Find the first three terms in the expansion of:
\((4a - 5b)^9\)
\(=262144a^9 - 2949120a^8b \\+14745600a^7b^2 ...\)
If £240 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 7 years. £340.33
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,4),(9,8),(1,8)\)
(5,12)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2-x-6\)
\((x+2)(x-3)\)
Factorise:
\(x^2-x-6\)
\((x+2)(x-3)\)
Draw a rough sketch of the graph of:
\(2y=x+2\)
Gradient 0.5
y intercept 1
What is the value of:
\(125^{\frac{1}{3}}\)
\(= 5\)
Find angle ABC if AB = 4.7m and BC = 6m. 38.4o
Find AB if angle ABC = 46o and BC = 3.9m. 2.71m
Describe the red region.
\(y = 6x^3 - 9x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 18x + 2\)
\(y = \dfrac{7}{x^{6}} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{42}{x^{7}} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=\sin (7x^2+8)\)
Find \( \dfrac{dy}{dx}\)
\(14xcos(7x^2+8)\)
\(y=x^6 \sin (x)\)
Find \( \dfrac{dy}{dx}\)
\(6x^5sinx+x^6cosx\)
\(y=\frac{ \ln x}{x^2}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(1-2lnx)}{x^3}\)
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:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(x = -3\)
\(y =12x^2 - 4x + 4\)
Find \( \int y \quad dx\)
\(4x^3 - 2x^2 + 4x+c\)
A game is played 11 times and the probability of winning is 0.7. Calculate the probability of winning exactly 10 times. 0.0932
Make up a maths question using this:
\( P(A|B) = \dfrac{P(A \cap B)}{P(B)} \)
Conditional probability formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = 30\)
\(u_{12} = 38\)
Find the sum of the first 32 terms.1792
Find the equations of the asymptotes of:
\(y=12-\dfrac{4x+3}{7-2x}\)
\(x=\frac{7}{2},y=14\)
In the triangle ABC,
AB = 6.9cm.
BC = 5.4cm.
CÂB = 33.4°.
Find angle BĈA.
44.7° or 135.3°
Evaluate:
$$\sum_{n=3}^{8} n^2 - 9n$$
-98
\(f(x)=8x^2+9x+8\)
What is the value of the discriminant and what does it indicate?
-175, No real roots
\(f(x)=x^2-4x+1\)
By completing the square find the coordinates of the vertex.
(2, -3)
Evaluate \(\log_5(625) \)
4
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:
(-9, -18) and (7, 14)
\(y=2x+0\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+9}{3}\)
\(3x-9\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
Write in standard form:
\(a \times 10^{-1} \times b\times 10^{-1}\)
where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)
\(\frac{ab}{100}\times10^0\)
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
$$\cos{0°} + \sin{\frac{\pi}{6}} + \cos{60°}$$\(2\)
Without a calculator find the exact value of
$$\sin{5\pi}$$\(0\)
Solve:
\( j+k+l= 14 \\ 2j-3k+9l= 39\\ -j+k-3l=-16\)
j = 9, k = 2, l = 3
Find the area of a sector with radius 5.8cm and angle \( \frac{2\pi}{3}\)
🍕
35.2cm2
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:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
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:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
In a bookstore with equally sized fiction and non-fiction sections, if a hardcover book is selected (70% of fiction, 20% of non-fiction are hardcovers), what's the probability it's non-fiction?
\(0.222\)
Find a vector perpendicular to both vectors below and with a length of 143 units (correct to 3sf).
\( \begin{pmatrix} 7 \\ 4 \\ 0 \end{pmatrix} \; \text{ and } \; \begin{pmatrix} 9 \\ -4 \\ 4 \end{pmatrix} \)
\( \left(\begin{smallmatrix} 32 \\ -56 \\ -128 \end{smallmatrix}\right) \)
Simplify
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$5\sin{x}+3\cos{x}\tan{x}$$\(8\sin{x}\)
Find the volume of revolution when \(y=e^x\) is rotated about the x-axis for \(0 \le x \le 3\)
\(\frac{\pi}{2}(e^6-1)\) cubic units
How do you solve a quadratic inequality?
Factorise the quadratic, then analyze the sign of each factor over its domain.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
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 the product of \( n \) consecutive integers is divisible by \( n! \) (n factorial)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{8}$$
\(2\sqrt{2}\)
Simplify:
$$\dfrac{5}{\sqrt{8}}$$\(\frac{5\sqrt{8}}{8} = \frac{5\sqrt{2}}{4}\)
Simplify
\(8\sqrt{3}(1 - \sqrt{3})\)
\(8\sqrt{3} - 24\)
Simplify:
$$\dfrac{5}{3 - \sqrt{2}}$$\(\frac{15 + 5\sqrt{2}}{7}\)
Calculate the standard deviation of the following numbers:
15, 19, 19, 21, 21, 25
3
Find the inverse function:
\(f(x)=2^x+1\)
\(f^{-1}(x)=\log_2(x-1), x>1\)
Make \(r\) the subject:
\({\small V=\frac{\pi h}{3}(R^2+Rr+r^2),}\\{\small r>0}\)
\(r=\dfrac{\sqrt{\dfrac{12V}{\pi h}-3R^2}-R}{2}\)
Find the scalar and vector products of:
\({\scriptsize\mathbf a=\left(\begin{smallmatrix}8\\3\\-1\end{smallmatrix}\right)\text{ and }\mathbf b=\left(\begin{smallmatrix}2\\9\\0\end{smallmatrix}\right)}\)
\( {\scriptsize \mathbf a\cdot\mathbf b=43,\quad \mathbf a\times\mathbf b=\left(\begin{smallmatrix}9\\-2\\66\end{smallmatrix}\right) } \)
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Thursday, December 12, 2024
"Would it be possible to refreshing revision to show the same option more than once? for example, selecting 'differentiation 4' three times and so having three different questions in three different tiles on display?
Obviously I can the refresh option three times, but for the kids that can complete the first step faster than others having a second one in the same category to move onto would be great.
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