Find the first three terms in the expansion of:
\((2a - 3b)^8\)
\(=256a^8 - 3072a^7b \\+16128a^6b^2 ...\)
If £120 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 8 years. £165.17
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,2),(11,6),(1,8)\)
(7,12)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2-4\)
\((x+2)(x-2)\)
Factorise:
\(5x^2+7x-6\)
\((x+2)(5x-3)\)
Draw a rough sketch of the graph of:
\(y=-2x-2\)
Gradient -2
y intercept -2
What is the value of:
\(27^{\frac{1}{3}}\)
\(= 3\)
Find angle BCA if AB = 4.3m and BC = 5.4m. 52.8o
Find AB if angle ABC = 26o and BC = 5.8m. 5.21m
Describe the red region.
\(y = 3x^3 - 7x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 14x + 4\)
\(y = \dfrac{5}{x^2} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{10}{x^3} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=\frac{1}{(8x+9)^7}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{56}{(8x+9)^8}\)
\(y=e^{9x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(9e^{9x}cosx-e^{9x}sinx\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =18x^2 - 8x + 4\)
Find \( \int y \quad dx\)
\(6x^3 - 4x^2 + 4x+c\)
A game is played 17 times and the probability of winning is 0.5. Calculate the probability of winning exactly 7 times. 0.148
Make up a maths question using this:
\( \triangle = b^2-4ac\)
Quadratic equation discriminant
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = 23\)
\(u_{19} = 50\)
Find the sum of the first 29 terms.1102
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
AB = 8.3cm.
BC = 8.5cm.
CA = 8.6cm.
Find angle CÂB.
60.4°
Evaluate:
$$\sum_{n=2}^{9} n^2 - 7n$$
-24
\(f(x)=7x^2-3x-5\)
What is the value of the discriminant and what does it indicate?
149, Two distinct roots
\(f(x)=x^2+7x-4\)
By completing the square find the coordinates of the vertex.
(-3.5, -16.25)
Solve for x:
\( \log(x) + \log(29-x) = 2\)
\(x = 4 \text{ or } x = 25 \)
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:
(-2, 4) and (9, -29)
\(y=-3x-2\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-2\)
\((x+2)²\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
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
\(y=\dfrac{5}{x}\)
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
$$\tan{\dfrac{19\pi}{6}}$$\(\dfrac{1}{\sqrt{3}}\)
Solve:
\( g-7h-7i=-92 \\ 2g-2h+i= 5\\ 5g+3h+i = 58\)
g = 6, h = 7, i = 7
Find the area of a sector with radius 9.1cm and angle \( \frac{5\pi}{6}\)
🍕
108cm2
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
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
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:
\(\int^{7}_{0} e^x dx\)
\(e^{7}- 1 \approx 1100\)
Tin A contains 3 red balls and 6 green balls. Tin B contains 9 red balls and 11 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B.
\(\frac{27}{37}\)
Find the point of intersection of these planes:
\(\Pi_1: \quad 2x + y - 3z = -5\)
\(\Pi_2: \quad x - 3y + 2z = 1\)
\(\Pi_3: \quad 3x - 2y + z = 2\)
\( (1,2,3) \)
Simplify
$$ (4-3i)(2-4i) $$
\(-4-22i\)
Evaluate:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
How do you determine if a geometric series converges?
Clue: common ratio test
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 \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
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:
$$\sqrt{32}$$
\(4\sqrt{2}\)
Simplify:
$$\dfrac{3}{4\sqrt{2}}$$\(\frac{3\sqrt{2}}{8}\)
Simplify
\((1 + \sqrt{2})(2 + \sqrt{2})\)
\(4 + 3\sqrt{2}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
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