Find the first three terms in the expansion of:
\((4a - 3b)^7\)
\(=16384a^7 - 86016a^6b \\+193536a^5b^2 ...\)
If £240 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 8 years. £305.01
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,1),(4,4),(-2,4)\)
(1,7)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2-2x-8\)
\((x+2)(x-4)\)
Factorise:
\(4x^2-7x-2\)
\((4x+1)(x-2)\)
Draw a rough sketch of the graph of:
\(2y=x\)
Gradient 0.5
y intercept 0
What is the value of:
\(8^{\frac{1}{3}}\)
\(= 2\)
Find angle BCA if AB = 5.5m and BC = 7.2m. 49.8o
Find AC if angle ABC = 65o and BC = 3.6m. 3.26m
Describe the red region.
\(y = 3x^3 - 8x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 16x + 6\)
\(y = \dfrac{8}{x^6} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{48}{x^7} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=(5x^2-9)^5\)
Find \( \dfrac{dy}{dx}\)
\(50x(5x^2-9)^4\)
\(y=(3x+6)(8x-2)\)
Find \( \dfrac{dy}{dx}\)
\(48x+42\)
\(y=\frac{x+5}{x-2}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{7}{(x-2)^2}\)
Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =21x^2 - 10x + 8\)
Find \( \int y \quad dx\)
\(7x^3 - 5x^2 + 8x+c\)
A game is played 11 times and the probability of winning is 0.9. Calculate the probability of winning exactly 10 times. 0.384
Make up a maths question using this:
\( A = 4\pi r^2 \)
Surface area of a sphere
What letter is this?
Two terms of an arithmetic sequence:
\(u_{7} = 30\)
\(u_{15} = 54\)
Find the sum of the first 48 terms.3960
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
BC = 8.2cm.
CA = 11.7cm.
BĈA = 41.7°
Find AB to 1 dp.
7.8cm
Evaluate:
$$\sum_{n=4}^{5} 109 - n^2$$
177
\(f(x)=-9x^2-6x-3\)
What is the value of the discriminent and what does it indicate?
-72, No real roots
\(f(x)=x^2+7x-8\)
By completing the square find the coordinates of the vertex.
(-3.5, -20.25)
Solve for x:
\( \log(x) + \log(29-x) = 2\)
\(x = 4 \text{ or } x = 25 \)
Find the integral:
\(\int 3xe^{x^2} \;dx\)
\(\frac{3}{2}e^{x^2}+c\)
Find the equation of the straight line that passes through:
(-1, 6) and (6, 20)
\(y=2x+8\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-9}\)
\(x²+9\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
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
\(y=x^3-4x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{4}} + \sin{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\tan{5\pi}$$\(0\)
Solve:
\(2d+3e-4f = 9 \\ d-e-f= -5\\ 9d+2e-2f=31\)
d = 3, e = 5, f = 3
Find the area of a sector with radius 8.3cm and angle \( \frac{\pi}{4}\)
🍕
27.1cm2
How many ways can twenty people be divided into two equal groups?
92378
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
The sum of the first 4 terms of a geometric sequence is 80 and the sum of the first 5 terms is 242. What is the first term?
2
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(3+x)^2}\)
\(\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
29 Scouts went hiking. 15 got lost, 19 got blisters, and 10 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{9}{14}\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 5 \\ 9 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 9 \\ -9 \\ 3 \end{pmatrix} \; \text{and} \; \begin{pmatrix} 4 \\ -18 \\ 3 \end{pmatrix} \)
64.9 square units
Simplify
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
Evaluate:
\(\int x^2 \ln{x}\; dx\)
\(\frac{x^3}{9}(3\ln x-1)+c\)
Simplify:
$$\cosec{x}\tan{x}$$\(\sec{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\ln{x}\) is rotated about the y-axis for \(0 \le y \le 1\)
\(\approx 10.0\) cubic units
What is the difference between a permutation and a combination?
Permutations consider order; combinations do not.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sqrt{x+1}\)
\(1 + \frac{x}{2} - \frac{x^2}{8} + \frac{x^3}{16}\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
A committee of 4 is randomly selected from 8 men and 11 women. Determine the likelihood that it consists of all men.
35/1938 or 1.81%
Prove by mathematical induction that \( 5^n - 1 \) is divisible by 4 for all natural numbers \( n \)
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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