| Main Course for Higher Students |
Number
&
Algebra | Diagnostic Test |  |
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| Diagnostic Test Answers | |
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| NA1 | 2a | Calculate Highest Common Factors & Least Common Multiples | |
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| NA2 | 2a 3a | Know What a Prime Number is & Write Whole Numbers as the Product of Primes | |
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| NA3 | 3a | Calculate with Negative Numbers with & without a Calculator using +- ÷ | |
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| NA4 | 5a 5g | Substitute Numbers into a Formula | |
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| NA5 | 2b 5d 3a | Know & Use the Index Laws (for Numbers and Letters) | |
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| NA6 | 3h | Round to a Given Number of Significant Figures | |
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| NA7 | 2b 3h 3m 3r | Write Numbers in Standard Index Form & Understand the Calculator Display | |
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| NA8 | 3f 2f | i) Simplify Ratio ii) Divide a Quantity in a Given Ratio | |
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| NA9 | 3d | Calculate with Fractions with & without a calculator using +- ÷ | |
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| NA10 | 3a | Interpret and Simplify Fractional and Negative Powers | |
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| NA11 | 2d 3c | Convert a Recurring Decimal to a Fraction | |
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| NA12 | 3e 3j 3k 3t | Solve Simple % Problems and Compound Interest Problems
Links to Exponential Growth and Large Calculations | |
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| NA13 | 3e 3j 3s | Solve Reverse Percentage Problems | |
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| NA14 | 3l 5h | Solve i)Direct Proportion Problems
ii)Inverse Proportion Problems
iii) Complex Proportion Problems | |
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| NA15 | 3q | Calculate the Upper and Lower Bounds of Calculations | |
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| NA16 | 5b | Expand Brackets i) Single ii) Double | |
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| NA17 | 5b | Factorise Expressions i) Linear ii) Quadratic | |
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| NA18 | 3n | i) Simplify Calculations using Surds and Pi Leaving These in your Answer
ii) Simplify Surds in the Denominator | |
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| NA19 | 5e | Set Up Simple Equations (Linear) | |
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| NA20 | 5e 5f | Solve Simple Equations (Linear) i) Basic ii) with Brackets iii) 'Over One' Equations | |
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| NA21 | 5g | Change the Subject of a Formula i) Basic
ii) where the Power of the Subject Appears & Equations iii) where the Subject occurs Twice | |
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| NA22 | 5j | Solve Simple Linear Inequalities | |
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| NA23 | 5j | Solve Several Linear Inequalities in Two Variables & find the Solution Set | |
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| NA24 | 6a | Continue Common Sequences | |
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| NA25 | 5m | Solve Problems using Trial & Improvement Methods | |
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| NA26 | 5k | Solve Quadratic Equations by Factorisation | |
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| NA27 | 5k | Solve Quadratic Equations by i) Completing the Square
ii) Using the Quadratic Formula | |
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| NA28 | 5h 5i | Solve Simultaneous Linear Equations | |
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| NA29 | 5l | Solve Simultaneous Equations with One Linear and One Quadratic | |
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| NA30 | 6a | Describe The nth term of a Sequence | |
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| NA31 | 6b | Understand the Straight Line Equation y = mx + c | |
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| NA32 | 6c | Know when Lines are i) Parallel ii) Perpendicular | |
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| NA33 | 6d | Understand i) a Distance-Time Graph ii) a Velocity-Time Graph | |
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| NA34 | 6e 6f | Plot Quadratics & Cubics | |
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| NA35 | 3a 6f | Understand the Word Reciprocal, Plot the Reciprocal Function and
Recognise the Shape of the Graph of the Reciprocal Function | |
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| NA36 | 6f | Plot i) Exponential Function Y = Kx for integer values of x
ii) y = sin x & y = cos x
iii) Recognise the Characteristic Shapes of these Functions | |
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| NA37 | 6g | Transform Linear, Quadratic, Sine and Cosine Functions f(x)
by the Functions y = f(x) + a, y = f(ax), y = f(x + a), y = af(x) | |
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| Your Turn & Acid Test Answers | |
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Shape
&
Space | Diagnostic Test | |
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| Diagnostic Test Answers | |
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| SS1 | 2f 3e | Calculate lengths using Pythagoras' theorem | |
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| SS2 | 2g | Calculate lengths & angles using trigonometry for right angled triangles | |
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| SS3 | 3f 2g | Solve Trigonometric and Pythagoras Problems in 3 Dimensions | |
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| SS4 | 2g | Calculate Lengths and Angles using the Sine and Cosine Rules | |
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| SS5 | 2g | Calculate the Area of a Traiangle using 1/2ab sin C | |
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| SS6 | 2g 4a | Draw/Sketch/Interpret a Diagram using Bearings | |
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| SS7 | 2i | Calculate the Surface Area of Prisms & Cylinders | |
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| SS8 | 2i 4d | Calculate the Volume of Prisms & Cylinders | |
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| SS9 | 2h | Know basic Circle Properties Know & Use the Circle Theorems
The Circle Properties are:
i) that tangent and radii are perpendicular
ii) tangents from an external point are equal in length
iii) the perpendicular from the centre to a chord, bisects the chord
The Circle Theorems are:
i) angle subtended by an arc at the centre of a circle is twice the angle
subtended at any point on the circumference
ii) the angle subtended at the circumference by a semicircle is a right angle
iii) angles in the same segment are equal
iv) opposite angles of a cyclic quadrilateral sum to 180 degrees | |
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| SS10 | 4d | Calculate Arc Lengths and Sector and Segment Areas within Circles | |
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| SS11 | 2e | Know the meaning of SSS, SAS, ASA & RHS conditions, for congruent triangles | |
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| SS12 | 4c | Draw Basic Constructions
i) equilateral triangle
ii) perpendicular bisector
iii) the perpendicular from a point to a line
iv) the angle bisector |
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| SS13 | 6h | Construct Basic Loci
i) The fixed distance from a single point : Circle
ii) The equidistance from two lines (or nearer to one line than another): Perpendicular Bisector
iii) The equidistance from two points (or nearer one point than another): Angle Bisector
iv) The fixed distance from a line: Race Track |
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| SS14 | 3a 3b | Describe the Transformations; Reflections/Rotations/Translations
Notes: Rotation from any point & calculate the angle of rotation. Translation as a vector. | |
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| SS15 | 3c 3b | Describe & construct Enlargements of objects using positive & fractional scale factors | |
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| SS16 | 2g | Calculate lengths in similar triangles | |
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| SS17 | 3d | Calculate Area and Volume of Similar Shapes | |
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| SS18 | 3d | Decide if a Formula is a Perimeter, Area or Volume by considering Dimensions | |
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| SS19 | 4a | Calculate Compound Measures like Speed & Density | |
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| SS20 | 4d | Convert between Volume Measures including cm3 and m3 | |
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| SS21 | 3a 3b | Vectors: i) Add/Subtract Vectors and Multiply by a Scalar and Understand This Graphically
ii) Solve Geometric Problems | |
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| Your Turn & Acid Test Answers | |
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