Refreshing Revision

Binomial Theorem (1)

Find the first three terms in the expansion of:

$(4a - 5b)^9$

$=262144a^9 - 2949120a^8b \\+14745600a^7b^2 ...$

Compound Interest

If £180 is invested with an interest rate of 1% compounded monthly, find the value of the investment after 6 years. £191.13

Coordinates (Square)

Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4^th?

$(3,2),(7,8),(-3,6)$

(1,12)

Normal Distribution

$ X \sim N(50, 5^2)$

Find

$ P(40\lt X \lt60) $

$0.955$

Factorise (Quadratic 1)

Factorise:

$x^2-2x-8$

$(x+2)(x-4)$

Factorise (Quadratic 2)

Factorise:

$x^2-16$

$(x+4)(x-4)$

Graph (Linear)

Draw a rough sketch of the graph of:

$y=x$

Gradient 1
y intercept 0

Indices

What is the value of:

$4^{0}$

$= 1$

Trigonometry (Angle)

Find angle BCA if AC = 4.2m and BC = 6.1m. 46.5^o

Trigonometry (Side)

Find AC if angle ABC = 34^o and BC = 4.4m. 2.46m

Venn Diagrams

Describe the red region.

Differentiation (1)

$y = 4x^3 - 6x^2 + 2x$

Find $ \dfrac{dy}{dx}$

$12x^2 - 12x + 2$

Differentiation (2)

$y = \dfrac{4}{x^4} - 8\sqrt[9]{x}$

Find $ \frac{dy}{dx}$

$-\frac{16}{x^5} - \frac{8}{9}x^{-\frac{8}{9}}$

Differentiation (3)

$y=\sqrt{7x^4+8}$

Find $ \dfrac{dy}{dx}$

$14x^3(7x^4+8)^{-\frac{1}{2}}$

Differentiation (4)

$y=x(5x^2+6)^7$

Find $ \dfrac{dy}{dx}$

$(5x^2+6)^7+70x^2(5x^2+6)^6$

Differentiation (5)

$y=\frac{x+3}{x-4}$

Find $ \dfrac{dy}{dx}$

$-\frac{7}{(x-4)^2}$

Differentiation (6)

Find the equation of the tangent to the curve:
$y = -4x^2 + 8x - 5$
where $x = -1$
$y = 16x - 1$

Differentiation (7)

Find the equation of the normal to the curve:
$y = x^2 + 6x + 9$
where $x = -3$
$x = -3$

Integration (1)

$y =12x^2 - 14x + 7$

Find $ \int y \quad dx$

$4x^3 - 7x^2 + 7x+c$

Binomial Distribution

A game is played 15 times and the probability of winning is 0.5. Calculate the probability of winning exactly 8 times. 0.196

Formulas

Make up a maths question using this:

$u_n=u_1+(n-1)d$

The n^th term of an arithmetic sequence

Greek Letters

What letter is this?

Sequences (Arithmetic)

Two terms of an arithmetic sequence:
$u_{8} = -71$
$u_{14} = -131$
Find the sum of the first 32 terms.-4992

Asymptotes (HV)

Find the equations of the asymptotes of:

$y=12-\dfrac{4x+3}{7-2x}$

$x=\frac{7}{2},y=14$

Trig Advanced

In the triangle ABC,
BĈA = 37.5°.
BC = 7.2cm.
AB̂C = 114.03°.
Find CA to 1 dp.

13.8cm

Sigma

Evaluate:

$$\sum_{n=3}^{4} 2^n$$

24

Discriminant

$f(x)=-4x^2-5x-8$

What is the value of the discriminent and what does it indicate?
-103, No real roots

Completing The Square

$f(x)=x^2+5x-7$

By completing the square find the coordinates of the vertex.
(-2.5, -13.25)

Logarithms

Evaluate $\log_2(32) $

5

Integration (3)

Find the integral:

$\int (x+3)\sqrt{x^2+6x+8} \;dx$

$\frac{1}{3}(x^2+6x+8)^{\frac32}+c$

Graph (2 points)

Find the equation of the straight line that passes through:

(-6, -11) and (5, 11)

$y=2x+1$

Functions (Inverse)

Find the inverse of the function $f$:

$f(x)=\frac{\sqrt{x}-14}{19}$

$(19x+14)²$

Functions (Composite)

$f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\$

$x^4-2x^2$

Standard Form

Write in standard form:
$(a \times 10^3) \div (b\times 10^5)$
where $a \div b $ is a two digit number $(10 \le \frac{a}{b} \lt 100)$

$\frac{a}{10b}\times10^{-1}$

Graph (Mixed)

Draw a rough sketch of

$y=\dfrac{5}{x}$

Graph (Fill)

Sketch a height-time graph as this jar is filled.

Trig (Special Angles)

Without a calculator find the exact value of

$$\tan{\frac{\pi}{6}} \times \cos{45°}$$

$\dfrac{1}{\sqrt{6}}$

Trig (Large Angles)

Without a calculator find the exact value of

$$\tan{\dfrac{19\pi}{6}}$$

$\dfrac{1}{\sqrt{3}}$

Simultaneous Eqns (3)*

Solve:

$ 5a+2b+c=38 \\ 3a+4b+2c= 34 \\ a+5b+c=20$

a = 6, b = 2, c = 4

Radian Measures

Find the area of a sector with radius 9.5cm and angle $ \frac{\pi}{4}$

🍕

35.4cm²

Combinatorics*

Ansh is with six people in a queue. How many ways can they line up without Ansh being at the back?

4320

Asymptotes (Ob)*

Find the equations of the asymptotes of:

$$y=\dfrac{2x^2+3x-9}{x+2}$$

x=-2,y=2x-1

Sequences (Geometric)

The sum of the first 3 terms of a geometric sequence is 65 and the sum of the first 4 terms is 200. What is the first term?

5

Binomial Theorem (2)*

Find the first 4 terms in the expansion of:

$\dfrac{1}{(3+x)^2}$

$\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}$

Integration (2)

Evaluate:

$\int^{7}_{0} e^x dx$

$e^{7}- 1 \approx 1100$

Probability (Conditional)

Every family in Happyland has either has a car or a motor scooter or both. 75% of the families have a car. 85% of the families have a scooter. A family is selected at random and it is found that they have a car. Find the probability they also have a scooter.

$\dfrac{4}{5}$

Vectors*

Find the cartesian equation of this plane:

$ \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} $

2x-6y+5z=-1

Graph (Advanced)*

Sketch the graph of:

$$y=\sin(x)\cos(x)$$

Graph Plotter

Complex Numbers 1*

Simplify
$$ \dfrac{1-4i}{1+5i}$$

$-\frac{19}{26}-\frac{9}{26}i$

Integration (4)*

Evaluate:

$\int \ln{x}\; dx$

$x\ln|x|-x+c$

Trig (Identities)*

Simplify:

$$5\sin{x}+3\cos{x}\tan{x}$$

$8\sin{x}$

$$ \DeclareMathOperator{cosec}{cosec} $$

Integration (Volume)*

Find the volume of revolution when $y=x^2$ is rotated about the x-axis for $-2 \le x \le 2$

$\frac{64\pi}{5}$ cubic units

Miscellaneous

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.

Maclaurin Series*

Show how the first four terms of the Maclaurin series are obtained for
$f(x) = x^3$

$x^3 \text{ only 1 term}$

Complex Numbers 2*

Given |z| = 8, find:
$$ |(3+4i)z| $$

$40$

Probability (Counting)*

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%

Proof by Induction*

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

Last Lesson

Write down a summary of your last Maths lesson focussing on what you learnt.

?

ADVANCED

Binomial Theorem (1)

Compound Interest

Coordinates (Square)

Normal Distribution

Factorise (Quadratic 1)

Factorise (Quadratic 2)

Graph (Linear)

Indices

Trigonometry (Angle)

Trigonometry (Side)

Venn Diagrams

Differentiation (1)

Differentiation (2)

Differentiation (3)

Differentiation (4)

Differentiation (5)

Differentiation (6)

Differentiation (7)

Integration (1)

Binomial Distribution

Formulas

Greek Letters

Sequences (Arithmetic)

Asymptotes (HV)

Trig Advanced

Sigma

Discriminant

Completing The Square

Logarithms

Integration (3)

Graph (2 points)

Functions (Inverse)

Functions (Composite)

Standard Form

Graph (Mixed)

Graph (Fill)

Trig (Special Angles)

Trig (Large Angles)

Simultaneous Eqns (3)*

Radian Measures

Combinatorics*

Asymptotes (Ob)*

Sequences (Geometric)

Binomial Theorem (2)*

Integration (2)

Probability (Conditional)

Vectors*

Graph (Advanced)*

Complex Numbers 1*

Integration (4)*

Trig (Identities)*

Integration (Volume)*

Miscellaneous

Maclaurin Series*

Complex Numbers 2*

Probability (Counting)*

Proof by Induction*

Last Lesson

An Advanced Mathematics Lesson Starter Of The Day

Concept Selection

Answers