra Questions with Answers and Solutions - Grade 12

Grade 12
algebra questions with answers and solutions are presented.

Order from greatest to least
a) 25^{100}
b) 2^{300}
c) 3^{400}
d) 4^{200}
e) 2^{600}

Find all rational zeros of P(x) = x^{3} - 7x + 6.

Round all real zeros in the graph to the nearest integer and find a polynomial function P of lowest degree, with the absolute value of the leading coefficient equal to 1, that has the indicated graph.

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2 - i, where i is the imaginary unit, is a zero of P(x) = x^{4} - 4x^{3} + 3x^{2} + 8x - 10. Find all zeros of P.

Find a, b and c so that the graph of the quadratic function f(x) = ax^{2} + bx + c has a vertex at (-2 , 1) and passes through the point (0 , -3).

f(x) is a quadratic function such that f(1) = 3 and f(5) = 3. Find the x coordinate of the vertex of the graph of f.

Find a and b so that the rational function f(x) = (ax^{4} + bx^{3} + 3) / (x^{3} - 2) has an oblique asymptote given by y = 2x - 3

Solve for x the equation log_{9}(x^{3}) = log_{2}(8)

Find the value of log_{y}(x^{4}) if log_{x}(y^{3}) = 2

Solve for x the equation log_{x}(8e^{3}) = 3

If 16^{x} + 16^{x - 1} = 10, find 2^{2x}.

If a^{2} - b^{2} = 8 and a*b = 2, find a^{4} + b^{4}.

What are the maximum value and minimum values of f(x) = |2sin(2x - pi/3) - 5| + 3

If x < -7, simplify |4 - |3 + x||

A car travels from A to B at an average speed of 50 km/hour. At what average speed would it have to travel from B to A to average 60 km/hour for the whole trip?

If x^{2} - y^{2} = -12 and x + y = 6, find x and y.

f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2).

f(x) is a function such that f(2x + 1) = 2f(x) + 1 for all real numbers x and f(0) = 2. Find the value of f(3).

Find b so that the line y = 2x + b is tangent to the circle x^{2} + y^{2} = 4.

What is the remainder of the division (x^{100} - x^{99} - x + 1) / (x^{2} - 3x + 2)

Evaluate the number represented by the infinite series sqrt(1/3 + sqrt(1/3 + sqrt(1/3 + ...))).

Show that the 3 by 3 system of equations given below has no solutions.
2x + y - 3z = 5
-5x + 3y + 2z = 7
3x - 4y + z = 8