Find the first three terms in the expansion of:
\((4a - 5b)^6\)
\(=4096a^6 - 30720a^5b \\+96000a^4b^2 ...\)
If £160 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 8 years. £219.99
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,1),(11,7),(-1,7)\)
(5,13)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2+x-6\)
\((x+3)(x-2)\)
Factorise:
\(x^2-2x-8\)
\((x+2)(x-4)\)
Draw a rough sketch of the graph of:
\(y=x-1\)
Gradient 1
y intercept -1
What is the value of:
\(2^{0}\)
\(= 1\)
Find angle ABC if AC = 3.2m and AB = 4.6m. 34.8o
Find BC if angle BCA = 70o and AC = 4m. 11.7m
Describe the red region.
\(y = 2x^3 - 6x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 12x + 3\)
\(y = \dfrac{6}{x^8} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{48}{x^9} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=\sqrt{4x^6+5}\)
Find \( \dfrac{dy}{dx}\)
\(12x^5(4x^6+5)^{-\frac{1}{2}}\)
\(y=e^{9x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(9e^{9x}cosx-e^{9x}sinx\)
\(y=\frac{x+2}{x-4}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{6}{(x-4)^2}\)
Find the equation of the tangent to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = -14x - 17\)
Find the equation of the normal to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 15\frac{1}{17} - \frac{x}{17}\)
\(y =21x^2 - 6x + 5\)
Find \( \int y \quad dx\)
\(7x^3 - 3x^2 + 5x+c\)
A game is played 14 times and the probability of winning is 0.4. Calculate the probability of winning exactly 2 times. 0.0317
Make up a maths question using this:
\( \tan \theta \equiv \dfrac{ \sin \theta}{ \cos \theta}\)
Trigonometric identity
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = 49\)
\(u_{20} = 133\)
Find the sum of the first 38 terms.4921
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
BC = 8.2cm.
CA = 9.6cm.
BĈA = 65.5°
Find AB to 1 dp.
9.7cm
Evaluate:
$$\sum_{n=1}^{9} 84 - n^2$$
471
\(f(x)=2x^2-2x+6\)
What is the value of the discriminant and what does it indicate?
-44, No real roots
\(f(x)=x^2+6x-6\)
By completing the square find the coordinates of the vertex.
(-3, -15)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-6, 13) and (1, -8)
\(y=-3x-5\)
Find the inverse of the function \(f\):
\(f(x)=\frac{4+ x}{6}\)
\(6x-4\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\((a \times 10^3) \div (b\times 10^5)\)
where \(a \div b \) is a two digit number \((10 \le \frac{a}{b} \lt 100)\)
\(\frac{a}{10b}\times10^{-1}\)
Draw a rough sketch of
\(y=2^x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\tan{30°} \times \tan{\frac{\pi}{3}}$$\(1\)
Without a calculator find the exact value of
$$\cos{720°}$$\(1\)
Solve:
\(2x+y-3z= 0 \\ 3x+y+z= 15 \\ x-y+2z = 6\)
x = 3, y = 3, z = 3
Find the area of a sector with radius 7.4cm and angle \( \frac{2\pi}{3}\)
🍕
57.3cm2
A safe has a eight-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
907200
Find the equations of the asymptotes of:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2
The fourth term of a geometric sequence is \(-16\) and the sum to infinity is \(32\). What is the common ratio?
-0.669
Find the first 4 terms in the expansion of:
\(\dfrac{1}{\sqrt{4+x}}\)
\(\frac{1}{2}-\frac{x}{16}+\frac{3x^2}{256}-\frac{5x^3}{2048}\)
Evaluate:
\(\int^{6}_{0} x^2-2x+7 \; dx\)
\(78.0\)
30 Scouts went hiking. 17 got lost, 14 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.
\(\dfrac{6}{13}\)
Find the point of intersection of these planes:
\(\Pi_1: \quad 2x + y - 3z = -5\)
\(\Pi_2: \quad x - 3y + 2z = 1\)
\(\Pi_3: \quad 3x - 2y + z = 2\)
\( (1,2,3) \)
Simplify
$$ \dfrac{1-4i}{1+5i}$$
\(-\frac{19}{26}-\frac{9}{26}i\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$\sin{x}\cot{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^2\) is rotated about the y-axis for \(0 \le y \le 4\)
\(8\pi\) 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
\(f(x) = \sin(x)\)
\(x - \frac{x^3}{6} + \frac{x^5}{120} - \frac{x^7}{5040}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
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 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
Simplify:
$$\sqrt{27}$$
\(3\sqrt{3}\)
Simplify:
$$\dfrac{2}{\sqrt{10}}$$\(\frac{2\sqrt{10}}{10} = \frac{\sqrt{10}}{5}\)
Simplify
\(7\sqrt{13} - 9\sqrt{13}\)
\(-2\sqrt{13}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
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