Find the first three terms in the expansion of:
\((3a - 4b)^4\)
\(=81a^4 - 432a^3b \\+864a^2b^2 ...\)
If £120 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 8 years. £152.50
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,3),(5,9),(-5,7)\)
(-1,13)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Factorise:
\(4x^2+7x-2\)
\((x+2)(4x-1)\)
Draw a rough sketch of the graph of:
\(y=-2x\)
Gradient -2
y intercept 0
What is the value of:
\(1^{-1}\)
\(= 1\)
Find angle ABC if AB = 5.7m and BC = 6.7m. 31.7o
Find BC if angle BCA = 36o and AC = 5.5m. 6.80m
Describe the red region.
\(y = 5x^3 - 8x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 16x + 9\)
\(y = \dfrac{6}{x^7} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{42}{x^8} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=e^{\cos x}\)
Find \( \dfrac{dy}{dx}\)
\(-sinxe^{cosx}\)
\(y=e^{3x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(3e^{3x}cosx-e^{3x}sinx\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = 1 - 2x\)
Find the equation of the normal to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 5\frac{1}{2} - \frac{x}{2}\)
\(y =12x^2 - 6x + 8\)
Find \( \int y \quad dx\)
\(4x^3 - 3x^2 + 8x+c\)
A game is played 16 times and the probability of winning is 0.8. Calculate the probability of winning exactly 5 times. 0.0000293
Make up a maths question using this:
\( A = 4\pi r^2 \)
Surface area of a sphere
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = -81\)
\(u_{13} = -108\)
Find the sum of the first 36 terms.-5670
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,
BĈA = 80.9°.
BC = 5.6cm.
AB̂C = 65.17°.
Find CA to 1 dp.
9.1cm
Evaluate:
$$\sum_{n=4}^{8} n^2 - 3n$$
100
\(f(x)=7x^2+5x+1\)
What is the value of the discriminant and what does it indicate?
-3, No real roots
\(f(x)=x^2-5x+5\)
By completing the square find the coordinates of the vertex.
(2.5, -1.25)
Write the following in terms of logs to base 10:
\(\log_a(z)\)
\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)
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:
(-8, -4) and (1, 5)
\(y=x+4\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-5\)
\((x+5)²\)
\(g(x)=5x-4 \\[1cm] \text{Find }g \circ g(x) \\\)
\(25x-24\)
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
\(y=2^x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \cos{60°}$$\(\dfrac{\sqrt{3}}{4}\)
Without a calculator find the exact value of
$$\cos{7\pi}$$\(-1\)
Solve:
\( g-7h-7i=-68 \\ 2g-2h+i= 5\\ 5g+3h+i = 26\)
g = 2, h = 3, i = 7
Find the area of a sector with radius 3.6cm and angle \( \frac{2\pi}{3}\)
🍕
13.6cm2
How many ways can fourteen people be divided into two equal groups?
1716
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\((1-4x)^{-3}\)
\(1+12x+96x^2+640x^3\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
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:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\ln{x}\) is rotated about the y-axis for \(0 \le y \le 1\)
\(\approx 10.0\) cubic units
How do you determine the domain of a function?
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \frac{1}{x^2 + 1}\)
\(1 - x^2 + x^4 - x^6\)
Given |z| = 8, find:
$$ |(3+4i)z| $$
\(40\)
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 \( 2^n > n^2 \) for all integers \( n \) greater
than four
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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