MANGAHIGH

# Save Our Dumb Planet

## Linear, Quadratic and Cubic Equations

Defend Earth from deadly meteorites using the planetary missile defences. A team of dumb scientists are on hand to suggest possible trajectories and trash-talk. Quickly plot your waypoints or find a new planet!

Linear, Quadratic and Cubic equations, Coordinates, BIDMAS

### Instructions

#### Game Goals

The object of this maths game is to protect Earth from meteors and other space hazards, by using your algebra skills to calculate accurate trajectories for Earth’s surface-to-space missiles.

Unfortunately, you are advised by poorly-educated and argumentative scientists who recommend conflicting trajectory formulae. It is up to you to choose the best formula, and calculate y for x in order to plot waypoints and guide your missile towards its target.

Eliminate all threats and save humanity, using as few missiles as possible.

#### How To Play

As soon as a meteor is identified it appears on the missile defence screen, and three scientists will each recommend a formula to you. Your first task is to identify a formula that is true for the x and y coordinates of the meteor.

Select the correct formula by clicking on it, and then use that formula to plot two waypoints for the missile. Plot waypoints by positioning your mouse at the appropriate coordinates, and then clicking. The missile will then arm automatically and be ready to fire.

If you miss a meteor by choosing an incorrect trajectory or not positioning the waypoints accurately, the meteor will move closer to Earth before you have the chance to fire again.

#### Level Guide

Levels Description Required Actions
The missile trajectories are described by increasingly-complex linear formulae. Select a formula that is true for the x, y coordinates of the meteor
Plot two waypoints for that formula.
Obstacles appear in space – use quadratic formulae to 'bend' your missiles around them. Select a formula that is true for the x, y coordinates of the meteor, BUT does not pass through the obstacle.
Plot two waypoints for that formula.
12 As above, but this time there are three obstacles to avoid. Select a formula that is true for the x, y coordinates of the meteor, BUT does not pass through the obstacle.
Plot two waypoints for that formula.
Multiple meteors are approaching on a linear trajectory, but only one is a threat to the Earth. Locate it, then destroy it! Select the meteor that will collide with Earth.
Select a trajectory that will strike the correct meteor.
Plot two waypoints for that formula.
The alien mothership appears! Use cubic formulae to slip your missiles past its defence systems. Select a formula that is true for the x, y coordinates of the alien ship.
Plot two waypoints for that formula.
18 The alien homeworld is revealed! The cowardly, terrified scientists are in disarray, so you must design a custom trajectory. Adjust variables with the up/down arrows to create your own formula.

#### Game Controls

You will have three opportunities to destroy each threat before it reaches the Earth.

Select a trajectory by clicking on it. If you change your mind about trajectories, you may simply click another trajectory to cancel the previous selection and any waypoints plotted.

Waypoints are plotted by clicking on a grid reference. They may be cleared by clicking on them a second time.

In Levels 13 and 14, three meteors appear at the same time, and each meteor is labelled with its own flight trajectory. You must first identify the meteor that represents a potential threat to Earth, and click it. Having selected the meteor, you must then go through the usual process of choosing a missile flight trajectory and plotting waypoints towards that meteor.

In Level 18, the terrified scientists are no longer willing to help and you must generate your own formula for the missile trajectory using the trajectory generator.

Operate the trajectory generator by clicking on the arrows to move the values up or down. You must create a formula that is true for both the Earth and the alien world.

#### Misslie Firing Sequence

The missile tracking system will report on the missile’s trajectory during flight and rate the accuracy of the plotted waypoints as 'Perfect!', 'Great', 'Okay' or 'Bad' in real-time.

If a missile is fired but the player has chosen an incorrect trajectory, then it will miss the meteor regardless of how well the waypoints have been plotted.

If a missile is fired on a correct trajectory but the waypoints have been incorrectly plotted, the missile will deviate from the anticipated trajectory and may miss the meteor altogether.

#### Scoring

Your overall score is the sum of the highest scores you achieved on each completed level. The formula for the score in a given level is:

(Waypoint 1 score + Waypoint 2 score + Time bonus) × Level multiplier × Missile factor
'Perfect!' waypoint score
5,000 points
'Great' waypoint score
2,000 points
'Okay' waypoint score
1,000 points
Time bonus
5 points per second left on the clock
Level multiplier
Equivalent to the level’s number
Missile factor
Hit meteor first time – 100%
Hit meteor second time – 50%
Hit meteor third time – 25%

For example: say you’ve just completed Level 4 (Level multiplier = 4). You hit the meteor with your second missile (Missile factor = 50%) and with 30 seconds left on the clock (Time bonus = 5 × 30 = 150 points). The missile passed through the first waypoint with a 'Perfect!' rating (Waypoint 1 score = 5000 points) and the second with an 'Okay' rating (Waypoint 2 score = 1000 points). Thus, your total score for the level would be: (5000 + 1000 + 150) × 4 × 0.5 = 12300 points.

So the rule for scoring high is simple: hit first, and hit fast!

Your performance at each level is recorded and retained.

#### Choosing the right equation

Earth is always on the curve of the correct formula, but may also be on the curve for other formulae. When trying to decide which equation to pick, try substituting the x-coordinate of the meteor into each equation. Then you will able to see if the y-coordinate produced by the equation matches that of the meteor. If they do, then that equation will fire a missile that will hit the meteor.

Remember to always follow the rules of BIDMAS when substituting values of x into the equations. For example: if y = 3x² + 6 and you are substituting x = 5, then you need to work out the value of y by first squaring x before you multiply by 3; in this example: y = 3 × 5² + 6 = 3 × 25 + 6 = 75 + 6 = 81.

For the harder levels, you will need to be able to multiply, add and subtract with negative numbers, i.e. you will need to know how to answer things like: − 5 × 7, 6 − (− 4), (− 4)².

Sometimes a calculation may give quite a big value and you should consider using an approximation to save time. If an approximation implies that a missile will pass close to the meteor then you have probably found the correct equation.

When trying to work out the y-coordinate that an equation gives, it is sometimes possible to tell if the answer will be positive or negative without actually working out values. Take y = 2x² + 3x + 10, for instance: if x = 2 then y will certainly be a positive number. If the meteor has a negative y-coordinate then you would be able to tell that this equation will not work. You can then try another equation.

When dealing with the early levels, if you know how to tell the gradient of a line from its equation, then this can help you to choose the correct equation.

#### Plotting the Waypoints

To plot waypoints accurately you will need to substitute the value for the x-coordinate into the correct equation. To make the calculation easier you should choose the easiest value of x that lies between the Earth and the meteor. The easiest values to use (easiest listed first) are: x = 0, 1, 2, 5, (-1), 3.

#### Obstacles

If your missile flies too close to an obstacle then the missile will explode and the meteor will not be destroyed. If there are lots of obstacles then you have to choose your equation even more carefully.
Try substituting an x-coordinate of a point near the obstacles into your chosen equation. This will give you an idea of how close your missile will be to the obstacles.

#### Multiple Meteors

On levels that involve multiple meteors, you need to decide which meteor is on a collision path with Earth. Use the x-coordinate of the Earth and substitute this value into the equation that is shown for each meteor (you will be able to find this equation by rolling the cursor over the meteors). Once you have substituted the x-coordinate of the Earth into the meteor’s flight path equation you will be able to see if the y-coordinate matches with the Earth's.

#### Customised Equations

The final level requires you to create your own trajectory equation to destroy the alien’s homeworld. You should try to use a quadratic or cubic equation for the missile’s flight path. You will need to make use of the coordinate of the Earth as well as the coordinate of the alien home world.

The Earth is always positioned at x = 0, so you can use its y-coordinate to determine the y-intercept of the equation. Now use the x-coordinate of the alien homeworld to determine a coefficient for x² or x³.

Good luck!