Find the first three terms in the expansion of:
\((3a - 4b)^5\)
\(=243a^5 - 1620a^4b \\+4320a^3b^2 ...\)
If £200 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 4 years. £253.80
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,5),(5,9),(-3,9)\)
(1,13)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2+x-12\)
\((x+4)(x-3)\)
Factorise:
\(2x^2-x-3\)
\((x+1)(2x-3)\)
Draw a rough sketch of the graph of:
\(y=2x-1\)
Gradient 2
y intercept -1
What is the value of:
\(4^{-3}\)
\(= \frac{1}{64}\)
Find angle ABC if AB = 4.4m and BC = 5.9m. 41.8o
Find BC if angle BCA = 23o and AC = 4.2m. 4.56m
Describe the red region.
\(y = 4x^3 - 2x^2 + 8x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 4x + 8\)
\(y = \dfrac{8}{x^4} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{32}{x^5} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=(3x^2-4)^6\)
Find \( \dfrac{dy}{dx}\)
\(36x(3x^2-4)^5\)
\(y=\sin x \cos x\)
Find \( \dfrac{dy}{dx}\)
\(cos^2x-sin^2x\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
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:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 5\frac{1}{2} - \frac{x}{2}\)
\(y =9x^2 - 8x + 7\)
Find \( \int y \quad dx\)
\(3x^3 - 4x^2 + 7x+c\)
A game is played 10 times and the probability of winning is 0.8. Calculate the probability of winning exactly 5 times. 0.0264
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:
\(u_{6} = -48\)
\(u_{16} = -138\)
Find the sum of the first 28 terms.-3486
Find the equations of the asymptotes of:
\(y=3\left(\dfrac{2x+3}{7-x}\right)\)
\(x=7,y=-6\)
In the triangle ABC,
AB = 9.3cm.
BC = 7.6cm.
CA = 12.1cm.
Find angle CÂB.
38.9°
Evaluate:
$$\sum_{n=3}^{8} n^2 - 4n$$
67
\(f(x)=-7x^2-7x-8\)
What is the value of the discriminent and what does it indicate?
-175, No real roots
\(f(x)=x^2-9x-2\)
By completing the square find the coordinates of the vertex.
(4.5, -22.25)
Write the following in terms of logs to base 10:
\(\log_a(z)\)
\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)
Find the integral:
\(\int (x+3)\sqrt{x^2+6x+8} \;dx\)
\(\frac{1}{3}(x^2+6x+8)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-8, 25) and (0, 1)
\(y=-3x+1\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-3}{8}}\)
\(8x²+3\)
\(f(x)=2x+3 \\ g(x)=2x^2 \\[1cm] \text{Find }fgf(x)\)
\(16x^2+48x+39\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^{p+q+1}\)
Draw a rough sketch of
\(y=x^2+7x\)
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:
\( j+k+l= 8 \\ 2j-3k+9l= 53\\ -j+k-3l=-18\)
j = 1, k = 1, l = 6
Find the perimeter of a sector with radius 4.3cm and angle \( \frac{2\pi}{3}\)
🍕
17.6cm
How many ways can eighteen people be divided into two equal groups?
24310
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The 7th term of a geometric sequence is 3645 and the sum of the first 7 terms is 5465. Find the first term.
5
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:
\(\int^{80}_{40} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
Tin A contains 7 red balls and 9 green balls. Tin B contains 11 red balls and 13 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B.
\(\frac{44}{65}\)
Find the cartesian equation of this plane:
\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)
2x-6y+5z=-1
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
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 \(y=\sqrt[3]{x^2}\) is rotated about the y-axis for \(2 \le y \le 3\)
\(\frac{65\pi}{4}\) cubic units
How do you determine the domain of a function?
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = (1 + x)^n\)
\(1 + nx + \frac{n(n-1)x^2}{2} + \frac{n(n-1)(n-2)x^3}{6}\)
Given |z| = 8, find:
$$ |(3+4i)z| $$
\(40\)
A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.
1/26 or 3.85%
Prove by mathematical induction that the sum of the first \( n \) odd numbers is \( n^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
Write down a summary of your last Maths lesson focussing on what you learnt.
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