Find the first three terms in the expansion of:
\((3a - 4b)^8\)
\(=6561a^8 - 69984a^7b \\+326592a^6b^2 ...\)
If £240 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 6 years. £343.08
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,5),(6,9),(-3,10)\)
(2,14)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2+2x-3\)
\((x+3)(x-1)\)
Factorise:
\(2x^2+7x-4\)
\((x+4)(2x-1)\)
Draw a rough sketch of the graph of:
\(y=x-1\)
Gradient 1
y intercept -1
What is the value of:
\(8^{\frac{1}{3}}\)
\(= 2\)
Find angle BCA if AB = 4m and AC = 5m. 38.7o
Find AB if angle ABC = 50o and BC = 3.5m. 2.25m
Describe the red region.
\(y = 6x^3 - 9x^2 + 7x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 18x + 7\)
\(y = \dfrac{5}{x^8} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{40}{x^9} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=\sqrt{2x^4-8x}\)
Find \( \dfrac{dy}{dx}\)
\((4x^3-4)(2x^4-8x)^{-\frac{1}{2}}\)
\(y=\sin x \cos x\)
Find \( \dfrac{dy}{dx}\)
\(cos^2x-sin^2x\)
\(y=\frac{x+2}{x-2}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{4}{(x-2)^2}\)
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:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(x = -3\)
\(y =15x^2 - 10x + 8\)
Find \( \int y \quad dx\)
\(5x^3 - 5x^2 + 8x+c\)
A game is played 11 times and the probability of winning is 0.5. Calculate the probability of winning exactly 8 times. 0.0806
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:
\(u_{5} = -15\)
\(u_{17} = -75\)
Find the sum of the first 33 terms.-2475
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,
BC = 6.2cm.
CA = 11.9cm.
BĈA = 51.6°
Find AB to 1 dp.
9.4cm
Evaluate:
$$\sum_{n=2}^{6} 3n+6$$
90
\(f(x)=7x^2-6x-3\)
What is the value of the discriminant and what does it indicate?
120, Two distinct roots
\(f(x)=x^2+4x+8\)
By completing the square find the coordinates of the vertex.
(-2, 4)
Solve for x:
\(\log_2(x) = 4\)
16
Find the integral:
\(\int 3xe^{x^2} \;dx\)
\(\frac{3}{2}e^{x^2}+c\)
Find the equation of the straight line that passes through:
(-7, 21) and (6, -18)
\(y=-3x+0\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-6}\)
\(x²+6\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
Write in standard form:
\(a \times 10^{-1} \times b\times 10^{-1}\)
where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)
\(\frac{ab}{100}\times10^0\)
Draw a rough sketch of
\(y+x=2\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{0°} + \sin{\frac{\pi}{6}} + \cos{60°}$$\(2\)
Without a calculator find the exact value of
$$\sin{780°}$$\(\dfrac{\sqrt{3}}{2}\)
Solve:
\( j+k+l= 11 \\ 2j-3k+9l= 16\\ -j+k-3l=-7\)
j = 5, k = 4, l = 2
Find the perimeter of a sector with radius 3.7cm and angle \( \frac{2\pi}{3}\)
🍕
15.1cm
How many ways can twenty four people be divided into two equal groups?
1352078
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
The 4th term of a geometric sequence is 16 and the sum of the first 4 terms is 30. Find the first term.
2
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(3+x)^2}\)
\(\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}\)
Evaluate:
\(\int^{4}_{2} (x-8)^2 \; dx\)
\(50.6666666666666\)
25 Scouts went hiking. 11 got lost, 13 got blisters, and 6 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{1}{2}\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 2 \\ 8 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 9 \\ -4 \\ 7 \end{pmatrix} \; \text{and} \; \begin{pmatrix} 7 \\ -12 \\ 7 \end{pmatrix} \)
49.3 square units
Simplify
$$ (1+i)^{4} $$
\(-4\)
Evaluate:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
Describe the behavior of a function at its inflection point.
The concavity of the function changes
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
\(1, i, -1, -i\)
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 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
\((3 + \sqrt{5})(3 - \sqrt{5})\)
\(4\)
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