Find the first three terms in the expansion of:
\((4a - 2b)^4\)
\(=256a^4 - 512a^3b \\+384a^2b^2 ...\)
If £100 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 6 years. £127.07
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,2),(7,8),(-5,8)\)
(1,14)
\( X \sim N(-25, 3^2)\)
Find
\( P(-20\lt X \lt-10) \)
\(0.0478\)
Factorise:
\(x^2-9\)
\((x+3)(x-3)\)
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:
\(2^{-3}\)
\(= \frac{1}{8}\)
Find angle BCA if AC = 5.6m and BC = 7m. 36.9o
Find AC if angle ABC = 38o and BC = 3.7m. 2.28m
Describe the red region.
\(y = 5x^3 - 6x^2 + 7x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 12x + 7\)
\(y = \dfrac{3}{x^{5}} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{15}{x^{6}} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=4\ln (8x^2+9)\)
Find \( \dfrac{dy}{dx}\)
\(64x(8x^2+9)^{-1}\)
\(y=x(2x+3)^3\)
Find \( \dfrac{dy}{dx}\)
\((2x+3)^3+6x(2x+3)^2\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 2x + 3\)
Find the equation of the normal to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 15\frac{1}{17} - \frac{x}{17}\)
\(y =15x^2 - 4x + 4\)
Find \( \int y \quad dx\)
\(5x^3 - 2x^2 + 4x+c\)
A game is played 18 times and the probability of winning is 0.8. Calculate the probability of winning exactly 17 times. 0.0811
Make up a maths question using this:
\(u_n=u_1+(n-1)d\)
The nth term of an arithmetic sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = -89\)
\(u_{12} = -119\)
Find the sum of the first 21 terms.-2289
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
AB = 5.6cm.
BC = 5.6cm.
CA = 6.7cm.
Find angle CÂB.
53.3°
Evaluate:
$$\sum_{n=3}^{9} n^2 - 6n$$
28
\(f(x)=4x^2-8x-2\)
What is the value of the discriminant and what does it indicate?
96, Two distinct roots
\(f(x)=x^2+5x+7\)
By completing the square find the coordinates of the vertex.
(-2.5, 0.75)
Solve for x:
\(\log_2(x) = 4\)
16
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:
(-3, -16) and (4, 5)
\(y=3x-7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-14}{19}\)
\((19x+14)²\)
\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)
\(-5-4\sqrt{m}\)
Write in standard form:
\((a \times 10^2) \div (b\times 10^4)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{-2}\)
Draw a rough sketch of
\(y=\dfrac{5}{x}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \sin{45°}$$\(\dfrac{\sqrt{6}}{4}\)
Without a calculator find the exact value of
$$\tan{4\pi}$$\(0\)
Solve:
\( g-7h-7i=-61 \\ 2g-2h+i= -2\\ 5g+3h+i = 29\)
g = 2, h = 5, i = 4
Find the perimeter of a sector with radius 4.5cm and angle \( \frac{\pi}{6}\)
🍕
11.4cm
How many ways can fifteen children sit in a row without the youngest being in the middle?
1220496076800
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The sum of the first 6 terms of a geometric sequence is 1092 and the sum of the first 7 terms is 3279. What is the first term?
3
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:
\(\int^{4}_{2} (x-8)^2 \; dx\)
\(50.6666666666666\)
Each afternoon the probability my cat sleeps is 0.6 and the probability that my dog sleeps is 0.5. The probability that the dog sleeps given that the cat is sleeping is 0.9. Find the probability that both sleep in the afternoon.
\(0.54\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 5 \\ 9 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 3 \\ -5 \\ 8 \end{pmatrix} \; \text{and} \; \begin{pmatrix} -2 \\ -14 \\ 8 \end{pmatrix} \)
48.7 square units
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int x^2 \ln{x}\; dx\)
\(\frac{x^3}{9}(3\ln x-1)+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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 solve a quadratic inequality?
Factorise the quadratic, then analyze the sign of each factor over its domain.
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 five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
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 \( 11^n - 6 \) is divisible by 5 for all natural numbers \( n \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{18}$$
\(3\sqrt{2}\)
Simplify:
$$\dfrac{6}{\sqrt{11}}$$\(\frac{6\sqrt{11}}{11}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
Simplify:
$$\dfrac{6}{5 + \sqrt{2}}$$\(\frac{30 - 6\sqrt{2}}{23}\)
Calculate the standard deviation of the following numbers:
27, 29, 30, 31, 33
2
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