Find the first three terms in the expansion of:
\((2a - 3b)^8\)
\(=256a^8 - 3072a^7b \\+16128a^6b^2 ...\)
If £100 is invested with an interest rate of 1% compounded monthly, find the value of the investment after 5 years. £105.12
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,3),(7,9),(-3,7)\)
(1,13)
\( X \sim N(50, 5^2)\)
Find
\( P(40\lt X \lt60) \)
\(0.955\)
Factorise:
\(x^2-x-2\)
\((x+1)(x-2)\)
Factorise:
\(10x^2-3x-4\)
\((2x+1)(5x-4)\)
Draw a rough sketch of the graph of:
\(y=x-1\)
Gradient 1
y intercept -1
What is the value of:
\(1^{-1}\)
\(= 1\)
Find angle ABC if AB = 5.6m and BC = 6.7m. 33.3o
Find AC if angle ABC = 65o and BC = 3.1m. 2.81m
Describe the red region.
\(y = 4x^3 - 4x^2 + 8x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 8x + 8\)
\(y = \dfrac{4}{x^{3}} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{12}{x^{4}} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=e^{3x+4}\)
Find \( \dfrac{dy}{dx}\)
\(3e^{3x+4}\)
\(y=x^2 \sin x\)
Find \( \dfrac{dy}{dx}\)
\(2x^1sinx+x^2cosx\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
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:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 5\frac{1}{2} - \frac{x}{2}\)
\(y =27x^2 - 16x + 9\)
Find \( \int y \quad dx\)
\(9x^3 - 8x^2 + 9x+c\)
A game is played 13 times and the probability of winning is 0.6. Calculate the probability of winning exactly 2 times. 0.00118
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:
\(u_{8} = 39\)
\(u_{16} = 95\)
Find the sum of the first 48 terms.7416
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
BC = 7.3cm.
CA = 6.1cm.
BĈA = 87.4°
Find AB to 1 dp.
9.3cm
Evaluate:
$$\sum_{n=0}^{7} 95 - n^2$$
620
\(f(x)=9x^2-7x+9\)
What is the value of the discriminant and what does it indicate?
-275, No real roots
\(f(x)=x^2-7x-6\)
By completing the square find the coordinates of the vertex.
(3.5, -18.25)
Simplify \(\log_{10}10^5\)
5
Find the integral:
\(\int \sin(x)\cos^2(x) \;dx\)
\(-\frac{1}{3} \cos^3(x)+c\)
Find the equation of the straight line that passes through:
(-4, -2) and (8, 22)
\(y=2x+6\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-17}{17}\)
\((17x+17)²\)
\(\text{Find }f(x) \text{ if} \\ f(a^3)=2a^6 \\\)
\(f(x)=2x^2\)
Write in standard form:
\(a \times 10^3 \times b\times 10^5\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^8\)
Draw a rough sketch of
\(y=x^2+7x\)
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
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( j+k+l= 14 \\ 2j-3k+9l= 48\\ -j+k-3l=-18\)
j = 6, k = 3, l = 5
Find the area of a sector with radius 6.7cm and angle \( \frac{\pi}{4}\)
🍕
17.6cm2
A safe has a nine-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
201600
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
Find the first 4 terms in the expansion of:
\((1-4x)^{-3}\)
\(1+12x+96x^2+640x^3\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
28 Scouts went hiking. 16 got lost, 11 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.
\(\dfrac{5}{12}\)
Find the parametric equation of the line:
\( \dfrac{x-5}{8} = \dfrac{3-y}{7} = \dfrac{z}{4} \)
\( x=5+8\lambda \quad y = 3 -7\lambda \quad z=4 \lambda \)
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:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^2\) is rotated about the x-axis for \(-2 \le x \le 2\)
\(\frac{64\pi}{5}\) cubic units
What is the difference between a permutation and a combination?
Permutations consider order; combinations do not.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
A team of 11 is randomly chosen from a squad of 18 including the club captain and vice captain. Determine the probability that both the captain and vice-captain are chosen.
55/153 or 35.9%
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:
$$\sqrt{48}$$
\(4\sqrt{3}\)
Simplify:
$$\dfrac{5}{2\sqrt{3}}$$\(\frac{5\sqrt{3}}{6}\)
Simplify
\(4\sqrt{7} - \sqrt{63}\)
\(\sqrt{7}\)
Simplify:
$$\dfrac{3}{4 + \sqrt{2}}$$\(\frac{12 - 3\sqrt{2}}{14} = \frac{6 - \sqrt{2}}{7}\)
Calculate the standard deviation of the following numbers:
27, 29, 30, 31, 33
2
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