Find the first three terms in the expansion of:
\((2a - 3b)^5\)
\(=32a^5 - 240a^4b \\+720a^3b^2 ...\)
If £160 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 8 years. £203.34
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,2),(8,5),(0,7)\)
(5,10)
\( X \sim N(50, 5^2)\)
Find
\( P(40\lt X \lt60) \)
\(0.955\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Factorise:
\(3x^2-x-4\)
\((x+1)(3x-4)\)
Draw a rough sketch of the graph of:
\(y=-x-2\)
Gradient -1
y intercept -2
What is the value of:
\(4^{-1}\)
\(= \frac{1}{4}\)
Find angle BCA if AB = 3.3m and AC = 4.8m. 34.5o
Find BC if angle BCA = 30o and AC = 5m. 5.77m
Describe the red region.
\(y = 5x^3 - 6x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 12x + 4\)
\(y = \dfrac{7}{x^3} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{21}{x^4} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=4\ln (4x^2+5)\)
Find \( \dfrac{dy}{dx}\)
\(32x(4x^2+5)^{-1}\)
\(y=\sin x \cos x\)
Find \( \dfrac{dy}{dx}\)
\(cos^2x-sin^2x\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = 24 - 16x\)
Find the equation of the normal to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)
\(y =15x^2 - 12x + 4\)
Find \( \int y \quad dx\)
\(5x^3 - 6x^2 + 4x+c\)
A game is played 12 times and the probability of winning is 0.4. Calculate the probability of winning exactly 10 times. 0.00249
Make up a maths question using this:
\( \int \dfrac{1}{x} = \ln |x| + c\)
Reciprocal Integral formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{7} = -60\)
\(u_{19} = -180\)
Find the sum of the first 35 terms.-5950
Find the equations of the asymptotes of:
\(y=12-\dfrac{4x+3}{7-2x}\)
\(x=\frac{7}{2},y=14\)
In the triangle ABC,
AB = 9.1cm.
BC = 8.4cm.
CA = 9.1cm.
Find angle CÂB.
55.0°
Evaluate:
$$\sum_{n=0}^{6} n^2 - 7n$$
-56
\(f(x)=-6x^2+8x+4\)
What is the value of the discriminent and what does it indicate?
160, Two distinct roots
\(f(x)=x^2+3x+2\)
By completing the square find the coordinates of the vertex.
(-1.5, -0.25)
Evaluate \(\log_2(32) \)
5
Find the integral:
\(\int \dfrac{x^2}{x^3-1} \;dx\)
\(\frac{1}{3} \ln(x^3-1)+c\)
Find the equation of the straight line that passes through:
(-1, -7) and (6, 7)
\(y=2x-5\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-6\)
\((x+6)²\)
\(\text{Find }f(x) \text{ if} \\ f(1-b)=3-b \\\)
\(f(x)=x+2\)
Write in standard form:
\(a \times 10^2 \times b\times 10^3\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^6\)
Draw a rough sketch of
\(y=x^2-8\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \sin{45°}$$\(\dfrac{\sqrt{6}}{4}\)
Without a calculator find the exact value of
$$\tan{4\pi}$$\(0\)
Solve:
\( j+k+l= 16 \\ 2j-3k+9l= 69\\ -j+k-3l=-26\)
j = 9, k = 1, l = 6
Find the area of a sector with radius 7.2cm and angle \( \frac{2\pi}{3}\)
🍕
54.3cm2
In how many ways can 7 different books be arranged on a shelf if 4 of them must be together?
576
Find the equations of the asymptotes of:
$$y=\dfrac{8x^2-19x-15}{1-2z}$$x=1/2,y=15/2-4x
The sum of the first 4 terms of a geometric sequence is 45 and the sum of the first 5 terms is 93. What is the first term?
3
Find the first 4 terms in the expansion of:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{5}_{1} (x-8)^2 \; dx\)
\(105.333333333333\)
What is the probability that it was machine B that broke down if at least one of the independent machines broke down today, given machine A has a 8% chance and machine B has a 10% chance of breaking down on any given day?
\(0.581\)
Find the parametric equation of the line:
\( \dfrac{x-5}{4} = \dfrac{5-y}{9} = \dfrac{z}{4} \)
\( x=5+4\lambda \quad y = 5 -9\lambda \quad z=4 \lambda \)
Simplify
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
Evaluate:
\(\int x\tan^{-1}x\; dx\)
\((\frac{x^2+1}{2})tan^{-1}x-\frac{x}{2}+c\)
Simplify:
$$\sin{x}\cot{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=e^x\) is rotated about the x-axis for \(0 \le x \le 3\)
\(\frac{\pi}{2}(e^6-1)\) cubic units
How do you use the discriminant to determine the nature of roots?
Clue: positive, negative or zero: \( b^2 - 4ac \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sin(x)\)
\(x - \frac{x^3}{6} + \frac{x^5}{120} - \frac{x^7}{5040}\)
Expand and simplify:
$$ (\sqrt{3}+i)^8 $$
\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)
6 girls sit at random on 6 seats in a row. Determine the probability that the two friends Karen and Julie sit at the ends of the row.
1/15 or 6.67%
Prove by mathematical induction that the sum of the cubes of the first \( n \) natural numbers is \( \left(\frac{n(n + 1)}{2}\right)^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
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