Questions: Quadratics
New numbers every time.
Expanding and factorising
- Expand two bracketsExpand, 2 marks, Plus
- Expand a squared bracketExpand, 2 marks, Plus
- Factorise x² + bx + cFactorise, 2 marks, Plus
- Difference of two squaresFactorise, 1 mark, Plus
- Factorise with a common factor of xFactorise, 2 marks, Plus
- Pick the right factorisationChoose, 1 mark, Plus
- Expand (ax + b)(cx + d)Expand, 2 marks, Plus
- Factorise ax² + bx + c (H)Factorise, 2 marks, Plus, Higher tier
- Expand three brackets (H)Expand, 3 marks, Plus, Higher tier
- Difference of two squares without a calculatorCalculate, 2 marks, Plus
Solving by factorising
- Solve by factorisingSolve, 3 marks, Plus
- Solve x² = kx (keep both answers)Solve, 2 marks, Plus
- Solve x² = kSolve, 2 marks, Plus
- Rearrange, then solveSolve, 3 marks, Plus
- Solve ax² + bx + c = 0 by factorising (H)Solve, 3 marks, Plus, Higher tier
- A rectangle problemSolve, 4 marks, Plus
- Consecutive numbersSolve, 3 marks, Plus
The quadratic formula
- The quadratic formula, to 2 decimal placesSolve, 3 marks, Plus, Higher tier
- The quadratic formula, to 3 significant figuresSolve, 3 marks, Plus, Higher tier
- How many solutions? The discriminantChoose, 2 marks, Plus, Higher tier
- Rearrange, then use the formulaSolve, 4 marks, Plus, Higher tier
- Show that a solution is about a valueShow that, 3 marks, Plus, Higher tier
- Exact solutions in surd formSolve, 3 marks, Plus, Higher tier
- When is the ball at this height?Solve, 4 marks, Plus, Higher tier
Completing the square
- Complete the squareWrite, 2 marks, Plus, Higher tier
- Turning point from the completed squareFind, 4 marks, Plus, Higher tier
- Solve by completing the squareSolve, 3 marks, Plus, Higher tier
- Complete the square with an odd coefficientWrite, 2 marks, Plus, Higher tier
- Complete the square when a is not 1 (H)Write, 3 marks, Plus, Higher tier
- Show an expression is always positiveShow that, 3 marks, Plus, Higher tier
Quadratic graphs
- Table of values for a quadratic graphComplete, 2 marks, Plus
- Plot a quadratic graphPlot, 2 marks, Plus
- Read the solutions from a graphUse, 2 marks, Plus
- Turning point and intercept from a graphWrite down, 3 marks, Plus
- Solve f(x) = k from a graphUse, 2 marks, Plus
- Match the equation to its sketchChoose, 1 mark, Plus
- Key points of y = (x − a)(x − b)Find, 5 marks, Plus
- Quadratic inequality (H)Solve, 3 marks, Plus, Higher tier
- Why there are no real solutionsExplain, 2 marks, Plus
- Find b and c from the rootsFind, 3 marks, Plus
- Line of symmetry from the rootsFind, 1 mark, Plus
- Area of an L-shapeShow that, 5 marks, Plus
- Height of a ballFind, 5 marks, Plus
Algebraic fractions
- Add two algebraic fractions (H)Write, 2 marks, Plus, Higher tier
- Subtract algebraic fractions (H)Write, 2 marks, Plus, Higher tier
- Simplify a quadratic over a difference of two squares (H)Simplify, 4 marks, Plus, Higher tier
- An equation with algebraic fractions that leads to a quadratic (H)Solve, 5 marks, Plus, Higher tier
- Which cancelling is right? (H)Choose, 1 mark, Plus, Higher tier
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