33509085
Description
| Question | Answer |
| How to Simplify Surds | Learn the Square Numbers: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169. Identify the largest square number factor that divides into the number being simplified, then take the root of it. Example: √50 = √?? × 2 = √?? × √2 = ?√2 |
| How to Multiply Surds | Put both numbers under one root sign and multiply. √5 × √15 = √75 = √25 × √3 = 5√3 |
| How to Divide Surds | Put both numbers under one root sign and divide. |
| How to Rationalise the Denominator | Multiply both top and bottom by the surd from the denominator. Check if you can simplify the numbers and/or the surd. |
| Adding/Subtracting Surds | Need like terms to add/subtract e.g. 2√5 + 3√5 = 5√5 Sometimes need to simplify first e.g. √50 - √8 = √25 × √2 - √4 × √2 = 5√2 - 2√2 = 3√2 |
| Indices - Multiplying Rule | Add powers |
| Indices - Dividing Rule | Subtract powers |
| Indices - Brackets Rule | Multiply powers |
| Indices - power of 0 Rule | |
| Indices - Negative Power Rule | |
| Indices - Fraction Rule | |
| Factorising - Common Factor | When factorising any expression, the first thing to look for is a common factor. A common factor is a factor that each of the terms share. The common factor can be a number, a letter or both. |
| Factorising - Difference of Two Squares | A difference of two squares is when one square number is taken away from another |
| Factorising - Trinomials | Step 1: Start by considering the First terms in the bracket. These will be factors of the first term of the trinomial. Step 2: Move to the Last terms in the brackets. These must be factors of the third term in the trinomial. Step 3: The Outsides and Insides of the brackets must add to give the middle term. |
| Factorising - Trinomials where the coefficient of x^2 is greater than 1 | |
| How do you complete the square? i.e. | |
| How do you simplify algebraic fractions by factorising? | Step 1: Factorise expression Step 2: Look for common factors. Step 3: Cancel and simplify |
| How do you multiply algebraic fractions? | Multiply the numerators, then multiply the denominators. Note: It is often better to simply before multiplying. |
| How do you divide algebraic fractions? | Invert the second fraction, then multiply |
| How do you add and subtract algebraic fractions? | Find a common denominator. This can be done either by working out the lowest common denominator, or by using Smile and Kiss |
| What is the Gradient Formula? | Need to know that gradient is represented by the letter m Step 1: Select two coordinates Step 2: Label them (?1, ?1) (?2,?2) Step 3: Substitute them into gradient formula |
| How do you calculate the Area of a Sector? | |
| How do you calculate the Length of an Arc of a Circle? | |
| How do you find an angle, radius or diameter of a Sector of a Circle? | Rearrange the formula (either area of a sector formula or arc length formula) and used to find other unknowns |
| How do you find the Volume of a Cylinder? | |
| How do you calculate a height or radius of a shape by using volume formulae? | Rearrange the formulae, then substitute in the given values |
| What is the gradient of a line? | • Represented by ? • Measure of steepness of slope • Positive gradient: the line is increasing • Negative gradient: the line is decreasing |
| What is the y-intercept of a line? | • Represented by ? • Shows where the line crosses the ?-axis • Find by making ? = 0 |
| How do you find the equation of a line from the gradient and ?-intercept? | Step 1: Find gradient ? using gradient formula Step 2: Find y-intercept ? Step 3: Substitute into ? = ?? + ? |
| How do you find the equation of a straight line from two points? | Step 1: Find gradient ? using gradient formula Step 2: Substitute into ? − ? = ?(? − ?) where (?,?) are taken from either one of the points |
| How do you find the gradient and intercepts from an equation? | To find the gradient and ?-intercept of a line, rearrange the line into the form ? = ?? + ?, then simply read the values for ? and ? Example: 3? + 6? = 12 3? = −6? + 12 ? = −?? + ? ? = −2, ? = 4 To find the x-axis intercept, substitute y=o into the equation and solve. |
| What do we need to know about parallel lines and their gradients? | Parallel lines have the same gradient |
| How do you evaluate a function? | Replace x with the given value and work out the answer. If ?(?) = 2? − 1, evaluate ?(?) when ? = 3. ?(?) = 2? − 1 ?(3) = 2(3) − 1 ?(3) = 6 − 1 ?(3) = 5 |
| How do you find the input of a function given the output? | Form an equation and set the function equal to the answer given. Example: If ?(?) = 4? − 3. Calculate ? when ?(?) = 29 4? − 3 = 29 4? = 32 ? = 8 |
| How do you solve equations that contain fractions? | To solve equations involving more than one fraction, multiply everything by the lowest common denominator of the fractions. |
| How do you solve inequalities? | Inequations are solved in the same way as equations, with one exception. If multiplying or dividing by a negative value, the inequality sign is reversed. |
| How do you solve simultaneous equations? | Step 1: Scale equations to make one unknown equal. Step 2: Add Equations ( if different signs) or Subtract Equations ( if same signs) to eliminate equal term and solve. Step 3: Substitute number to find second term. |
| How do you change the subject of a formula? | The subject of a formula is the value that is on its own on one side of the formula (usually the left). Change the subject in each of the following questions to ?. |
| What is the graph of a quadratic function called? What shape is it? | The graph of a quadratic function is called a parabola. Parabolas are either ‘n’ or ‘u’ shaped. When the coefficient of the ?^2 term is positive, the graph has a minimum turning point and a 'u' shape. When the coefficient of the ?^2 term is negative, the graph has a maximum turning point and a ‘n’ shape. |
| What can you tell about a quadratic written in completed square form? | The turning point, which is (-a,b) and the equation of the axis of symmetry is x = -a e.g. for the following equation, the axis of symmetry is x = -3 and the turning point is (-3,-14) |
| How do you solve Quadratic equations? e.g. | To solve a quadratic function is to find the ?-coordinates at which the graph of the quadratic function is equal to zero, i.e. where the graph intersects the ?-axis. This can be done by factorising or using the quadratic formula. (Use the quadratic formula if you cannot factorise). |
| How do you determine the nature of the roots of a quadratic? | Use the discriminant to determine the nature. There are 3 options - no real roots, one real and repeated root, 2 real and distinct roots. |
| How do you calculate the size of an interior angle and an exterior angle of a polygon? | |
| Angles in Circles - what size angle is made when a tangent meets a radius? | |
| Angles in Circles - what angle is made at the circumference in a triangle contained within a semi circle? | |
| Angles in circles - what do we need to know about isosceles triangles inside circles? | Isosceles triangles can be present in circles if two of the sides are radii - look out for this. Isosceles triangles have 2 equal sides and 2 equal angles. |
| The Converse of Pythagoras | The converse of Pythagoras’ Theorem is used to determine whether a triangle is right-angled or not. |
| When do we use Pythagoras' Theorem in Circles? | Pythagoras’ Theorem is used within circles where right-angled triangles can be formed. This occurs when a radius and chord intersect at right-angles. |
| What does the sine graph look like? | |
| What does the cosine graph look like? | |
| How do we find the equation of a trig function? | In trigonometric functions of the form ? = ?sin ?? + ? and ? = ? cos?? + ?, ? is the amplitude, ? is the number of waves and the value of ? translates the graph vertically (up and down). The amplitude of the graph is the positive value of ?. This is half the distance from the maximum to the minimum value. The period of the graph is the length of one full wave. For ??? and ??? graphs, the period can be found by dividing 360° by ?. In trigonometric functions of the form ?=?sin(? + ?) and ? = ? cos(? + ?), ? is the amplitude, the value of ? translates the graph horizontally. If b is positive, the graph moves left, if b is negative, the graph moves right. |
| How do you solve Trig Equations? | Most trig equations have two solutions. Always draw a CAST diagram to help. |
| What trig identities do you need to know? | |
| When do you use the Sine Rule to find a missing side? | Use in non-right angled triangles when you know 2 angles and 1 side |
| When do you use the Sine Rule to find a missing angle? | Use in non-right angled triangles when you know 2 sides and 1 angle |
| When do you use the Cosine Rule to find a missing side? | Use in non-right angled triangles when you know two sides and the containing angle |
| When do you use the Cosine Rule to find a missing angle? | Use in non-right angles triangles when you know all 3 sides and no angles |
| What do you need to know about Bearings? | Bearings are angles measured from north in a clockwise direction, written with three figures. NB: It can be helpful to extend North arrows vertically and use alternate or corresponding angles to find unknowns. |
| What do you answer Appreciation/Depreciation Percentage Questions? | 1. Add/subtract percentage to/from 100% 2. Change the percentage into a decimal 3. Add a power to the decimal (this power is the number of yeats/months etc.) 4. Multiply value by the decimal with power. This applies to compound interest too. |
| How do you answer Reverse Percentages Questions? | 1. Add/Subtract percentage to/from 100% 2. Make this percentage equal to amount given 3. Find what 1% equals 4. Multiply by 100 to find 100%, the original amount |
| How do you calculate Percentage Change e.g. percentage loss/gain, percentage increase/decrease? | |
| How do you Add/Subtract Fractions? | 1. Make the denominators the same and change the numerators as well. 2.Now add/subtract the top numbers and keep the bottom number so that you now have one fraction 3. Simplify the fraction and change back to a mixed number if required |
| How do you Multiply Fractions? | 1. Change all the mixed numbers to improper fractions. 2. Simplify by crossing out any common factors. 3. Multiply the numerators together and the denominators together. 4. Simplify the answer if required and change back to a mixed number. |
| How do you Divide Fractions? | 1. Change all the mixed number to improper fractions. 2. Keep the first fraction the same, change the divide to a multiply and flip the second fraction. 3. Multiply the numerators together and the denominators together. 4. Simplify the answer if required and change back to a mixed number. |
| What are Quartiles and what are they used for? | Q1 is the lower quartile, the middle number between the smallest number and the median of the set. Q2 is the median - the middle number of the set Q3 is the upper quartile, the middle number between the median and the highest number. They are used to draw box plots. |
| How do you find the Interquartile Range (IQR)? |
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Iqr (binary/octet-stream)
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| How do you find the Semi-Interquartile Range (SIQR)? What does it measure? |
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Siqr (binary/octet-stream)
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| How do you calculate the mean of a set of data? | Add all the numbers together then divide by the amount of numbers in the set. |
| What do you say when asked to compare two different standard deviations and two different means? | Standard Deviation is a measure of how spread out a set of data is. The smaller the standard deviation, the less spread out the data is (the data is more consistent). The mean tells us about the set of data 'on average'. |
| How do you write numbers in standard form (scientific notation). ? | Standard form is used to rewrite either very large or very small numbers in a usable and convenient way. They are always written with the leading number being greater than or equal to 1 and less than 10. |
| What does a line with a positive gradient look like? | |
| What does a line with a negative gradient look like? | |
| What is the gradient of a horizontal line? | m = 0 |
| What is the gradient of a vertical line? | m is undefined |
| What does the tan graph look like? |
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