Find the first three terms in the expansion of:
\((2a - 3b)^6\)
\(=64a^6 - 576a^5b \\+2160a^4b^2 ...\)
If £100 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 7 years. £123.34
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,2),(9,6),(1,6)\)
(5,10)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2+x-2\)
\((x+2)(x-1)\)
Factorise:
\(x^2-3x-4\)
\((x+1)(x-4)\)
Draw a rough sketch of the graph of:
\(2y=x-4\)
Gradient 0.5
y intercept -2
What is the value of:
\(4^{-2}\)
\(= \frac{1}{16}\)
Find angle BCA if AB = 3.3m and AC = 5.1m. 32.9o
Find BC if angle BCA = 24o and AC = 3.9m. 4.27m
Describe the red region.
\(y = 6x^3 - 4x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 8x + 3\)
\(y = \dfrac{9}{x^4} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{36}{x^5} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=\sqrt{7x^6-6x}\)
Find \( \dfrac{dy}{dx}\)
\((21x^5-3)(7x^6-6x)^{-\frac{1}{2}}\)
\(y=x^3 \ln x\)
Find \( \dfrac{dy}{dx}\)
\(3x^2lnx+x^2\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 6x + 3\)
Find the equation of the normal to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)
\(y =15x^2 - 8x + 5\)
Find \( \int y \quad dx\)
\(5x^3 - 4x^2 + 5x+c\)
A game is played 10 times and the probability of winning is 0.7. Calculate the probability of winning exactly 3 times. 0.00900
Make up a maths question using this:
\(^nC_r=\dfrac{n!}{r!(n-r)!}\)
Combinations
(from n choose r)
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 9\)
\(u_{14} = 19\)
Find the sum of the first 17 terms.153
Find the equations of the asymptotes of:
\(y=\dfrac{3x-5}{6x-12}\)
\(x=2,y=\frac{1}{2}\)
In the triangle ABC,
BĈA = 38.6°.
BC = 8.2cm.
AB̂C = 41.34°.
Find CA to 1 dp.
5.5cm
Evaluate:
$$\sum_{n=2}^{8} 97 - n^2$$
476
\(f(x)=-8x^2+8x-6\)
What is the value of the discriminant and what does it indicate?
-128, No real roots
\(f(x)=x^2-3x+1\)
By completing the square find the coordinates of the vertex.
(1.5, -1.25)
Simplify \(\log_{10}10^5\)
5
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-3, 12) and (9, 0)
\(y=-x+9\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-6}{3}}\)
\(3x²+6\)
\(\text{Find }f(x) \text{ if} \\ f(a^3)=2a^6 \\\)
\(f(x)=2x^2\)
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
\(y=x^3-4x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{4}} + \sin{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\(2x+y-3z= -1 \\ 3x+y+z= 20 \\ x-y+2z = 12\)
x = 5, y = 1, z = 4
Find the perimeter of a sector with radius 2.1cm and angle \( \frac{5\pi}{6}\)
🍕
9.70cm
In how many ways can 11 different books be arranged on a shelf if 4 of them must be together?
967680
Find the equations of the asymptotes of:
$$y=\dfrac{8x^2-19x-15}{1-2x}$$x=1/2,y=15/2-4x
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
-109230
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{2}_{0} x^2-2x+7 \; dx\)
\(12.7\)
Each afternoon the probability my cat sleeps is 0.5 and the probability that my dog sleeps is 0.8. The probability that the dog sleeps given that the cat is sleeping is 0.9. Find the probability that both sleep in the afternoon.
\(0.45\)
Find the angle between the plane and the line:
\(\Pi: \quad 4x+4y-2z=7\)
\(L: \quad x+1= \dfrac{4-y}{2} = 3-z \)
\( \approx 7.82^o \)
Simplify
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
Evaluate:
\(\int x^2 \ln{x}\; dx\)
\(\frac{x^3}{9}(3\ln x-1)+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt[3]{x^2}\) is rotated about the y-axis for \(2 \le y \le 3\)
\(\frac{65\pi}{4}\) cubic units
Describe the behavior of a function at its asymptote.
Clue: approaches but never reaches
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \ln(1 + x)\)
\(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4}\)
Solve for \(z\)
$$ z^4 = - 16 $$
\(\sqrt{2}+i\sqrt{2},-\sqrt{2}+i\sqrt{2} \\ \sqrt{2}-i\sqrt{2},-\sqrt{2}-i\sqrt{2}\)
6 girls sit at random on 6 seats in a row. Determine the probability that the two friends Karen and Julie sit at the ends of the row.
1/15 or 6.67%
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
Simplify
\(7\sqrt{13} - 9\sqrt{13}\)
\(-2\sqrt{13}\)
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