Find the first three terms in the expansion of:
\((4a - 5b)^5\)
\(=1024a^5 - 6400a^4b \\+16000a^3b^2 ...\)
If £160 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 5 years. £176.78
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,1),(8,4),(1,5)\)
(5,8)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2+3x-4\)
\((x+4)(x-1)\)
Factorise:
\(4x^2+4x-3\)
\((2x+3)(2x-1)\)
Draw a rough sketch of the graph of:
\(y=-x+2\)
Gradient -1
y intercept 2
What is the value of:
\(27^{\frac{1}{3}}\)
\(= 3\)
Find angle ABC if AC = 3m and BC = 4.5m. 41.8o
Find BC if angle BCA = 46o and AC = 4.2m. 6.05m
Describe the red region.
\(y = 9x^3 - 9x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(27x^2 - 18x + 3\)
\(y = \dfrac{3}{x^7} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{21}{x^8} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=(7x+4)^4\)
Find \( \dfrac{dy}{dx}\)
\(28(7x+4)^3\)
\(y=e^{7x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(7e^{7x}cosx-e^{7x}sinx\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
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:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = \frac{x}{2} + 1\)
\(y =18x^2 - 18x + 4\)
Find \( \int y \quad dx\)
\(6x^3 - 9x^2 + 4x+c\)
A game is played 14 times and the probability of winning is 0.1. Calculate the probability of winning exactly 7 times. 0.000164
Make up a maths question using this:
\(\log_ax=\dfrac{\log_bx}{\log_ba}\)
Logarithm changing base formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = -37\)
\(u_{18} = -128\)
Find the sum of the first 47 terms.-7990
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
BĈA = 66.6°.
BC = 7.3cm.
AB̂C = 54.26°.
Find CA to 1 dp.
6.9cm
Evaluate:
$$\sum_{n=0}^{6} 116 - n^2$$
721
\(f(x)=2x^2+6x-3\)
What is the value of the discriminant and what does it indicate?
60, Two distinct roots
\(f(x)=x^2+4x-4\)
By completing the square find the coordinates of the vertex.
(-2, -8)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int \dfrac{5x}{x^2-3} \;dx\)
\(\frac{5}{2} \ln(x^2-3)+c\)
Find the equation of the straight line that passes through:
(-8, 23) and (0, 7)
\(y=-2x+7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x-9}}{4}\)
\(16x²+9\)
\(\text{Find }f(x) \text{ if} \\ f(1-b)=3-b \\\)
\(f(x)=x+2\)
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
\(y=x^3-4x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\sin{\frac{\pi}{4}} \times \cos{45°}$$\(\dfrac{1}{2}\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( j+k+l= 18 \\ 2j-3k+9l= 65\\ -j+k-3l=-24\)
j = 7, k = 4, l = 7
Find the area of a sector with radius 3.6cm and angle \( \frac{5\pi}{6}\)
🍕
17.0cm2
How many ways can ten people be divided into two equal groups?
126
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
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:
\(\int^{6}_{0} (x-8)^2 \; dx\)
\(168\)
Every family in Happyland has either has a car or a motor scooter or both. 74% of the families have a car. 78% of the families have a scooter. A family is selected at random and it is found that they have a car. Find the probability they also have a scooter.
\(\dfrac{26}{37}\)
Find the vector equation of the line:
\( \dfrac{x-7}{5} = \dfrac{8-y}{4} = \dfrac{z}{2} \)
\( \mathbf{r} = \begin{pmatrix} 7 \\ 8 \\ 0 \end{pmatrix} \quad + \quad t \begin{pmatrix} 5 \\ -4 \\ 2 \end{pmatrix} \)
Simplify
$$ (6-4i)(3-4i) $$
\(2-36i\)
Evaluate:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$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 formula for compound interest?
\( FV = PV(1 + \frac{r}{100k})^{kn} \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
5 alphabet blocks A, E, P, R and S are placed at random in a row. What is the likelihood that they spell out either SPEAR or PARSE?
1/60 or 1.67%
Prove by mathematical induction that the sum of the first \( n \) natural numbers is \( \frac{n(n + 1)}{2} \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{20}$$
\(2\sqrt{5}\)
Simplify:
$$\dfrac{7}{\sqrt{5}}$$\(\frac{7\sqrt{5}}{5}\)
Simplify
\((9 + 2\sqrt{2})(9 - 2\sqrt{2})\)
\(73\)
Simplify:
$$\dfrac{2}{5 - \sqrt{7}}$$\(\frac{10 + 2\sqrt{7}}{18}\)
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