Find the first three terms in the expansion of:
\((2a - 3b)^7\)
\(=128a^7 - 1344a^6b \\+6048a^5b^2 ...\)
If £140 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 7 years. £185.15
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,4),(8,9),(-2,9)\)
(3,14)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2+3x-4\)
\((x+4)(x-1)\)
Factorise:
\(5x^2+13x-6\)
\((x+3)(5x-2)\)
Draw a rough sketch of the graph of:
\(2y=x+4\)
Gradient 0.5
y intercept 2
What is the value of:
\(3^{1}\)
\(= 3\)
Find angle ABC if AC = 4.9m and BC = 6.2m. 52.2o
Find BC if angle BCA = 30o and AB = 3.1m. 6.20m
Describe the red region.
\(y = 5x^3 - 6x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 12x + 2\)
\(y = \dfrac{8}{x^{5}} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{40}{x^{6}} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=4\ln (5x^2+6)\)
Find \( \dfrac{dy}{dx}\)
\(40x(5x^2+6)^{-1}\)
\(y=(4x+6)(7x-4)\)
Find \( \dfrac{dy}{dx}\)
\(56x+26\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = 17 - 13x\)
Find the equation of the normal to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 5\frac{1}{2} - \frac{x}{2}\)
\(y =21x^2 - 14x + 6\)
Find \( \int y \quad dx\)
\(7x^3 - 7x^2 + 6x+c\)
A game is played 14 times and the probability of winning is 0.7. Calculate the probability of winning exactly 6 times. 0.0232
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:
\(u_{7} = -25\)
\(u_{14} = -53\)
Find the sum of the first 19 terms.-703
Find the equations of the asymptotes of:
\(y=\dfrac{2x-7}{6-2x}-5\)
\(x=3,y=-6\)
In the triangle ABC,
AB = 8.4cm.
BC = 5.1cm.
CÂB = 28.2°.
Find angle BĈA.
51.2° or 128.8°
Evaluate:
$$\sum_{n=2}^{4} 2^n$$
28
\(f(x)=5x^2-8x+4\)
What is the value of the discriminant and what does it indicate?
-16, No real roots
\(f(x)=x^2-6x+5\)
By completing the square find the coordinates of the vertex.
(3, -4)
Write the following in terms of logs to base 10:
\(\log_a(z)\)
\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)
Find the integral:
\(\int \sin(x)\cos^2(x) \;dx\)
\(-\frac{1}{3} \cos^3(x)+c\)
Find the equation of the straight line that passes through:
(-4, -13) and (7, 9)
\(y=2x-5\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-16}{12}\)
\((12x+16)²\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^{p+q+1}\)
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
$$\tan{45°} - \sin{\frac{\pi}{6}} - \cos{\frac{\pi}{3}}$$\(0\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( 5a+2b+c=29 \\ 3a+4b+2c= 37 \\ a+5b+c=29\)
a = 3, b = 4, c = 6
Find the perimeter of a sector with radius 7.5cm and angle \( \frac{\pi}{3}\)
🍕
22.9cm
How many ways can twenty people be divided into two equal groups?
92378
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
-109230
Find the first 4 terms in the expansion of:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{4}_{2} (x-8)^2 \; dx\)
\(50.6666666666666\)
28 Scouts went hiking. 12 got lost, 14 got blisters, and 5 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{9}{16}\)
Find the vector product:
\( \begin{pmatrix} 8 \\ 7 \\ 0 \end{pmatrix} \; \times \; \begin{pmatrix} 3 \\ -4 \\ 9 \end{pmatrix} \)
\( \begin{pmatrix} 63 \\ -72 \\ -53 \end{pmatrix} \)
Simplify
$$ (2-5i)(6-4i) $$
\(-8-38i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\cosec{x}\tan{x}$$\(\sec{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x(4-x)\) is rotated about the x-axis for \(0 \le x \le 4\)
\(\frac{512\pi}{15}\) cubic units
Describe the behavior of a function at its inflection point.
The concavity of the function changes
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sin(x)\)
\(x - \frac{x^3}{6} + \frac{x^5}{120} - \frac{x^7}{5040}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
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 \( n \) even numbers is \( n(n + 1) \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{32}$$
\(4\sqrt{2}\)
Simplify:
$$\dfrac{5}{2\sqrt{3}}$$\(\frac{5\sqrt{3}}{6}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
Simplify:
$$\dfrac{6}{5 + \sqrt{2}}$$\(\frac{30 - 6\sqrt{2}}{23}\)
Calculate the standard deviation of the following numbers:
9, 13, 15, 17, 21
4
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