top of page
.png)
Solver Ninja
Jumpstart your A* Journey
Flashcards
What is circumference of a circle formula?
Circumference $C=2\pi r$.
In circle formulas, what is $r$?
The radius of the circle.
How can you write circumference using diameter?
Use $C=\pi d$.
What is cuboid surface area formula?
Surface area $S=2(lw+lh+wh)$.
What is total surface area of a cylinder?
Area $2\pi rh+2\pi r^2$.
What is a prism?
Solid with constant cross-section along its length.
How do you find volume of a cylinder?
Use $V=\pi r^2h$.
What is an arc of a circle?
Part of the circumference between two points.
What is a sector of a circle?
Region between two radii and an arc.
What is volume formula for a sphere?
Volume $V=\tfrac{4}{3}\pi r^3$.
What is a pyramid in geometry?
Solid with a polygon base and triangular faces meeting at a vertex.
What is perpendicular height of a pyramid?
Distance from vertex to base measured at right angles.
T/F: Rectangle area is $2(l+b)$.
False, its area is $lb$; $2(l+b)$ is perimeter.
T/F: Circle circumference equals $\pi r^2$.
False, that is the area formula.
What is the gradient of a line?
The rate of change of $y$ with $x$.
What is gradient formula between points?
Use $m=\dfrac{y_2-y_1}{x_2-x_1}$.
What does negative gradient mean?
Line slopes downwards from left to right.
What is gradient of a vertical line?
Its gradient is undefined or infinite.
How can you check gradient sign quickly?
Look to see if line rises or falls.
What is general straight-line form?
It is $y=mx+c$.
In $y=mx+c$, what is $c$?
The $y$-intercept of the line.
How do you find gradient from equation?
Rewrite as $y=mx+c$ and read $m$.
How do you find equation from gradient and point?
Use $y-y_1=m(x-x_1)$ then simplify.
What is equation of horizontal line through $(0,4)$?
It is $y=4$.
When are two lines parallel?
When they have the same gradient.
When are two lines perpendicular?
When gradients multiply to $-1$.
If line has gradient $2$, perpendicular gradient?
It is $-\dfrac{1}{2}$.
How many points are needed to draw a line?
Two points determine a straight line.
What does intersection of two lines represent?
Common solution of their simultaneous equations.
What is distance formula between two points?
Use $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
What does midpoint of segment represent?
Point exactly halfway between the endpoints.
T/F: Vertical lines have gradient zero.
False, their gradient is undefined.
T/F: Product of perpendicular gradients is $1$.
False, their product is $-1$.
T/F: Two points are enough to define a line.
True, exactly one line passes through them.
From which direction are bearings measured?
From North.
What units are bearings measured in?
Degrees $^\circ$.
How is North written as a bearing?
$000^\circ$ or $360^\circ$.
How is South written as a bearing?
$180^\circ$.
How is North-East written as a bearing?
$045^\circ$.
How is South-West written as a bearing?
$225^\circ$.
What is first step in drawing a bearing?
Draw a North line through the point.
Which instrument measures the angle?
A protractor.
What is a scale drawing used for?
To show distances and bearings accurately.
What is a back bearing?
Bearing in the reverse direction between two points.
Back bearing of $060^\circ$?
$240^\circ$.
Back bearing of $135^\circ$?
$315^\circ$.
What angles are equal with parallel North lines?
Alternate interior angles are equal.
How do you plot a journey from a point?
Draw bearing line then mark distance to scale.
How do you find distance between two points?
Measure line on scale drawing and convert using the scale.
T/F: Bearing $45^\circ$ should be written $045^\circ$.
True, bearings use three figures.
What is area of a circle formula?
Area $A=\pi r^2$.
How does diameter relate to radius?
Diameter $d=2r$.
What is surface area of a cuboid?
Sum of areas of all six rectangular faces.
What is curved surface area of a cylinder?
Area $2\pi rh$.
In cylinder formulas, what is $h$?
The height of the cylinder.
How do you find prism volume?
Volume $V=\text{area of cross-section}\times\text{length}$.
How do you find volume of a cuboid?
Use $V=lwh$.
How do you find arc length of angle $\theta$?
Use $\text{arc length}=\dfrac{\theta}{360^\circ}\times2\pi r$.
How do you find sector area of angle $\theta$?
Use $A=\dfrac{\theta}{360^\circ}\times\pi r^2$.
What is surface area formula for a sphere?
Surface area $S=4\pi r^2$.
What is pyramid volume formula?
Volume $V=\tfrac{1}{3}\times\text{area of base}\times\text{height}$.
How do you find pyramid surface area?
Add areas of base and all triangular faces.
T/F: Triangle area is half base times height.
True, $A=\tfrac{1}{2}bh$.
T/F: All prisms use volume $V=\text{area of cross-section}\times\text{length}$.
True, that rule defines prism volume.
How do you define gradient visually?
Rise divided by run between two points.
What does positive gradient mean?
Line slopes upwards from left to right.
What is gradient of a horizontal line?
Its gradient is $0$.
How does larger gradient affect steepness?
Larger gradient makes the line steeper.
How many points are needed for gradient?
Any two distinct points on the line.
In $y=mx+c$, what is $m$?
The gradient of the line.
What does $y$-intercept mean?
Point where line crosses the $y$-axis.
How do you find intercept from equation?
Rewrite as $y=mx+c$ and read $c$.
How do you find equation from two points?
First find $m$, then use one point to get $c$.
What is equation of vertical line through $x=3$?
It is $x=3$.
How do equations of parallel lines compare?
They share $m$ but have different $c$ values.
What is gradient of line perpendicular to $m$?
It is $-\dfrac{1}{m}$.
If line has gradient $-\dfrac{3}{4}$, perpendicular gradient?
It is $\dfrac{4}{3}$.
How do you plot a line from equation?
Find two points that satisfy it and join them.
How do you solve equations graphically?
Plot both lines and read their intersection point.
What is midpoint formula for two points?
Midpoint is $\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$.
T/F: Horizontal lines always have gradient zero.
True, there is no vertical change in $y$.
T/F: Lines with equal gradients are parallel.
True, same $m$ means they never meet.
T/F: Form $y=mx+c$ represents straight lines.
True, it is the general linear form.
What is a bearing?
Angle giving a direction from North.
In which direction are bearings measured?
Clockwise from North.
How many figures are in a bearing?
Three figures, for example $045^\circ$.
How is East written as a bearing?
$090^\circ$.
How is West written as a bearing?
$270^\circ$.
How is South-East written as a bearing?
$135^\circ$.
How is North-West written as a bearing?
$315^\circ$.
How do you measure a bearing?
Use a protractor to measure clockwise from North.
Which instrument draws the route line?
A ruler or straight edge.
How do you show distance on paper?
Use a chosen scale, such as $1\text{ cm}:1\text{ km}$.
How do you find a back bearing?
Add or subtract $180^\circ$ then adjust to $0$�$360^\circ$.
Back bearing of $245^\circ$?
$065^\circ$.
Why are parallel North lines drawn?
So bearings at different points can be compared.
What information defines a journey?
Starting point, distance and bearing.
How do you find bearing of one point from another?
Join points and measure clockwise from North at starting point.
T/F: Bearings are measured anticlockwise from North.
False, they are measured clockwise.
T/F: Bearing $200^\circ$ lies between South and West.
True, it is between $180^\circ$ and $270^\circ$.
bottom of page