Find the first three terms in the expansion of:

\((3a - 2b)^4\)

\(=81a^4 - 216a^3b \\+216a^2b^2 ...\)

If £160 is invested with an interest rate of 6% compounded monthly, find the value of the investment after 9 years. £274.19

Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4^{th}?

\((2,4),(6,9),(-3,8)\)

(1,13)

\( X \sim N(50, 5^2)\)

Find

\( P(40\lt X \lt60) \)

\(0.955\)

Factorise:

\(x^2-1\)

\((x+1)(x-1)\)

Factorise:

\(10x^2+x-2\)

\((2x+1)(5x-2)\)

Draw a rough sketch of the graph of:

\(y=-2x-1\)

Gradient -2

y intercept -1

What is the value of:

\(4^{\frac{1}{2}}\)

\(= 2\)

Find angle ABC if AC = 4.9m and BC = 6.1m. 53.4^{o}

Find AB if angle ABC = 43^{o} and BC = 3.3m. 2.41m

Describe the red region.

\(y = 2x^3 - 8x^2 + 2x\)

Find \( \dfrac{dy}{dx}\)

\(6x^2 - 16x + 2\)

\(y = \dfrac{7}{x^4} - 7\sqrt[8]{x}\)

Find \( \frac{dy}{dx}\)

\(-\frac{28}{x^5} - \frac{7}{8}x^{-\frac{7}{8}}\)

\(y=(6x+5)^4\)

Find \( \dfrac{dy}{dx}\)

\(24(6x+5)^3\)

\(y=x(3x^2+4)^6\)

Find \( \dfrac{dy}{dx}\)

\((3x^2+4)^6+36x^2(3x^2+4)^5\)

\(y=\frac{x^2+5}{3x-7}\)

Find \( \dfrac{dy}{dx}\)

\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)

Find the equation of the tangent to the curve:

\(y = 5x^2 + 7x + 3\)

where \(x = 1\)

\(y = 17x - 2\)

Find the equation of the normal to the curve:

\(y = -x^2 + 4x + 2\)

where \(x = 1\)

\(y = 5\frac{1}{2} - \frac{x}{2}\)

\(y =24x^2 - 8x + 2\)

Find \( \int y \quad dx\)

\(8x^3 - 4x^2 + 2x+c\)

A game is played 15 times and the probability of winning is 0.3. Calculate the probability of winning exactly 2 times. 0.0916

Make up a maths question using this:

\( \int \dfrac{1}{x} = \ln |x| + c\)

Reciprocal Integral formula

What letter is this?

Two terms of an arithmetic sequence:

\(u_{9} = 78\)

\(u_{18} = 168\)

Find the sum of the first 46 terms.10258

Find the equations of the asymptotes of:

\(y=\dfrac{2x-7}{6-2x}-5\)

\(x=3,y=-6\)

In the triangle ABC,

BĈA = 55.2°.

BC = 8.6cm.

AB̂C = 40.4°.

Find CA to 1 dp.

5.6cm

Evaluate:

$$\sum_{n=2}^{6} n^2 - 9n$$

-90

\(f(x)=5x^2+8x-9\)

What is the value of the discriminent and what does it indicate?

244, Two distinct roots

\(f(x)=x^2+5x+2\)

By completing the square find the coordinates of the vertex.

(-2.5, -4.25)

Solve for x:

\(\log_3x = 2\)

9

Find the integral:

\(\int \dfrac{\ln(x)}{x} \;dx\)

\(\dfrac{\ln(x)^2}{2}+c\)

Find the equation of the straight line that passes through:

(-5, 4) and (1, -8)

\(y=-2x-6\)

Find the inverse of the function \(f\):

\(f(x)= \sqrt{x+15}\)

\(x²-15\)

\(f(x)=2x+3 \\ g(x)=2x^2 \\[1cm] \text{Find }fgf(x)\)

\(16x^2+48x+39\)

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

\(y=x(5-x)\)

Sketch a height-time graph as this jar is filled.

Without a calculator find the exact value of

$$\cos{30°} \div \sin{\frac{\pi}{3}}$$\(1\)

Without a calculator find the exact value of

$$\sin{5\pi}$$\(0\)

Solve:

\(2x+y-3z= 9 \\ 3x+y+z= 33 \\ x-y+2z = 11\)

x = 8, y = 5, z = 4

Find the perimeter of a sector with radius 4.6cm and angle \( \frac{2\pi}{3}\)

🍕

18.8cm

A safe has a four-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?

2520

Find the equations of the asymptotes of:

$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2

The 6^{th} term of a geometric sequence is 15625 and the sum of the first 6 terms is 19530. 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:

\(\int^{5}_{1} (x-8)^2 \; dx\)

\(105.333333333333\)

The probability that I drop and brake my phone when I visit a coffee shop is 0.1. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?

\(0.526\)

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

$$ (2-i)^{-2} $$

\(\frac{3}{25}+\frac{4}{25}i\)

Evaluate:

\(\int x\tan^{-1}x\; dx\)

\((\frac{x^2+1}{2})tan^{-1}x-\frac{x}{2}+c\)

Simplify:

$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)

$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\frac{1}{x}\) is rotated about the x-axis for \(1 \le x \le 2\)

\(\frac{\pi}{2}\) cubic units

What is the binomial theorem?

Clue: Expand \( (a + b)^n \)

Show how the first four terms of the Maclaurin series are obtained for

\(f(x) = e^x\)

\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)

Find the four 4th roots of 1

\(1, i, -1, -i\)

A committee of 5 is chosen from 15 people by random selection. Two Londoners were amongst the group from which the selection was made. Find the probability that both Londoners are chosen for the committee.

2/21 or 9.52%

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

Write down a summary of your last Maths lesson focussing on what you learnt.

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