Find the first three terms in the expansion of:
\((2a - 3b)^4\)
\(=16a^4 - 96a^3b \\+216a^2b^2 ...\)
If £140 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 4 years. £151.63
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,2),(9,5),(1,7)\)
(6,10)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2+2x-8\)
\((x+4)(x-2)\)
Factorise:
\(5x^2+14x-3\)
\((x+3)(5x-1)\)
Draw a rough sketch of the graph of:
\(y=x\)
Gradient 1
y intercept 0
What is the value of:
\(2^{-2}\)
\(= \frac{1}{4}\)
Find angle BCA if AB = 5.6m and AC = 6.9m. 39.1o
Find AC if angle BCA = 47o and AB = 4m. 3.73m
Describe the red region.
\(y = 4x^3 - 2x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 4x + 4\)
\(y = \dfrac{8}{x^8} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{64}{x^9} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=\frac{1}{(6x+7)^3}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{18}{(6x+7)^4}\)
\(y=e^{4x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(4e^{4x}cosx-e^{4x}sinx\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 6x + 3\)
Find the equation of the normal to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 9\frac{1}{3} - \frac{x}{6}\)
\(y =6x^2 - 16x + 6\)
Find \( \int y \quad dx\)
\(2x^3 - 8x^2 + 6x+c\)
A game is played 16 times and the probability of winning is 0.7. Calculate the probability of winning exactly 4 times. 0.000232
Make up a maths question using this:
\(S_n = \dfrac{u_1(r^n-1)}{r-1}\)
The sum of a geometric sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = 20\)
\(u_{15} = 50\)
Find the sum of the first 47 terms.3619
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-{1}{5}\)
In the triangle ABC,
AB = 5.6cm.
BC = 5.2cm.
CÂB = 57.4°.
Find angle BĈA.
65.2° or 114.8°
Evaluate:
$$\sum_{n=2}^{6} 2^n$$
124
\(f(x)=-3x^2+2x-5\)
What is the value of the discriminant and what does it indicate?
-56, No real roots
\(f(x)=x^2-7x+1\)
By completing the square find the coordinates of the vertex.
(3.5, -11.25)
Simplify:
\(\log_2(4\sqrt{16})\)
4
Find the integral:
\(\int x\sqrt{x^2+3} \;dx\)
\(\frac{1}{3}(x^2+3)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-2, -11) and (2, -3)
\(y=2x-7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+8}{5}\)
\(5x-8\)
\(\text{Find }f(x) \text{ if} \\ f(1-b)=3-b \\\)
\(f(x)=x+2\)
Write in standard form:
\((a \times 10^4) \div (b\times 10^{-2})\)
where \(a \div b \) is a decimal number \((0.1 \le \frac{a}{b} \lt 1)\)
\(\frac{10a}{b}\times10^5\)
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
$$\cos{0°} + \sin{\frac{\pi}{6}} + \cos{60°}$$\(2\)
Without a calculator find the exact value of
$$\sin{5\pi}$$\(0\)
Solve:
\( j+k+l= 13 \\ 2j-3k+9l= 14\\ -j+k-3l=-5\)
j = 1, k = 8, l = 4
Find the area of a sector with radius 9.6cm and angle \( \frac{\pi}{4}\)
🍕
36.2cm2
How many ways can fourteen people be divided into two equal groups?
1716
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
-109230
Find the first 4 terms in the expansion of:
\(\dfrac{1}{2-x}\)
\(\frac{1}{2}+\frac{x}{4}+\frac{x^2}{8}+\frac{x^3}{16}\)
Evaluate:
\(\int^{5}_{0} x^2-2x+7 \; dx\)
\(51.7\)
32 Scouts went hiking. 14 got lost, 17 got blisters, and 8 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{1}{2}\)
Find the vector equation of the line:
\( \dfrac{x-9}{5} = \dfrac{2-y}{8} = \dfrac{z}{2} \)
\( \mathbf{r} = \begin{pmatrix} 9 \\ 2 \\ 0 \end{pmatrix} \quad + \quad t \begin{pmatrix} 5 \\ -8 \\ 2 \end{pmatrix} \)
Simplify
$$ \dfrac{2-i}{1+3i}$$
\(-\frac{1}{10}-\frac{7}{10}i\)
Evaluate:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^2\) is rotated about the x-axis for \(-2 \le x \le 2\)
\(\frac{64\pi}{5}\) cubic units
Describe the behavior of a function at its asymptote.
Clue: approaches but never reaches
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
A team of 11 is randomly chosen from a squad of 18 including the club captain and vice captain. Determine the probability that both the captain and vice-captain are chosen.
55/153 or 35.9%
Prove by mathematical induction that \( 2^n > n^2 \) for all integers \( n \) greater
than four
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify
\((2 - 2\sqrt{2})^2\)
\(12 - 8\sqrt{2}\)
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