Algebra Questions with Answers and Solutions - Grade 12
Grade 12
algebra questions with answers and solutions are presented. Some of these questions may be challenging; you need to spend time on them as these are the ones that make you think and learn how to solve problems. Also group work on challenging questions is an excellent opportunity to interact with others and learn from them. Let me know of any other possible solutions to any of the questions below.
Order from greatest to least
a) 25100
b) 2300
c) 3400
d) 4200
e) 2600
Find all rational zeros of P(x) = x3 - 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) = x4 - 4x3 + 3x2 + 8x - 10. Find all zeros of P.
Find a, b and c so that the graph of the quadratic function f(x) = ax2 + 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) = (ax4 + bx3 + 3) / (x3 - 2) has an oblique asymptote given by y = 2x - 3
Solve for x the equation log9 (x3) = log2(8)
Find the value of logy (x4) if logx (y3) = 2
Solve for x the equation logx (8e3) = 3
If 16x + 16x - 1 = 10, find 22x.
If a2 - b2 = 8 and a×b = 2, find a4 + b4.
What are the maximum value and minimum values of f(x) = |2sin(2x - ?/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 x2 - y2 = -12 and x + y = 6, find x and y.
f(x) is a function such that f(x) + 3 f(8 - x) = x for all real numbers x. Find the value of f(2).
f(x) is a function such that f(2x + 1) = 2 f(x) + 1 for all real numbers x and f(0) = 2. Find the value of f(3).
Find b so that the line y = 2 x + b is tangent to the circle x2 + y2 = 4.
What is the remainder of the division (x100 - x99 - x + 1) / (x2 - 3x + 2)
Evaluate the number represented by the infinite series √(1/3 + √(1/3 + √(1/3 + ...))).
Show that the 3 by 3 system of equations given below has no solutions.
2 x + y - 3z = 5
-5 x + 3 y + 2 z = 7
3 x - 4 y + z = 8