Find the first three terms in the expansion of:
\((4a - 5b)^5\)
\(=1024a^5 - 6400a^4b \\+16000a^3b^2 ...\)
If £240 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 9 years. £376.04
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,3),(4,9),(-5,6)\)
(-2,12)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2-2x-3\)
\((x+1)(x-3)\)
Factorise:
\(3x^2-8x-3\)
\((3x+1)(x-3)\)
Draw a rough sketch of the graph of:
\(y=2x-1\)
Gradient 2
y intercept -1
What is the value of:
\(1^{1}\)
\(= 1\)
Find angle ABC if AB = 5m and BC = 6.5m. 39.7o
Find BC if angle BCA = 36o and AC = 5.1m. 6.30m
Describe the red region.
\(y = 5x^3 - 7x^2 + 7x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 14x + 7\)
\(y = \dfrac{5}{x^4} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{20}{x^5} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=\sqrt{8x^2-8x}\)
Find \( \dfrac{dy}{dx}\)
\((8x^1-4)(8x^2-8x)^{-\frac{1}{2}}\)
\(y=e^{7x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(7e^{7x}cosx-e^{7x}sinx\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
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:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =24x^2 - 14x + 4\)
Find \( \int y \quad dx\)
\(8x^3 - 7x^2 + 4x+c\)
A game is played 17 times and the probability of winning is 0.8. Calculate the probability of winning exactly 9 times. 0.00835
Make up a maths question using this:
\(S_n = \dfrac{u_1(r^n-1)}{r-1}\)
The sum of a geometric sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{7} = 54\)
\(u_{15} = 134\)
Find the sum of the first 47 terms.10528
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
AB = 7.4cm.
BC = 8.4cm.
CA = 5.7cm.
Find angle CÂB.
78.6°
Evaluate:
$$\sum_{n=3}^{5} 2^n$$
56
\(f(x)=5x^2+9x-3\)
What is the value of the discriminent and what does it indicate?
141, Two distinct roots
\(f(x)=x^2+3x-9\)
By completing the square find the coordinates of the vertex.
(-1.5, -11.25)
Solve for x:
\(\log_2(x) = 4\)
16
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:
(-3, -2) and (4, -9)
\(y=-x-5\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x+20}\)
\(x²-20\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
Write in standard form:
\((a \times 10^p) \div (b\times 10^q)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{p-q}\)
Draw a rough sketch of
\(y=x(5-x)\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\tan{30°} \times \tan{\frac{\pi}{3}}$$\(1\)
Without a calculator find the exact value of
$$\cos{7\pi}$$\(-1\)
Solve:
\( 5a+2b+c=42 \\ 3a+4b+2c= 42 \\ a+5b+c=30\)
a = 6, b = 4, c = 4
Find the area of a sector with radius 6.9cm and angle \( \frac{\pi}{4}\)
🍕
18.7cm2
In how many ways can 8 different books be arranged on a shelf if 2 of them must be together?
10080
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
The sum of the first 3 terms of a geometric sequence is 26 and the sum of the first 4 terms is 80. What is the first term?
2
Find the first 4 terms in the expansion of:
\((1+2x)^{\frac12}\)
\(1+x-\frac{x^2}{2}+\frac{x^3}{2}\)
Evaluate:
\(\int^{140}_{70} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
The probability that it is cloudy on a particular day is 0.4. The probability that it is cloudy with a high level of pollution on a particular day is 0.2. Find the probability that there will be a high level of pollution on a day when it is cloudy.
\(0.500\)
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
$$ (1+i)^{4} $$
\(-4\)
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 \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)
\(\approx 4.10\) cubic units
How do you determine the convergence of a series?
Clue: common ratio test
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sec(x)\)
\(1 + \frac{x^2}{2} + \frac{5x^4}{24} + \frac{61x^6}{720}\)
Expand and simplify:
$$ (\sqrt{3}+i)^8 $$
\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)
A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.
1/26 or 3.85%
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
Write down a summary of your last Maths lesson focussing on what you learnt.
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