Question 1 of 8graph transformations
A curated set of real ZIMSEC past paper questions with answers and explanations. The full question bank is in the Danho app.
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The diagram shows the graph of y = f(x), passing through A(-1, 0), B(0, 1) and C(1, 0). On the graph of y = f(-x) + 3, the image of B is
In a circle of radius r and centre O, the shaded region is bounded by the chord AC, the diameter AB and the arc BC, with \widehat{BAC} =…
Solve the inequality |3^{-3x} - 54| < 27.
Find the set of values of x which satisfy |3x + 2| < -x + 1.
Given that -4 < x < 2 is the solution of the inequality |x + a| < b, find the values of a and b.
In triangle ABC, AB = m cm, AC = 12 cm and angle B\hat{A}C = 60°. Given that the area of the triangle is \sqrt{675} cm^2, find the exact…
Solve the simultaneous equations 2^x + 3^y = 5 and 2^{x+2} - 3^{y+1} = 13.
Solve the equation 5^{x-1} + 5^{x-2} = 30.
Express \dfrac{6}{3 + \sqrt{5} + \sqrt{14}} in the form a + b\sqrt{c} + d\sqrt{e}.
A polynomial f(x) leaves remainder -9 when divided by (x-3) and remainder -6 when divided by (2x-1). Find the remainder when f(x) is…
Find the inverse of f(x) = ax + b, where a \ne 0 and b are constants.
The complex number u = \dfrac{1}{-2+i}. Find |u|.
Solve the inequality |x-1| < x.
Given w = 1 + 2i and u = 3 - i, express uw in the form a + ib.
Solve the equation e^{2x} = 4e^{2-x}, giving your answer in exact form.
The equation x^3 - 2x^2 + 4x - 8 = 0 has a root x = 2i. Find the other two roots.
Find, in terms of k, the equation of the perpendicular bisector of the line joining A(2k, k) and B(4k, 9k).
Solve the equation 3^{x-1} + 3^{x-2} = 12.