Use the quadratic equation curve to answer this questions
What is the minimum value of the graph?
-5.3
0.5
3
8
Correct answer is A
The minimum value is the lowest value of the curve on y axis which gives a value of -5.3
Find the equation of the tangent at the point (2, 0) to the curve y = x\(^2\) - 2x
y = 2x - 4
y = 2x + 4
y = 2x - 2
y = 2x + 2
Correct answer is A
The gradient to the curve is found by differentiating the curve equation with respect to x
So \(\frac{dy}{dx}\) 2x - 2
The gradient of the curve is the same with that of the tangent.
At point (2, 0) \(\frac{dy}{dx}\) = 2(2) - 2
= 4 – 2 = 2
The equation of the tangent is given by (y - y1) \(\frac{dy}{dx}\) (x – x1)
At point (x1, y1) = (2, 0)
y - 0 = 2(x - 2)
y = 2x - 4
-4
-2
2
4
Correct answer is A
2√3 - 4) ( 2√3 + 4) = 12 + 8√3 - 8√3 – 16 = 12 – 16 = -4 The two expressions in the bracket are conjugate of each other
Express 495g as a percentage of 16.5kg
3%
3 \(\frac{1}{3}\)%
15%
30%
Correct answer is A
The two numbers must be expressed in the same unit. To convert 495g to kg, it will be divided by 1000
495g = \(\frac{495}{1000}\)
= 0.495kg
To express in percentage, 0.495 will be divided by 16.5 and then multiplied by 100
% will be added to the answer \(\frac{0.4950}{16.5}\) x 100
= 3%
In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/
32cm
24 cm
16 cm
12 cm
Correct answer is C
From the figure,
∠ XMN = ∠ XZY
Angle X is common
So, ∠ XNM = ∠ XYZ
Then from the angle relationship
\(\frac{XM}{XZ}\) = \(\frac{XN}{XY}\) = \(\frac{MN}{ZY}\)
XM = 8, XZ = 12 + 4 = 16,
XN = 12, XY = 8 + YM
\(\frac{8}{16}\) = \(\frac{12}{(8 + YM) }\)
Cross multiply
8(8 + YM) = 192
64 + 8YM = 192
8YM = 128
YM = \(\frac{128}{8}\)
= 16cm
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