Find the first three terms in the expansion of:

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

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

If £120 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 5 years. £146.42

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

\((5,2),(9,8),(-1,6)\)

(3,12)

\( X \sim N(65, 9^2)\)

Find

\( P(36\lt X \lt48) \)

\(0.0288\)

Factorise:

\(x^2-2x-3\)

\((x+1)(x-3)\)

Factorise:

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

\((4x+3)(2x-1)\)

Draw a rough sketch of the graph of:

\(y=x\)

Gradient 1

y intercept 0

What is the value of:

\(1^{1}\)

\(= 1\)

Find angle BCA if AB = 4.8m and BC = 6.1m. 51.9^{o}

Find AB if angle ABC = 33^{o} and BC = 4.2m. 3.52m

Describe the red region.

\(y = 5x^3 - 6x^2 + 5x\)

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

\(15x^2 - 12x + 5\)

\(y = \dfrac{5}{x^3} - 7\sqrt[8]{x}\)

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

\(-\frac{15}{x^4} - \frac{7}{8}x^{-\frac{7}{8}}\)

\(y=5\ln (4x^2+5)\)

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

\(40x(4x^2+5)^{-1}\)

\(y=x(5x^2+6)^4\)

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

\((5x^2+6)^4+40x^2(5x^2+6)^3\)

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

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

\(-\frac{7}{(x-5)^2}\)

Find the equation of the tangent to the curve:

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

where \(x = 2\)

\(y = 17 - 13x\)

Find the equation of the normal to the curve:

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

where \(x = 2\)

\(y = \frac{x}{13} - \frac{119}{13}\)

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

Find \( \int y \quad dx\)

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

A game is played 16 times and the probability of winning is 0.6. Calculate the probability of winning exactly 6 times. 0.0392

What's this?

\( P(A|B) = \dfrac{P(A \cap B)}{P(B)} \)

Conditional probability formula

What letter is this?

Two terms of an arithmetic sequence:

\(u_{8} = -31\)

\(u_{18} = -61\)

Find the sum of the first 47 terms.-3713

Find the equations of the asymptotes of:

\(y=\dfrac{4-7x}{3-14x}\)

\(x=\frac{3}{14},y=\frac{1}{2}\)

In the triangle ABC,

AB = 9.3cm.

BC = 8.4cm.

CA = 12.5cm.

Find angle CÂB.

42.2°

Evaluate:

$$\sum_{n=1}^{4} 2^n$$

30

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

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

104, Two distinct roots

\(f(x)=x^2-3x-1\)

By completing the square find the coordinates of the vertex.

(1.5, -3.25)

What is the value of \(\ln{e^3}\) ?

3

Find the integral:

\(\int x\sqrt{x^2+3} \;dx\)

\(\frac{1}{3}(x^2+3)^{\frac32}+c\)

Find the equation of the straight line that passes through:

(-8, -18) and (2, 2)

\(y=2x-2\)

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

\(f(x)=\frac{\sqrt{x}-17}{18}\)

\((18x+17)²\)

\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)

\(x^4-2x^2\)

Write in standard form:

\(a \times 10^p \times b\times 10^q\)

where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)

\(ab\times10^{p+q}\)

Draw a rough sketch of

\(y=x^2-8\)

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

$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)

Solve:

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

x = 2, y = 2, z = 1

Find the perimeter of a sector with radius 6.6cm and angle \( \frac{\pi}{4}\)

🍕

18.4cm

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

1814400

Find the equations of the asymptotes of:

$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2

The sum of the first 7 terms of a geometric sequence is 39062 and the sum of the first 8 terms is 195312. What is the first term?

2

Find the first 4 terms in the expansion of:

\(\dfrac{1}{(1+3x)^3}\)

\(1-9x+54x^2-270x^3\)

Evaluate:

\(\int^{80}_{40} \dfrac{1}{x} dx\)

\(\ln{2} \approx 0.693\)

In a bookstore with equally sized fiction and non-fiction sections, if a hardcover book is selected (70% of fiction, 40% of non-fiction are hardcovers), what's the probability it's non-fiction?

\(0.364\)

There are eight different ways that three planes can relate in three dimensions. One is where they all intersect at a point. How many of the other seven ways can you sketch or describe?

Simplify

$$ \dfrac{1-4i}{1+5i}$$

\(\frac{21}{26}-\frac{9}{26}i\)

Evaluate:

\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)

\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)

Simplify:

$$\tan{x}\cot{x}$$\(1\)

$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x\) is rotated about the x-axis for \(0 \le x \le 1\)

\(\frac{\pi}{3}\) 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

\(f(x) = (1 + x)^n\)

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

Expand and simplify:

$$ (\sqrt{3}+i)^8 $$

\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)

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 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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